Package 'fetwfe'

A catt_df object.

Row / column selectors; see ⁠[.data.frame⁠.

Further arguments passed through.

A catt_df object (data frame with class c("catt_df", "data.frame")).

Index; passed through to ⁠[[.data.frame⁠. Character indices matching an old column name are intercepted; other indices fall through.

Further arguments passed through.

A catt_df object.

Index; passed through to ⁠[[<-.data.frame⁠. Character indices matching an old column name are intercepted.

Further arguments passed through.

The value to assign.

A catt_df object.

Row / column selectors; see ⁠[<-.data.frame⁠.

Further arguments passed through.

The value to assign.

A catt_df object.

Character; the column name being accessed via $.

A catt_df object.

Character; the column name being assigned via $.

The value to assign.

A data.frame in long format containing at least the four columns used by did::att_gt(): outcome yname, time tname, unit id idname, and the first-treatment period gname (which is 0 for the never-treated group).

Character scalar. Name of the outcome column.

Character scalar. Name of the time variable (numeric or integer). This becomes time_var in the returned dataframe.

Character scalar. Name of the unit identifier. Converted to character and returned as unit_var.

Character scalar. Name of the group variable holding the first period of treatment. Values must be 0 for never-treated, or a positive integer representing the first treated period.

Character vector of additional covariate column names to carry through (default character(0)). These columns are left untouched and appear after the required columns in the returned dataframe.

Logical. If TRUE (default), units that are already treated in the first sample period are removed before creating the treatment dummy. fetwfe() would do this internally, but dropping them here keeps the returned dataframe cleaner.

A named list giving the column names to use in the resulting dataframe. Defaults are list(time = "time_var", unit = "unit_var", treatment = "treatment", response = "response"). Override if you prefer different names (for instance, to keep the original yname). The vector must contain exactly these four names.

Logical. If TRUE, a message() reports the count of first-period-treated unit-period rows dropped when drop_first_period_treated = TRUE. Default FALSE (silent).

An object of class "betwfe".

A panel data.frame with the response column under x$response_col_name. Any sort order; first-period-treated units are auto-trimmed.

Unused.

An object of class "etwfe".

A panel data.frame with the response column under x$response_col_name. Any sort order; first-period-treated units are auto-trimmed.

Unused.

An object of class "fetwfe".

A panel data.frame with one row per unit-period (any sort order — augment auto-sorts), containing the response column under the same name used at fit time (see x$response_col_name). First-period-treated units, if present, are auto-trimmed.

Unused.

An object of class "twfeCovs".

Ignored.

Ignored.

Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.

Character; the name of a single column containing a variable for the time period. This column is expected to contain integer values (for example, years). Recommended encodings for dates include format YYYY, YYYYMM, or YYYYMMDD, whichever is appropriate for your data.

Character; the name of a single column containing a variable for each unit. This column is expected to contain character values (i.e. the "name" of each unit).

Character; the name of a single column containing a variable for the treatment dummy indicator. This column is expected to contain integer values, and in particular, should equal 0 if the unit was untreated at that time and 1 otherwise. Treatment should be an absorbing state; that is, if unit i is treated at time t, then it must also be treated at all times t + 1, ..., T. Any units treated in the first time period will be removed automatically. Please make sure yourself that at least some units remain untreated at the final time period ("never-treated units").

Character; the name of a single column containing the response for each unit at each time. The response must be an integer or numeric value.

(Optional.) Either a character vector containing the names of the columns for covariates (e.g., covs = c("x1", "x2")), or a one-sided formula (e.g., covs = ~ x1 + x2) – the formula form mirrors the convention used by did::att_gt(xformla = ...). Only additive bare variable names are supported in the formula form; for derived variables, compute them in the data frame first and pass via the character-vector form. All of these columns are expected to contain integer, numeric, or factor values, and any categorical values will be automatically encoded as binary indicators. If no covariates are provided, the treatment effect estimation will proceed, but it will only be valid under unconditional versions of the parallel trends and no anticipation assumptions. Default is c().

(Optional.) Integer; a vector. If you have a sufficiently large number of units, you can optionally randomly split your data set in half (with N units in each data set). The data for half of the units should go in the pdata argument provided above. For the other N units, simply provide the counts for how many units appear in the untreated cohort plus each of the other G cohorts in this argument indep_counts. The benefit of doing this is that the standard error for the average treatment effect will be (asymptotically) exact instead of conservative. The length of indep_counts must equal 1 plus the number of treated cohorts in pdata. All entries of indep_counts must be strictly positive (if you are concerned that this might not work out, maybe your data set is on the small side and it's best to just leave your full data set in pdata). The sum of all the counts in indep_counts must match the total number of units in pdata. Default is NA (in which case conservative standard errors will be calculated if q < 1.)

(Optional.) Numeric; the variance of the row-level IID noise assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated by REML on the linear mixed-effects model y ~ X + (1 | unit) via lme4::lmer (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

(Optional.) Numeric; the variance of the unit-level IID noise (random effects) assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated by REML via lme4::lmer on the linear mixed-effects model y ~ X + (1 | unit) (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

(Optional.) Numeric. A penalty parameter lambda will be selected over a grid search by BIC in order to select a single model. The largest lambda in the grid will be lambda.max. If no lambda.max is provided, one will be selected automatically. When q <= 1, the model will be sparse, and ideally all of the following are true at once: the smallest model (the one corresponding to lambda.max) selects close to 0 features, the largest model (the one corresponding to lambda.min) selects close to p features, nlambda is large enough so that models are considered at every feasible model size, and nlambda is small enough so that the computation doesn't become infeasible. You may want to manually tweak lambda.max, lambda.min, and nlambda to try to achieve these goals, particularly if the selected model size is very close to the model corresponding to lambda.max or lambda.min, which could indicate that the range of lambda values was too narrow or coarse. You can use the function outputs lambda.max_model_size, lambda.min_model_size, and lambda_star_model_size to try to assess this. Default is NA.

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

(Optional.) Numeric; determines what L_q penalty is used for the regularization. q = 1 is the lasso, and for 0 < q < 1, it is possible to get standard errors and confidence intervals. q = 2 is ridge regression. See Faletto (2025) for details. Default is 0.5.

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default", "conservative", or "cluster". "default" returns the tight Gaussian variance sqrt(att_var_1 + att_var_2) from Theorem (c$'$) under Assumption (Psi-IF); this is asymptotically exact for the package's default cohort sample-proportions estimator and for every standard propensity-score estimator that satisfies (Psi-IF) (multinomial logit, any GLM on W | X, kernel/series regression of ⁠1{W = g}⁠ on X). "conservative" returns the Cauchy-Schwarz upper bound from Theorem (c); use only if the propensity-score estimator violates (Psi-IF). "cluster" is an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support (see the companion vignette inference_vignette for details). "cluster" is only meaningful when q < 1 (the bridge oracle property is required); for q >= 1 the SE will be NA regardless of se_type. The default "default" was the conservative Cauchy-Schwarz formula in versions <= 1.11.7; v1.12.0 switched the default to the tight Gaussian variance. Default is "default".

Character; method for selecting the bridge penalty parameter lambda. Either "cv" (10-fold cross-validation on cv.grpreg; the v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default for v1.12.0 and earlier). The default changed in v1.13.0 to address a finite-sample bias issue documented in simulation studies (see issue #164). Pass lambda_selection = "bic" to recover the prior behavior. See the inference vignette section "Choosing the bridge penalty parameter" for details.

Integer; number of folds for the CV path. Ignored when lambda_selection = "bic". Default is 10.

Integer or NULL; the seed passed to set.seed() immediately before the cv.grpreg() call. If NULL (the default), the seed defaults internally to as.integer(N * T). Ignored when lambda_selection = "bic".

Character; one of "simultaneous" (default) or "pointwise". Controls the confidence-interval bounds reported for the cohort-specific ATTs (in catt_df) and the event-study effects (from eventStudy(), shown by print / summary / plot, and surfaced by broom::tidy() on the fitted object and on the eventStudy() / cohortStudy() outputs). "simultaneous" reports parametric simultaneous (family-wise, uniform) bands computed via simultaneousCIs(): each family's band covers all of its effects jointly with probability 1 - alpha, matching the default presentation of did::aggte(cband = TRUE). "pointwise" reports per-effect Wald intervals (each covers its own effect with probability 1 - alpha, no joint guarantee — the behavior of versions <= 1.15.1). Both the interval bounds and the per-cohort p-values (p_value) follow ci_type: under "simultaneous" the p_value is the single-step max-T multiplicity- adjusted p-value matching the band, under "pointwise" the per-cohort Wald p-value (#200). The standard errors (se) and selection flags (selected) are identical under both settings, and the overall-ATT confidence interval (a single scalar) is unaffected. When standard errors are unavailable (q >= 1, or a rank-deficient design) the bounds are NA under both settings. Default is "simultaneous".

The estimated overall average treatment effect for a randomly selected treated unit.

If q < 1, a standard error for the ATT. If indep_counts was provided, this standard error is asymptotically exact; if not, it is asymptotically conservative. If q >= 1, this will be NA.

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback).

Logical scalar; TRUE if att_hat is not exactly zero, FALSE otherwise. BETWFE uses bridge regression directly on the coefficients (rather than on the fused restrictions used by FETWFE); under the bridge oracle property of Kock (2013), att_selected = FALSE is an analogous asymptotic statement that the truth is zero under a sparsity assumption different from the one Theorem 6.2 establishes for FETWFE. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

A named vector containing the estimated average treatment effects for each cohort.

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

A vector of the estimated probabilities of being in each cohort conditional on being treated, which was used in calculating att_hat. If indep_counts was provided, cohort_probs was calculated from that; otherwise, it was calculated from the counts of units in each treated cohort in pdata.

A data frame (with S3 class c("catt_df", "data.frame")) displaying the cohort names (cohort), average treatment effects (estimate), standard errors (se), 1 - alpha confidence interval bounds (ci_low, ci_high), per-cohort p-values (p_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), p_value is NA. The catt_df S3 class makes [[ / $ / [ access on the pre-1.11.0 Title-Case column names (Cohort, ⁠Estimated TE⁠, SE, ConfIntLow, ConfIntHigh, P_value) stop() with a migration message pointing to the new name. See NEWS.md for the rename table.

The full vector of estimated coefficients.

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

Either the provided lambda.max or the one that was used, if a value wasn't provided. (This is returned to help with getting a reasonable range of lambda values for grid search.)

The number of selected features (excluding the always-present intercept) at lambda.max (for q <= 1, the smallest model). As mentioned above, for q <= 1 ideally this value is close to 0.

Either the provided lambda.min or the one that was used, if a value wasn't provided.

The number of selected features (excluding the always-present intercept) at lambda.min (for q <= 1, the largest model). As mentioned above, for q <= 1 ideally this value is close to p.

The value of lambda chosen by the method recorded in lambda_selection. If this value is close to lambda.min or lambda.max, that could suggest that the range of lambda values should be expanded.

The number of selected features (excluding the always-present intercept) in the chosen model. If this value is close to lambda.max_model_size or lambda.min_model_size, that could suggest that the range of lambda values should be expanded.

Character scalar; either "cv" or "bic". Mirrors the lambda_selection argument the user passed.

Integer scalar; the cv_folds value used when lambda_selection = "cv", NA_integer_ when lambda_selection = "bic".

Integer scalar; the seed actually fed to set.seed() immediately before cv.grpreg() was called. Defaults to as.integer(N * T) when the user did not pass a seed. NA_integer_ when lambda_selection = "bic".

Character scalar; the ci_type argument the user passed ("simultaneous" or "pointwise"), controlling whether the reported catt_df / eventStudy() confidence-interval bounds are simultaneous (family-wise) or pointwise.

The design matrix created containing all interactions, time and cohort dummies, etc.

The vector of responses, containing nrow(X_ints) entries.

The design matrix after applying the change in coordinates to fit the model and also multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final number of units that were in the data set used for estimation (after any units may have been removed because they were treated in the first time period).

The number of time periods in the final data set.

The final number of treated cohorts that appear in the final data set.

Deprecated alias for G, retained for backward compatibility; populated with the same value. Use G. Will be removed in a future release.

The final number of covariates that appear in the final data set (after any covariates may have been removed because they contained missing values or all contained the same value for every unit).

The final number of columns in the full set of covariates used to estimate the model.

Numeric scalar; mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the response column name in the original pdata. Consumed by augment.betwfe().

Character scalars; the corresponding arguments the user passed. Consumed by augment.betwfe() when auto-aligning a user-supplied panel to the fitted design.

Character vector; the original covs argument (pre-factor- expansion). Consumed by augment.betwfe().

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default", "conservative", or "cluster").

A list containing internal outputs that are typically not needed for interpretation, packaged here for parity with fetwfe() so downstream consumers can use a single canonical access path across all four estimator classes (#144). The first five sub-slots (X_ints, y, X_final, y_final, calc_ses) are also duplicated at top level for backward compat; variance_components and first_year live only under ⁠$internal⁠:

X_ints

The design matrix containing all interactions, time and cohort dummies, etc. Same value as top-level X_ints.

y

The vector of responses. Same as top-level y.

X_final

The design matrix after the change-of-coordinates step. Same as top-level X_final.

y_final

The transformed response vector. Same as top-level y_final.

calc_ses

Logical indicating whether standard errors were calculated. Same as top-level calc_ses.

variance_components

A list exposing the two variance pieces (att_var_1, att_var_2) plus paper-notation counterparts (V_1, V_2) and unit-scaled variance estimators (tilde_v_N, hat_v_N, tilde_v_N_C, tilde_v_N_C_pi_hat, tilde_v_N_C_pi_hat_cons, tilde_v_N_cons). The Wald CI is ⁠[hat_T_N +- qnorm(1-alpha/2) * sqrt(tilde_v_N / N)]⁠ (paper Eq. conf.int.form). New in v1.12.0 (issue #141 + #146).

first_year

Integer or numeric scalar; the first (earliest) time_var value in the panel after idCohorts() processing. Consumed by eventStudy() to map cohort_probs' cohort labels (treatment-start years) to 1-based panel-time-index offsets when the labels are integer-coercible. New in v1.13.3 (issue #174).

An object of class "FETWFE_simulated" containing the simulated panel data and design matrix.

(Optional.) Numeric. A penalty parameter lambda will be selected over a grid search by BIC in order to select a single model. The largest lambda in the grid will be lambda.max. If no lambda.max is provided, one will be selected automatically. For lambda <= 1, the model will be sparse, and ideally all of the following are true at once: the smallest model (the one corresponding to lambda.max) selects close to 0 features, the largest model (the one corresponding to lambda.min) selects close to p features, nlambda is large enough so that models are considered at every feasible model size, and nlambda is small enough so that the computation doesn't become infeasible. You may want to manually tweak lambda.max, lambda.min, and nlambda to try to achieve these goals, particularly if the selected model size is very close to the model corresponding to lambda.max or lambda.min, which could indicate that the range of lambda values was too narrow. You can use the function outputs lambda.max_model_size, lambda.min_model_size, and lambda_star_model_size to try to assess this. Default is NA.

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

(Optional.) Numeric; determines what L_q penalty is used for the fusion regularization. q = 1 is the lasso, and for 0 < q < 1, it is possible to get standard errors and confidence intervals. q = 2 is ridge regression. See Faletto (2025) for details. Default is 0.5.

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default", "conservative", or "cluster". "default" returns the tight Gaussian variance sqrt(att_var_1 + att_var_2) from Theorem (c$'$) under Assumption (Psi-IF); this is asymptotically exact for the package's default cohort sample-proportions estimator and for every standard propensity-score estimator that satisfies (Psi-IF) (multinomial logit, any GLM on W | X, kernel/series regression of ⁠1{W = g}⁠ on X). "conservative" returns the Cauchy-Schwarz upper bound from Theorem (c); use only if the propensity-score estimator violates (Psi-IF). "cluster" is an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support (see the companion vignette inference_vignette for details). "cluster" is only meaningful when q < 1 (the bridge oracle property is required); for q >= 1 the SE will be NA regardless of se_type. The default "default" was the conservative Cauchy-Schwarz formula in versions <= 1.11.7; v1.12.0 switched the default to the tight Gaussian variance. Default is "default".

Character; method for selecting the bridge penalty parameter lambda. Either "cv" (10-fold cross-validation on cv.grpreg; the v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default for v1.12.0 and earlier). The default changed in v1.13.0 to address a finite-sample bias issue documented in simulation studies (see issue #164). Pass lambda_selection = "bic" to recover the prior behavior. See the inference vignette section "Choosing the bridge penalty parameter" for details.

Integer; number of folds for the CV path. Ignored when lambda_selection = "bic". Default is 10.

Integer or NULL; the seed passed to set.seed() immediately before the cv.grpreg() call. If NULL (the default), the seed defaults internally to as.integer(N * T). Ignored when lambda_selection = "bic".

Character; one of "simultaneous" (default) or "pointwise". Controls the confidence-interval bounds reported for the cohort-specific ATTs (in catt_df) and the event-study effects (from eventStudy(), shown by print / summary / plot, and surfaced by broom::tidy() on the fitted object and on the eventStudy() / cohortStudy() outputs). "simultaneous" reports parametric simultaneous (family-wise, uniform) bands computed via simultaneousCIs(): each family's band covers all of its effects jointly with probability 1 - alpha, matching the default presentation of did::aggte(cband = TRUE). "pointwise" reports per-effect Wald intervals (each covers its own effect with probability 1 - alpha, no joint guarantee — the behavior of versions <= 1.15.1). Both the interval bounds and the per-cohort p-values (p_value) follow ci_type: under "simultaneous" the p_value is the single-step max-T multiplicity- adjusted p-value matching the band, under "pointwise" the per-cohort Wald p-value (#200). The standard errors (se) and selection flags (selected) are identical under both settings, and the overall-ATT confidence interval (a single scalar) is unaffected. When standard errors are unavailable (q >= 1, or a rank-deficient design) the bounds are NA under both settings. Default is "simultaneous".

The estimated overall average treatment effect for a randomly selected treated unit.

If q < 1, a standard error for the ATT. If indep_counts was provided, this standard error is asymptotically exact; if not, it is asymptotically conservative. If q >= 1, this will be NA.

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback).

Logical scalar; TRUE if att_hat is not exactly zero, FALSE otherwise. BETWFE uses bridge regression directly on the coefficients (rather than on the fused restrictions used by FETWFE); under the bridge oracle property of Kock (2013), att_selected = FALSE is an analogous asymptotic statement that the truth is zero under a sparsity assumption different from the one Theorem 6.2 establishes for FETWFE. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

A named vector containing the estimated average treatment effects for each cohort.

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

A vector of the estimated probabilities of being in each cohort conditional on being treated, which was used in calculating att_hat. If indep_counts was provided, cohort_probs was calculated from that; otherwise, it was calculated from the counts of units in each treated cohort in pdata.

A data frame (with S3 class c("catt_df", "data.frame")) displaying the cohort names (cohort), average treatment effects (estimate), standard errors (se), 1 - alpha confidence interval bounds (ci_low, ci_high), per-cohort p-values (p_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), p_value is NA. The catt_df S3 class makes [[ / $ / [ access on the pre-1.11.0 Title-Case column names (Cohort, ⁠Estimated TE⁠, SE, ConfIntLow, ConfIntHigh, P_value) stop() with a migration message pointing to the new name. See NEWS.md for the rename table.

The full vector of estimated coefficients.

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

Either the provided lambda.max or the one that was used, if a value wasn't provided. (This is returned to help with getting a reasonable range of lambda values for grid search.)

The number of selected features (excluding the always-present intercept) at lambda.max (for q <= 1, the smallest model). As mentioned above, for q <= 1 ideally this value is close to 0.

Either the provided lambda.min or the one that was used, if a value wasn't provided.

The number of selected features (excluding the always-present intercept) at lambda.min (for q <= 1, the largest model). As mentioned above, for q <= 1 ideally this value is close to p.

The value of lambda chosen by the method recorded in lambda_selection. If this value is close to lambda.min or lambda.max, that could suggest that the range of lambda values should be expanded.

The number of selected features (excluding the always-present intercept) in the chosen model. If this value is close to lambda.max_model_size or lambda.min_model_size, that could suggest that the range of lambda values should be expanded.

Character scalar; either "cv" or "bic". Mirrors the lambda_selection argument the user passed.

Integer scalar; the cv_folds value used when lambda_selection = "cv", NA_integer_ when lambda_selection = "bic".

Integer scalar; the seed actually fed to set.seed() immediately before cv.grpreg() was called. Defaults to as.integer(N * T) when the user did not pass a seed. NA_integer_ when lambda_selection = "bic".

Character scalar; the ci_type argument the user passed ("simultaneous" or "pointwise"), controlling whether the reported catt_df / eventStudy() confidence-interval bounds are simultaneous (family-wise) or pointwise.

The design matrix created containing all interactions, time and cohort dummies, etc.

The vector of responses, containing nrow(X_ints) entries.

The design matrix after applying the change in coordinates to fit the model and also multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final number of units that were in the data set used for estimation (after any units may have been removed because they were treated in the first time period).

The number of time periods in the final data set.

The final number of treated cohorts that appear in the final data set.

Deprecated alias for G, retained for backward compatibility; populated with the same value. Use G. Will be removed in a future release.

The final number of covariates that appear in the final data set (after any covariates may have been removed because they contained missing values or all contained the same value for every unit).

The final number of columns in the full set of covariates used to estimate the model.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default", "conservative", or "cluster").

Numeric scalar; mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the response column name in the original pdata. Consumed by augment.betwfe().

Character scalars; the corresponding arguments the user passed.

Character vector; the original covs argument (pre-factor- expansion).

A list containing internal outputs that are typically not needed for interpretation, packaged here for parity with fetwfe() so downstream consumers can use a single canonical access path across all four estimator classes (#144). The first five sub-slots (X_ints, y, X_final, y_final, calc_ses) are also duplicated at top level for backward compat; variance_components and first_year live only under ⁠$internal⁠:

X_ints

The design matrix containing all interactions, time and cohort dummies, etc. Same value as top-level X_ints.

y

The vector of responses. Same as top-level y.

X_final

The design matrix after the change-of-coordinates step. Same as top-level X_final.

y_final

The transformed response vector. Same as top-level y_final.

calc_ses

Logical indicating whether standard errors were calculated. Same as top-level calc_ses.

variance_components

A list exposing the two variance pieces (att_var_1, att_var_2) plus paper-notation counterparts (V_1, V_2) and unit-scaled variance estimators (tilde_v_N, hat_v_N, tilde_v_N_C, tilde_v_N_C_pi_hat, tilde_v_N_C_pi_hat_cons, tilde_v_N_cons). The Wald CI is ⁠[hat_T_N +- qnorm(1-alpha/2) * sqrt(tilde_v_N / N)]⁠ (paper Eq. conf.int.form). New in v1.12.0 (issue #141 + #146).

first_year

Integer or numeric scalar; the first (earliest) time_var value in the panel after idCohorts() processing. Consumed by eventStudy() to map cohort_probs' cohort labels (treatment-start years) to 1-based panel-time-index offsets when the labels are integer-coercible. New in v1.13.3 (issue #174).

A fitted object from fetwfe(), etwfe(), betwfe(), or twfeCovs() (or their ⁠*WithSimulatedData()⁠ wrapper analogs, which return the same classes).

A fitted object from fetwfe(), etwfe(), or betwfe() (or their ⁠*WithSimulatedData()⁠ wrapper analogs, which return the same classes). twfeCovs() objects are not supported (see Description).

Numeric in ⁠(0, 1)⁠; the pointwise confidence level is 1 - alpha. Defaults to the alpha stored on the fit.

Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.

Character; the name of a single column containing a variable for the time period. This column is expected to contain integer values (for example, years). Recommended encodings for dates include format YYYY, YYYYMM, or YYYYMMDD, whichever is appropriate for your data.

Character; the name of a single column containing a variable for each unit. This column is expected to contain character values (i.e. the "name" of each unit).

Character; the name of a single column containing a variable for the treatment dummy indicator. This column is expected to contain integer values, and in particular, should equal 0 if the unit was untreated at that time and 1 otherwise. Treatment should be an absorbing state; that is, if unit i is treated at time t, then it must also be treated at all times t + 1, ..., T. Any units treated in the first time period will be removed automatically. Please make sure yourself that at least some units remain untreated at the final time period ("never-treated units").

Character; the name of a single column containing the response for each unit at each time. The response must be an integer or numeric value.

(Optional.) Either a character vector containing the names of the columns for covariates (e.g., covs = c("x1", "x2")), or a one-sided formula (e.g., covs = ~ x1 + x2) – the formula form mirrors the convention used by did::att_gt(xformla = ...). Only additive bare variable names are supported in the formula form; for derived variables, compute them in the data frame first and pass via the character-vector form. All of these columns are expected to contain integer, numeric, or factor values, and any categorical values will be automatically encoded as binary indicators. If no covariates are provided, the treatment effect estimation will proceed, but it will only be valid under unconditional versions of the parallel trends and no anticipation assumptions. Default is c().

(Optional.) Integer; a vector. If you have a sufficiently large number of units, you can optionally randomly split your data set in half (with N units in each data set). The data for half of the units should go in the pdata argument provided above. For the other N units, simply provide the counts for how many units appear in the untreated cohort plus each of the other G cohorts in this argument indep_counts. The benefit of doing this is that the standard error for the average treatment effect will be (asymptotically) exact instead of conservative. The length of indep_counts must equal 1 plus the number of treated cohorts in pdata. All entries of indep_counts must be strictly positive (if you are concerned that this might not work out, maybe your data set is on the small side and it's best to just leave your full data set in pdata). The sum of all the counts in indep_counts must match the total number of units in pdata. Default is NA (in which case conservative standard errors will be calculated if q < 1.)

(Optional.) Numeric; the variance of the row-level IID noise assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated by REML on the linear mixed-effects model y ~ X + (1 | unit) via lme4::lmer (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

(Optional.) Numeric; the variance of the unit-level IID noise (random effects) assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated by REML via lme4::lmer on the linear mixed-effects model y ~ X + (1 | unit) (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default", "conservative", or "cluster". "default" returns the tight Gaussian variance sqrt(att_var_1 + att_var_2) from Theorem (c$'$) under Assumption (Psi-IF); this is asymptotically exact for the package's default cohort sample-proportions estimator and for every standard propensity-score estimator that satisfies (Psi-IF) (multinomial logit, any GLM on W | X, kernel/series regression of ⁠1{W = g}⁠ on X). "conservative" returns the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c); use only if the propensity-score estimator violates (Psi-IF) (e.g., a Robins-Rotnitzky-augmented doubly-robust estimator, which the package does not currently implement). "cluster" is an experimental unit-clustered Liang-Zeger sandwich SE on the OLS-selected support (see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). The default value of "default" corresponds to the new tight Gaussian default introduced in version 1.12.0; previous versions used the conservative Cauchy-Schwarz formula as the default. To recover the prior conservative default behavior, pass se_type = "conservative".

Character; one of "simultaneous" (default) or "pointwise". Controls the confidence-interval bounds reported for the cohort-specific ATTs (in catt_df) and the event-study effects (from eventStudy(), shown by print / summary / plot, and surfaced by broom::tidy() on the fitted object and on the eventStudy() / cohortStudy() outputs). "simultaneous" reports parametric simultaneous (family-wise, uniform) bands computed via simultaneousCIs(): each family's band covers all of its effects jointly with probability 1 - alpha, matching the default presentation of did::aggte(cband = TRUE). "pointwise" reports per-effect Wald intervals (each covers its own effect with probability 1 - alpha, no joint guarantee — the behavior of versions <= 1.15.1). Both the interval bounds and the per-cohort p-values (p_value) follow ci_type (max-T multiplicity-adjusted under "simultaneous", per-cohort Wald under "pointwise"; #200); the standard errors (se) and the overall-ATT confidence interval (a single scalar) are identical under both settings. When standard errors are unavailable (e.g., a rank-deficient design) the bounds are NA under both settings. Default is "simultaneous".

The estimated overall average treatment effect for a randomly selected treated unit.

A standard error for the ATT. If the Gram matrix is not invertible, this will be NA.

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA. Standard post-OLS interpretation; ETWFE does not perform selection.

A named vector containing the estimated average treatment effects for each cohort.

A named vector containing the (asymptotically exact) standard errors for the estimated average treatment effects within each cohort.

A vector of the estimated probabilities of being in each cohort conditional on being treated, which was used in calculating att_hat. If indep_counts was provided, cohort_probs was calculated from that; otherwise, it was calculated from the counts of units in each treated cohort in pdata.

A data frame (with S3 class c("catt_df", "data.frame")) displaying the cohort names (cohort), average treatment effects (estimate), standard errors (se), 1 - alpha confidence interval bounds (ci_low, ci_high), and per-cohort p-values (p_value). No selected column; ETWFE does not perform selection. The catt_df S3 class makes [[ / $ / [ access on the pre-1.11.0 Title-Case column names (Cohort, ⁠Estimated TE⁠, SE, ConfIntLow, ConfIntHigh, P_value) stop() with a migration message pointing to the new name. See NEWS.md for the rename table.

The full vector of estimated coefficients.

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

The design matrix created containing all interactions, time and cohort dummies, etc.

The vector of responses, containing nrow(X_ints) entries.

The design matrix after applying the change in coordinates to fit the model and also multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final number of units that were in the data set used for estimation (after any units may have been removed because they were treated in the first time period).

The number of time periods in the final data set.

The final number of treated cohorts that appear in the final data set.

Deprecated alias for G, retained for backward compatibility; populated with the same value. Use G. Will be removed in a future release.

The final number of covariates that appear in the final data set (after any covariates may have been removed because they contained missing values or all contained the same value for every unit).

The final number of columns in the full set of covariates used to estimate the model.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default", "conservative", or "cluster").

Character scalar; the ci_type argument the user passed ("simultaneous" or "pointwise"), controlling whether the reported catt_df / eventStudy() confidence-interval bounds are simultaneous (family-wise) or pointwise.

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed. Consumed by ⁠augment.<class>()⁠ when auto-aligning a user-supplied panel to the fitted design.

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally). Consumed by ⁠augment.<class>()⁠.

A list containing internal outputs that are typically not needed for interpretation, packaged here for parity with fetwfe() so downstream consumers can use a single canonical access path across all four estimator classes (#144). The first five sub-slots (X_ints, y, X_final, y_final, calc_ses) are also duplicated at top level for backward compat; variance_components and first_year live only under ⁠$internal⁠:

X_ints

The design matrix containing all interactions, time and cohort dummies, etc. Same value as top-level X_ints.

y

The vector of responses. Same as top-level y.

X_final

The design matrix after the change-of-coordinates step. Same as top-level X_final.

y_final

The transformed response vector. Same as top-level y_final.

calc_ses

Logical indicating whether standard errors were calculated. Same as top-level calc_ses.

variance_components

A list exposing the two variance pieces (att_var_1, att_var_2) plus paper-notation counterparts (V_1, V_2) and unit-scaled variance estimators (tilde_v_N, hat_v_N, tilde_v_N_C, tilde_v_N_C_pi_hat, tilde_v_N_C_pi_hat_cons, tilde_v_N_cons). The Wald CI is ⁠[hat_T_N +- qnorm(1-alpha/2) * sqrt(tilde_v_N / N)]⁠ (paper Eq. conf.int.form). New in v1.12.0 (issue #141 + #146).

first_year

Integer or numeric scalar; the first (earliest) time_var value in the panel after idCohorts() processing. Consumed by eventStudy() to map cohort_probs' cohort labels (treatment-start years) to 1-based panel-time-index offsets when the labels are integer-coercible. New in v1.13.3 (issue #174).

A long-format data.frame that you could already feed to etwfe().

Character. Column name of the outcome (left-hand side in your fml).

Character. Column name of the time variable that you pass to etwfe() as tvar.

Character. Column name of the unit identifier (the variable you would cluster on, or pass to etwfe(..., ivar = idvar) if you were using unit FEs).

Character. Column name of the "first treated" cohort variable passed to etwfe() as gvar. Must be 0 for never-treated units, or the (strictly positive) first treated period.

Character vector of additional covariate columns to keep (default character(0)).

Logical. Should units already treated in the very first sample period be removed? (fetwfe() will drop them internally anyway, but doing it here keeps the returned dataframe clean.) Default TRUE.

Named list giving the column names that the returned dataframe should have. The default (time_var, unit_var, treatment, response) matches the arguments usually supplied to fetwfe(). Do not change the names of this list – only the values – and keep all four.

Logical. If TRUE, a message() reports the count of first-period-treated unit-period rows dropped when drop_first_period_treated = TRUE. Default FALSE (silent).

An object of class "FETWFE_simulated" containing the simulated panel data and design matrix.

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default", "conservative", or "cluster". "default" returns the tight Gaussian variance sqrt(att_var_1 + att_var_2) from Theorem (c$'$) under Assumption (Psi-IF); this is asymptotically exact for the package's default cohort sample-proportions estimator and for every standard propensity-score estimator that satisfies (Psi-IF) (multinomial logit, any GLM on W | X, kernel/series regression of ⁠1{W = g}⁠ on X). "conservative" returns the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c); use only if the propensity-score estimator violates (Psi-IF) (e.g., a Robins-Rotnitzky-augmented doubly-robust estimator, which the package does not currently implement). "cluster" is an experimental unit-clustered Liang-Zeger sandwich SE on the OLS-selected support (see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). The default value of "default" corresponds to the new tight Gaussian default introduced in version 1.12.0; previous versions used the conservative Cauchy-Schwarz formula as the default. To recover the prior conservative default behavior, pass se_type = "conservative".

Character; one of "simultaneous" (default) or "pointwise". Controls the confidence-interval bounds reported for the cohort-specific ATTs (in catt_df) and the event-study effects (from eventStudy(), shown by print / summary / plot, and surfaced by broom::tidy() on the fitted object and on the eventStudy() / cohortStudy() outputs). "simultaneous" reports parametric simultaneous (family-wise, uniform) bands computed via simultaneousCIs(): each family's band covers all of its effects jointly with probability 1 - alpha, matching the default presentation of did::aggte(cband = TRUE). "pointwise" reports per-effect Wald intervals (each covers its own effect with probability 1 - alpha, no joint guarantee — the behavior of versions <= 1.15.1). Both the interval bounds and the per-cohort p-values (p_value) follow ci_type (max-T multiplicity-adjusted under "simultaneous", per-cohort Wald under "pointwise"; #200); the standard errors (se) and the overall-ATT confidence interval (a single scalar) are identical under both settings. When standard errors are unavailable (e.g., a rank-deficient design) the bounds are NA under both settings. Default is "simultaneous".

The estimated overall average treatment effect for a randomly selected treated unit.

A standard error for the ATT. If the Gram matrix is not invertible, this will be NA.

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA. Standard post-OLS interpretation; ETWFE does not perform selection.

A named vector containing the estimated average treatment effects for each cohort.

A named vector containing the (asymptotically exact) standard errors for the estimated average treatment effects within each cohort.

A vector of the estimated probabilities of being in each cohort conditional on being treated, which was used in calculating att_hat. If indep_counts was provided, cohort_probs was calculated from that; otherwise, it was calculated from the counts of units in each treated cohort in pdata.

A data frame (with S3 class c("catt_df", "data.frame")) displaying the cohort names (cohort), average treatment effects (estimate), standard errors (se), 1 - alpha confidence interval bounds (ci_low, ci_high), and per-cohort p-values (p_value). No selected column; ETWFE does not perform selection. The catt_df S3 class makes [[ / $ / [ access on the pre-1.11.0 Title-Case column names (Cohort, ⁠Estimated TE⁠, SE, ConfIntLow, ConfIntHigh, P_value) stop() with a migration message pointing to the new name. See NEWS.md for the rename table.

The full vector of estimated coefficients.

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

The design matrix created containing all interactions, time and cohort dummies, etc.

The vector of responses, containing nrow(X_ints) entries.

The design matrix after applying the change in coordinates to fit the model and also multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

The final number of units that were in the data set used for estimation (after any units may have been removed because they were treated in the first time period).

The number of time periods in the final data set.

The final number of treated cohorts that appear in the final data set.

Deprecated alias for G, retained for backward compatibility; populated with the same value. Use G. Will be removed in a future release.

The final number of covariates that appear in the final data set (after any covariates may have been removed because they contained missing values or all contained the same value for every unit).

The final number of columns in the full set of covariates used to estimate the model.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default", "conservative", or "cluster").

Character scalar; the ci_type argument the user passed ("simultaneous" or "pointwise"), controlling whether the reported catt_df / eventStudy() confidence-interval bounds are simultaneous (family-wise) or pointwise.

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed.

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally).

A list containing internal outputs that are typically not needed for interpretation, packaged here for parity with fetwfe() so downstream consumers can use a single canonical access path across all four estimator classes (#144). The first five sub-slots (X_ints, y, X_final, y_final, calc_ses) are also duplicated at top level for backward compat; variance_components and first_year live only under ⁠$internal⁠:

X_ints

The design matrix containing all interactions, time and cohort dummies, etc. Same value as top-level X_ints.

y

The vector of responses. Same as top-level y.

X_final

The design matrix after the change-of-coordinates step. Same as top-level X_final.

y_final

The transformed response vector. Same as top-level y_final.

calc_ses

Logical indicating whether standard errors were calculated. Same as top-level calc_ses.

variance_components

A list exposing the two variance pieces (att_var_1, att_var_2) plus paper-notation counterparts (V_1, V_2) and unit-scaled variance estimators (tilde_v_N, hat_v_N, tilde_v_N_C, tilde_v_N_C_pi_hat, tilde_v_N_C_pi_hat_cons, tilde_v_N_cons). The Wald CI is ⁠[hat_T_N +- qnorm(1-alpha/2) * sqrt(tilde_v_N / N)]⁠ (paper Eq. conf.int.form). New in v1.12.0 (issue #141 + #146).

first_year

Integer or numeric scalar; the first (earliest) time_var value in the panel after idCohorts() processing. Consumed by eventStudy() to map cohort_probs' cohort labels (treatment-start years) to 1-based panel-time-index offsets when the labels are integer-coercible. New in v1.13.3 (issue #174).

A fitted object of class "fetwfe", "etwfe", or "betwfe".

(Optional) Significance level for confidence intervals. Defaults to x$alpha (the alpha used at fit time).

(Optional) Character; one of "simultaneous" or "pointwise", or NULL (default). Controls whether the returned ci_low / ci_high are the event-study-family simultaneous (family-wise, uniform) band or the per-event-time pointwise Wald intervals. NULL inherits the fit's stored ci_type (so a fit made with the default ci_type = "simultaneous" yields simultaneous event-study bands, which print / summary / plot then display); for objects fitted before version 1.16.0 (no ci_type slot) NULL falls back to "pointwise". The se column is identical under both settings; the interval bounds, their critical-value multiplier, and the p_value differ (under "simultaneous" the p_value is the single-step max-T multiplicity- adjusted dual of the band, under "pointwise" the per-effect Wald p-value; #200). Degenerate event times (no valid contributing cohorts) carry NA bounds and NA p_value under both settings.

Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.

Character; the name of a single column containing a variable for the time period. This column is expected to contain integer values (for example, years). Recommended encodings for dates include format YYYY, YYYYMM, or YYYYMMDD, whichever is appropriate for your data.

Character; the name of a single column containing a variable for each unit. This column is expected to contain character values (i.e. the "name" of each unit).

Character; the name of a single column containing a variable for the treatment dummy indicator. This column is expected to contain integer values, and in particular, should equal 0 if the unit was untreated at that time and 1 otherwise. Treatment should be an absorbing state; that is, if unit i is treated at time t, then it must also be treated at all times t + 1, ..., T. Any units treated in the first time period will be removed automatically. Please make sure yourself that at least some units remain untreated at the final time period ("never-treated units").

Character; the name of a single column containing the response for each unit at each time. The response must be an integer or numeric value.

(Optional.) Either a character vector containing the names of the columns for covariates (e.g., covs = c("x1", "x2")), or a one-sided formula (e.g., covs = ~ x1 + x2) – the formula form mirrors the convention used by did::att_gt(xformla = ...). Only additive bare variable names are supported in the formula form; for derived variables, compute them in the data frame first and pass via the character-vector form. All of these columns are expected to contain integer, numeric, or factor values, and any categorical values will be automatically encoded as binary indicators. If no covariates are provided, the treatment effect estimation will proceed, but it will only be valid under unconditional versions of the parallel trends and no anticipation assumptions. Default is c().

(Optional.) Integer; a vector. If you have a sufficiently large number of units, you can optionally randomly split your data set in half (with N units in each data set). The data for half of the units should go in the pdata argument provided above. For the other N units, simply provide the counts for how many units appear in the untreated cohort plus each of the other G cohorts in this argument indep_counts. The benefit of doing this is that the standard error for the average treatment effect will be (asymptotically) exact instead of conservative. The length of indep_counts must equal 1 plus the number of treated cohorts in pdata. All entries of indep_counts must be strictly positive (if you are concerned that this might not work out, maybe your data set is on the small side and it's best to just leave your full data set in pdata). The sum of all the counts in indep_counts must match the total number of units in pdata. Default is NA (in which case conservative standard errors will be calculated if q < 1.)

(Optional.) Numeric; the variance of the row-level IID noise assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated by REML on the linear mixed-effects model y ~ X + (1 | unit) via lme4::lmer (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

(Optional.) Numeric; the variance of the unit-level IID noise (random effects) assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated by REML via lme4::lmer on the linear mixed-effects model y ~ X + (1 | unit) (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

(Optional.) Numeric. A penalty parameter lambda will be selected over a grid search by BIC in order to select a single model. The largest lambda in the grid will be lambda.max. If no lambda.max is provided, one will be selected automatically. When q <= 1, the model will be sparse, and ideally all of the following are true at once: the smallest model (the one corresponding to lambda.max) selects close to 0 features, the largest model (the one corresponding to lambda.min) selects close to p features, nlambda is large enough so that models are considered at every feasible model size, and nlambda is small enough so that the computation doesn't become infeasible. You may want to manually tweak lambda.max, lambda.min, and nlambda to try to achieve these goals, particularly if the selected model size is very close to the model corresponding to lambda.max or lambda.min, which could indicate that the range of lambda values was too narrow or coarse. You can use the function outputs lambda.max_model_size, lambda.min_model_size, and lambda_star_model_size to try to assess this. Default is NA.

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

(Optional.) Numeric; determines what L_q penalty is used for the fusion regularization. q = 1 is the lasso, and for 0 < q < 1, it is possible to get standard errors and confidence intervals. q = 2 is ridge regression. See Faletto (2025) for details. Default is 0.5.

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default", "conservative", or "cluster". "default" returns the tight Gaussian variance sqrt(att_var_1 + att_var_2) from Theorem (c$'$) under Assumption (Psi-IF); this is asymptotically exact for the package's default cohort sample-proportions estimator and for every standard propensity-score estimator that satisfies (Psi-IF) (multinomial logit, any GLM on W | X, kernel/series regression of ⁠1{W = g}⁠ on X). "conservative" returns the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c); use only if the propensity-score estimator violates (Psi-IF) (e.g., a Robins-Rotnitzky-augmented doubly-robust estimator, which the package does not currently implement). "cluster" is an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support (see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat); only meaningful when q < 1 (the bridge oracle property is required), and for q >= 1 the SE will be NA regardless of se_type. The default value of "default" corresponds to the new tight Gaussian default introduced in version 1.12.0; previous versions used the conservative Cauchy-Schwarz formula as the default. To recover the prior conservative default behavior, pass se_type = "conservative".

Character; method for selecting the bridge penalty parameter lambda. Either "cv" (10-fold cross-validation on cv.grpreg; the v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default for v1.12.0 and earlier). The default changed in v1.13.0 to address a finite-sample bias issue documented in simulation studies (see issue #164): under the prior BIC default, the overall-ATT estimator was biased toward zero at moderate sample sizes, producing 95% confidence intervals whose empirical coverage was as low as 0.00 in some regimes. Cross-validation restores near-nominal coverage in every regime tested. To recover the prior behavior — for example, when reproducing analyses run against v1.12.0 or earlier — pass lambda_selection = "bic". See the inference vignette section "Choosing the bridge penalty parameter" for details.

Integer; number of folds for the CV path. Ignored when lambda_selection = "bic". Default is 10.

Integer or NULL; the seed passed to set.seed() immediately before the cv.grpreg() call, controlling fold assignment. If NULL (the default), the seed defaults internally to as.integer(N * T) so consecutive calls on the same dataset are reproducible without the user having to specify a seed. The seed actually used is stored on the returned object as cv_seed. Ignored when lambda_selection = "bic".

Character; one of "simultaneous" (default) or "pointwise". Controls the confidence-interval bounds reported for the cohort-specific ATTs (in catt_df) and the event-study effects (from eventStudy(), shown by print / summary / plot, and surfaced by broom::tidy() on the fitted object and on the eventStudy() / cohortStudy() outputs). "simultaneous" reports parametric simultaneous (family-wise, uniform) bands computed via simultaneousCIs(): each family's band covers all of its effects jointly with probability 1 - alpha, matching the default presentation of did::aggte(cband = TRUE). "pointwise" reports per-effect Wald intervals (each covers its own effect with probability 1 - alpha, no joint guarantee — the behavior of versions <= 1.15.1). Both the interval bounds and the per-cohort p-values (p_value) follow ci_type: under "simultaneous" the p_value is the single-step max-T multiplicity- adjusted p-value matching the band, under "pointwise" the per-cohort Wald p-value (#200). The standard errors (se) and selection flags (selected) are identical under both settings, and the overall-ATT confidence interval (a single scalar) is unaffected. When standard errors are unavailable (q >= 1, or a rank-deficient design) the bounds are NA under both settings. Default is "simultaneous".

Character; one of "cohort" or "event_study". "cohort" (the default) uses the within-cohort / between-cohort two-way fusion penalty. "event_study" instead fuses treatment effects at the same time since treatment (event time e = t - g) across cohorts. The event-study penalty carries the same theoretical guarantees as the default (Faletto 2025); only the treatment-effect fusion structure changes.

(Optional.) Numeric matrix or NULL (the default). An advanced-use override: a user-supplied ⁠num_treats x num_treats⁠ forward differences matrix D_N for the treatment-effect block, encoding an arbitrary fusion structure beyond the two built-ins. When non-NULL it overrides fusion_structure for the treatment-effect block only (the fixed-effect blocks are unchanged); the estimator uses solve(fusion_matrix) internally. The rows/columns are interpreted in the cohort-major ⁠(g, t)⁠ order used internally for the treatment effects (the order getFirstInds() / getTreatInds() encode): row/column i corresponds to base treatment effect i, with cohort g occupying rows first_inds[g]:(first_inds[g + 1] - 1) ordered by event time. num_treats equals T * G - G * (G + 1) / 2. fusion_matrix must be a finite, invertible numeric matrix of that exact dimension (otherwise fetwfe() stops). Under the paper's fixed-dimension scoping, any finite invertible D_N of that dimension inherits the paper's inferential guarantees: the theory depends on D_N only through its invertibility and singular-value bounds (Assumption (D) of Faletto 2025), which a fixed invertible matrix automatically satisfies, and swapping in a different D_N from this class changes only constant factors. A numerically near-singular (ill-conditioned) D_N still yields a valid point estimator but emits a warning() that its inverse may be unreliable. Default is NULL (use the built-in fusion_structure).

The estimated overall average treatment effect for a randomly selected treated unit.

If q < 1, a standard error for the ATT. Under the default se_type = "default", the SE is the tight Gaussian variance sqrt(att_var_1 + att_var_2) (Theorem (c$'$) under Assumption (Psi-IF); paper line 1233 onwards). Assumption (Psi-IF) is satisfied by the package's default cohort sample-proportions estimator hat_pi_g = N_g / N (and by multinomial logit, any GLM on W | X, and kernel/series regression of ⁠1{W = g}⁠ on X), so the default SE is asymptotically exact for the package's default estimator. Under se_type = "conservative" (or in version <= 1.11.7 by default), the SE is the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c). When indep_counts is provided, the two-sample exact formula sqrt(att_var_1 + att_var_2) is used regardless of se_type. If q >= 1, this will be NA.

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback). See the package vignette section "Testing the zero-effect null" for interpretation guidance under selection consistency.

Logical scalar; TRUE if att_hat is not exactly zero (i.e., at least one cohort's bridge-penalized coefficient survived selection), FALSE otherwise. Under FETWFE Theorem 6.2 (restriction selection consistency), att_selected = FALSE is the asymptotic statement that the truth is zero. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

A named vector containing the estimated average treatment effects for each cohort.

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

A vector of the estimated probabilities of being in each cohort conditional on being treated, which was used in calculating att_hat. If indep_counts was provided, cohort_probs was calculated from that; otherwise, it was calculated from the counts of units in each treated cohort in pdata.

A data frame (with S3 class c("catt_df", "data.frame")) displaying the cohort names (cohort), average treatment effects (estimate), standard errors (se), 1 - alpha confidence interval bounds (ci_low, ci_high), per-cohort p-values (p_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), p_value is NA — the inferential content lives in selected. The catt_df S3 class makes [[ / $ / [ access on the pre-1.11.0 Title-Case column names (Cohort, ⁠Estimated TE⁠, SE, ConfIntLow, ConfIntHigh, P_value) stop() with a migration message pointing to the new name. See NEWS.md for the rename table.

The full vector of estimated coefficients.

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

Either the provided lambda.max or the one that was used, if a value wasn't provided. (This is returned to help with getting a reasonable range of lambda values for grid search.)

The number of selected features (excluding the always-present intercept) at lambda.max (for q <= 1, this will be the smallest model size). As mentioned above, for q <= 1 ideally this value is close to 0.

Either the provided lambda.min or the one that was used, if a value wasn't provided.

The number of selected features (excluding the always-present intercept) at lambda.min (for q <= 1, this will be the largest model size). As mentioned above, for q <= 1 ideally this value is close to p.

The value of lambda chosen by the selection method recorded in lambda_selection. If this value is close to lambda.min or lambda.max, that could suggest that the range of lambda values should be expanded.

The number of selected features (excluding the always-present intercept) in the chosen model. If this value is close to lambda.max_model_size or lambda.min_model_size, that could suggest that the range of lambda values should be expanded.

Character scalar; either "cv" (10-fold cross-validation on cv.grpreg; v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default). Mirrors the lambda_selection argument the user passed.

Integer scalar; the cv_folds value used when lambda_selection = "cv", NA_integer_ when lambda_selection = "bic".

Integer scalar; the seed actually fed to set.seed() immediately before cv.grpreg() was called. Defaults to as.integer(N * T) when the user did not pass a seed. NA_integer_ when lambda_selection = "bic".

Character scalar; the fusion_structure argument the user passed ("cohort" or "event_study"), recording which fusion-penalty differences matrix was used for the treatment effects.

The user-supplied custom forward differences matrix D_N (a ⁠num_treats x num_treats⁠ numeric matrix), or NULL if none was supplied. When non-NULL it overrode fusion_structure for the treatment-effect block; the estimator used solve(fusion_matrix) internally. See the fusion_matrix argument.

The final number of units that were in the data set used for estimation (after any units may have been removed because they were treated in the first time period).

The number of time periods in the final data set.

The final number of treated cohorts that appear in the final data set.

Deprecated alias for G, retained for backward compatibility; populated with the same value. Use G. Will be removed in a future release.

The final number of covariates that appear in the final data set (after any covariates may have been removed because they contained missing values or all contained the same value for every unit).

The final number of columns in the full set of covariates used to estimate the model.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated. Same as ⁠$internal$calc_ses⁠; duplicated at top level for parity with etwfe(), betwfe(), and twfeCovs() (#180).

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default", "conservative", or "cluster").

Character scalar; the ci_type argument the user passed ("simultaneous" or "pointwise"), controlling whether the reported catt_df / eventStudy() confidence-interval bounds are simultaneous (family-wise) or pointwise.

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed. Consumed by ⁠augment.<class>()⁠ when auto-aligning a user-supplied panel to the fitted design (e.g., dropping first-period-treated units the estimator removed internally, and sorting rows to match the design matrix's internal ⁠(unit, time)⁠ order).

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally). Consumed by ⁠augment.<class>()⁠.

A list containing internal outputs that are typically not needed for interpretation:

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

The design matrix after applying the change in coordinates to fit the model and also multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

theta_hat

The vector of estimated coefficients in the transformed (fused) space, including the intercept as the first element.

calc_ses

Logical indicating whether standard errors were calculated.

variance_components

A list exposing the two variance pieces (att_var_1, att_var_2) plus their paper-notation counterparts (V_1, V_2) and the unit-scaled variance estimators (tilde_v_N, hat_v_N, tilde_v_N_C, tilde_v_N_C_pi_hat, tilde_v_N_C_pi_hat_cons, tilde_v_N_cons) catalogued at paper line 2006. The Wald CI is ⁠[hat_T_N +- qnorm(1-alpha/2) * sqrt(tilde_v_N / N)]⁠ (paper Eq. conf.int.form). New in v1.12.0 (issue #141 + #146).

first_year

Integer or numeric scalar; the first (earliest) time_var value in the panel after idCohorts() processing. Consumed by eventStudy() to map cohort_probs' cohort labels (treatment-start years) to 1-based panel-time-index offsets when the labels are integer-coercible. New in v1.13.3 (issue #174).

d_inv_treat

The inverted custom treatment-effect fusion block solve(fusion_matrix) (a ⁠num_treats x num_treats⁠ numeric matrix), or NULL if no fusion_matrix was supplied. Consumed by eventStudy() and simultaneousCIs() so the access-time bands reuse the same fusion block the fit used (#236).

An object of class "FETWFE_simulated" containing the simulated panel data and design matrix.

(Optional.) Numeric. A penalty parameter lambda will be selected over a grid search by BIC in order to select a single model. The largest lambda in the grid will be lambda.max. If no lambda.max is provided, one will be selected automatically. For lambda <= 1, the model will be sparse, and ideally all of the following are true at once: the smallest model (the one corresponding to lambda.max) selects close to 0 features, the largest model (the one corresponding to lambda.min) selects close to p features, nlambda is large enough so that models are considered at every feasible model size, and nlambda is small enough so that the computation doesn't become infeasible. You may want to manually tweak lambda.max, lambda.min, and nlambda to try to achieve these goals, particularly if the selected model size is very close to the model corresponding to lambda.max or lambda.min, which could indicate that the range of lambda values was too narrow. You can use the function outputs lambda.max_model_size, lambda.min_model_size, and lambda_star_model_size to try to assess this. Default is NA.

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

(Optional.) Numeric; determines what L_q penalty is used for the fusion regularization. q = 1 is the lasso, and for 0 < q < 1, it is possible to get standard errors and confidence intervals. q = 2 is ridge regression. See Faletto (2025) for details. Default is 0.5.

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default", "conservative", or "cluster". "default" returns the tight Gaussian variance sqrt(att_var_1 + att_var_2) from Theorem (c$'$) under Assumption (Psi-IF); this is asymptotically exact for the package's default cohort sample-proportions estimator and for every standard propensity-score estimator that satisfies (Psi-IF) (multinomial logit, any GLM on W | X, kernel/series regression of ⁠1{W = g}⁠ on X). "conservative" returns the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c); use only if the propensity-score estimator violates (Psi-IF) (e.g., a Robins-Rotnitzky-augmented doubly-robust estimator, which the package does not currently implement). "cluster" is an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support (see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat); only meaningful when q < 1 (the bridge oracle property is required), and for q >= 1 the SE will be NA regardless of se_type. The default value of "default" corresponds to the new tight Gaussian default introduced in version 1.12.0; previous versions used the conservative Cauchy-Schwarz formula as the default. To recover the prior conservative default behavior, pass se_type = "conservative".

Character; method for selecting the bridge penalty parameter lambda. Either "cv" (10-fold cross-validation on cv.grpreg; the v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default for v1.12.0 and earlier). The default changed in v1.13.0 to address a finite-sample bias issue documented in simulation studies (see issue #164): under the prior BIC default, the overall-ATT estimator was biased toward zero at moderate sample sizes, producing 95% confidence intervals whose empirical coverage was as low as 0.00 in some regimes. Cross-validation restores near-nominal coverage in every regime tested. To recover the prior behavior — for example, when reproducing analyses run against v1.12.0 or earlier — pass lambda_selection = "bic". See the inference vignette section "Choosing the bridge penalty parameter" for details.

Integer; number of folds for the CV path. Ignored when lambda_selection = "bic". Default is 10.

Integer or NULL; the seed passed to set.seed() immediately before the cv.grpreg() call, controlling fold assignment. If NULL (the default), the seed defaults internally to as.integer(N * T) so consecutive calls on the same dataset are reproducible without the user having to specify a seed. The seed actually used is stored on the returned object as cv_seed. Ignored when lambda_selection = "bic".

Character; one of "simultaneous" (default) or "pointwise". Controls the confidence-interval bounds reported for the cohort-specific ATTs (in catt_df) and the event-study effects (from eventStudy(), shown by print / summary / plot, and surfaced by broom::tidy() on the fitted object and on the eventStudy() / cohortStudy() outputs). "simultaneous" reports parametric simultaneous (family-wise, uniform) bands computed via simultaneousCIs(): each family's band covers all of its effects jointly with probability 1 - alpha, matching the default presentation of did::aggte(cband = TRUE). "pointwise" reports per-effect Wald intervals (each covers its own effect with probability 1 - alpha, no joint guarantee — the behavior of versions <= 1.15.1). Both the interval bounds and the per-cohort p-values (p_value) follow ci_type: under "simultaneous" the p_value is the single-step max-T multiplicity- adjusted p-value matching the band, under "pointwise" the per-cohort Wald p-value (#200). The standard errors (se) and selection flags (selected) are identical under both settings, and the overall-ATT confidence interval (a single scalar) is unaffected. When standard errors are unavailable (q >= 1, or a rank-deficient design) the bounds are NA under both settings. Default is "simultaneous".

Character; one of "cohort" or "event_study". "cohort" (the default) uses the within-cohort / between-cohort two-way fusion penalty. "event_study" instead fuses treatment effects at the same time since treatment (event time e = t - g) across cohorts. The event-study penalty carries the same theoretical guarantees as the default (Faletto 2025); only the treatment-effect fusion structure changes.

(Optional.) Numeric matrix or NULL (the default). An advanced-use override: a user-supplied ⁠num_treats x num_treats⁠ forward differences matrix D_N for the treatment-effect block, encoding an arbitrary fusion structure beyond the two built-ins. When non-NULL it overrides fusion_structure for the treatment-effect block only (the fixed-effect blocks are unchanged); the estimator uses solve(fusion_matrix) internally. The rows/columns are interpreted in the cohort-major ⁠(g, t)⁠ order used internally for the treatment effects (the order getFirstInds() / getTreatInds() encode): row/column i corresponds to base treatment effect i, with cohort g occupying rows first_inds[g]:(first_inds[g + 1] - 1) ordered by event time. num_treats equals T * G - G * (G + 1) / 2. fusion_matrix must be a finite, invertible numeric matrix of that exact dimension (otherwise fetwfe() stops). Under the paper's fixed-dimension scoping, any finite invertible D_N of that dimension inherits the paper's inferential guarantees: the theory depends on D_N only through its invertibility and singular-value bounds (Assumption (D) of Faletto 2025), which a fixed invertible matrix automatically satisfies, and swapping in a different D_N from this class changes only constant factors. A numerically near-singular (ill-conditioned) D_N still yields a valid point estimator but emits a warning() that its inverse may be unreliable. Default is NULL (use the built-in fusion_structure).

The estimated overall average treatment effect for a randomly selected treated unit.

If q < 1, a standard error for the ATT. Under the default se_type = "default", the SE is the tight Gaussian variance sqrt(att_var_1 + att_var_2) (Theorem (c$'$) under Assumption (Psi-IF); paper line 1233 onwards). Assumption (Psi-IF) is satisfied by the package's default cohort sample-proportions estimator hat_pi_g = N_g / N (and by multinomial logit, any GLM on W | X, and kernel/series regression of ⁠1{W = g}⁠ on X), so the default SE is asymptotically exact for the package's default estimator. Under se_type = "conservative" (or in version <= 1.11.7 by default), the SE is the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c). When indep_counts is provided, the two-sample exact formula sqrt(att_var_1 + att_var_2) is used regardless of se_type. If q >= 1, this will be NA.

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback). See the package vignette section "Testing the zero-effect null" for interpretation guidance under selection consistency.

Logical scalar; TRUE if att_hat is not exactly zero (i.e., at least one cohort's bridge-penalized coefficient survived selection), FALSE otherwise. Under FETWFE Theorem 6.2 (restriction selection consistency), att_selected = FALSE is the asymptotic statement that the truth is zero. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

A named vector containing the estimated average treatment effects for each cohort.

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

A vector of the estimated probabilities of being in each cohort conditional on being treated, which was used in calculating att_hat. If indep_counts was provided, cohort_probs was calculated from that; otherwise, it was calculated from the counts of units in each treated cohort in pdata.

A data frame (with S3 class c("catt_df", "data.frame")) displaying the cohort names (cohort), average treatment effects (estimate), standard errors (se), 1 - alpha confidence interval bounds (ci_low, ci_high), per-cohort p-values (p_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), p_value is NA — the inferential content lives in selected. The catt_df S3 class makes [[ / $ / [ access on the pre-1.11.0 Title-Case column names (Cohort, ⁠Estimated TE⁠, SE, ConfIntLow, ConfIntHigh, P_value) stop() with a migration message pointing to the new name. See NEWS.md for the rename table.

The full vector of estimated coefficients.

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

Either the provided lambda.max or the one that was used, if a value wasn't provided. (This is returned to help with getting a reasonable range of lambda values for grid search.)

The number of selected features (excluding the always-present intercept) at lambda.max (for q <= 1, this will be the smallest model size). As mentioned above, for q <= 1 ideally this value is close to 0.

Either the provided lambda.min or the one that was used, if a value wasn't provided.

The number of selected features (excluding the always-present intercept) at lambda.min (for q <= 1, this will be the largest model size). As mentioned above, for q <= 1 ideally this value is close to p.

The value of lambda chosen by the selection method recorded in lambda_selection. If this value is close to lambda.min or lambda.max, that could suggest that the range of lambda values should be expanded.

The number of selected features (excluding the always-present intercept) in the chosen model. If this value is close to lambda.max_model_size or lambda.min_model_size, that could suggest that the range of lambda values should be expanded.

Character scalar; either "cv" (10-fold cross-validation on cv.grpreg; v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default). Mirrors the lambda_selection argument the user passed.

Integer scalar; the cv_folds value used when lambda_selection = "cv", NA_integer_ when lambda_selection = "bic".

Integer scalar; the seed actually fed to set.seed() immediately before cv.grpreg() was called. Defaults to as.integer(N * T) when the user did not pass a seed. NA_integer_ when lambda_selection = "bic".

Character scalar; the fusion_structure argument the user passed ("cohort" or "event_study"), recording which fusion-penalty differences matrix was used for the treatment effects.

The user-supplied custom forward differences matrix D_N (a ⁠num_treats x num_treats⁠ numeric matrix), or NULL if none was supplied. When non-NULL it overrode fusion_structure for the treatment-effect block; the estimator used solve(fusion_matrix) internally. See the fusion_matrix argument.

The final number of units that were in the data set used for estimation (after any units may have been removed because they were treated in the first time period).

The number of time periods in the final data set.

The final number of treated cohorts that appear in the final data set.

Deprecated alias for G, retained for backward compatibility; populated with the same value. Use G. Will be removed in a future release.

The final number of covariates that appear in the final data set (after any covariates may have been removed because they contained missing values or all contained the same value for every unit).

The final number of columns in the full set of covariates used to estimate the model.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated. Same as ⁠$internal$calc_ses⁠; duplicated at top level for parity with etwfe(), betwfe(), and twfeCovs() (#180).

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default", "conservative", or "cluster").

Character scalar; the ci_type argument the user passed ("simultaneous" or "pointwise"), controlling whether the reported catt_df / eventStudy() confidence-interval bounds are simultaneous (family-wise) or pointwise.

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed. Consumed by ⁠augment.<class>()⁠ when auto-aligning a user-supplied panel to the fitted design (e.g., dropping first-period-treated units the estimator removed internally, and sorting rows to match the design matrix's internal ⁠(unit, time)⁠ order).

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally). Consumed by ⁠augment.<class>()⁠.

A list containing internal outputs that are typically not needed for interpretation:

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

The design matrix after applying the change in coordinates to fit the model and also multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

theta_hat

The vector of estimated coefficients in the transformed (fused) space, including the intercept as the first element.

calc_ses

Logical indicating whether standard errors were calculated.

variance_components

A list exposing the two variance pieces (att_var_1, att_var_2) plus their paper-notation counterparts (V_1, V_2) and the unit-scaled variance estimators (tilde_v_N, hat_v_N, tilde_v_N_C, tilde_v_N_C_pi_hat, tilde_v_N_C_pi_hat_cons, tilde_v_N_cons) catalogued at paper line 2006. The Wald CI is ⁠[hat_T_N +- qnorm(1-alpha/2) * sqrt(tilde_v_N / N)]⁠ (paper Eq. conf.int.form). New in v1.12.0 (issue #141 + #146).

first_year

Integer or numeric scalar; the first (earliest) time_var value in the panel after idCohorts() processing. Consumed by eventStudy() to map cohort_probs' cohort labels (treatment-start years) to 1-based panel-time-index offsets when the labels are integer-coercible. New in v1.13.3 (issue #174).

d_inv_treat

The inverted custom treatment-effect fusion block solve(fusion_matrix) (a ⁠num_treats x num_treats⁠ numeric matrix), or NULL if no fusion_matrix was supplied. Consumed by eventStudy() and simultaneousCIs() so the access-time bands reuse the same fusion block the fit used (#236).

Optional integer. The number of treated cohorts (treatment is assumed to start in periods 2 to G + 1). Defaults to NULL; supply either G or the deprecated alias R (described below).

Integer. The total number of time periods.

Integer. The number of time-invariant covariates. If d > 0, additional terms corresponding to covariate main effects and interactions are included in beta.

Numeric in (0,1]. The probability that any given entry in the initial coefficient vector theta is nonzero. density = 1 gives a fully dense (non-sparse) coefficient vector.

Numeric. The magnitude used to scale nonzero entries in theta. Each nonzero entry is set to eff_size or -eff_size (with a 60 percent chance for a positive value).

Character. One of "cohort" (default) or "event_study". Controls the basis in which the true treatment-effect coefficients are sparse. Under "cohort" the sparse transformed coefficients theta are mapped back through the default two-way (cohort) inverse fusion transform (byte-identical to previous behavior); under "event_study" they are mapped through the event-study inverse fusion transform, so the true treatment effects are sparse in the event-study basis (effects sharing the same time since treatment, $e = t - g$, tend to be equal across cohorts). This is the simulation-side companion to the fusion_structure argument of fetwfe().

Character. One of "marginal" (default), "multinomial", or "ordered". Selects the data-generating process for cohort assignment in simulateData().

• "marginal": each unit's cohort is drawn uniformly, independent of its covariates. Original pre-1.14.0 behavior, preserved byte-identically.

• "multinomial": cohort assignment follows a multinomial-logit propensity-score model $\pi_g(x) = \exp(\gamma_g^\top x) / \sum_{g'} \exp(\gamma_{g'}^\top x)$ with $\gamma_0 \equiv 0$ (never-treated reference). Requires $d \ge 1$.

• "ordered": cohort assignment follows a proportional-odds (ordered-logit) model with cumulative probabilities $P(W \le g | x) = \mathrm{plogis}(\alpha_g - \gamma^\top x)$. Cutpoints $\alpha_g$ are chosen so the marginal cohort probabilities are approximately uniform 1/(G + 1). Requires $d \ge 1$.

Non-negative numeric scalar. Scales the logit coefficients in the propensity-score model. 0 reduces both non-marginal types to the uniform marginal distribution by construction. Larger values produce stronger covariate-cohort coupling. Defaults to 1.0. Ignored when assignment_type = "marginal".

Optional. A list of length-2 integer vectors, each naming a pair of covariate indices $(j, k)$ in $[1, d]$ whose elementwise product $x_{i,j} \cdot x_{i,k}$ enters the propensity model as an additional column. Self-interactions c(j, j) are allowed and yield a quadratic term $x_j^2$. Unordered pairs are canonicalized to c(min(j, k), max(j, k)) and duplicates are silently deduplicated (inspect coefs$assignment_coefs$interactions on the returned object to verify the retained list). The interaction columns enter the propensity model only; the outcome model continues to use the original covariates. Defaults to NULL (no interactions — v1.14.0 behavior is preserved byte-identically). Passing list() (empty list) is treated as equivalent to NULL — no interactions specified, behavior is identical to the v1.14.0 marginal-cohort path within multinomial / ordered DGPs. Errors when assignment_type = "marginal" (the marginal DGP has no propensity model to augment). New in 1.14.1.

Optional non-negative numeric scalar. Scales the Gaussian draws of the interaction coefficients independently of assignment_strength. Defaults to NULL, which means "fall through to assignment_strength". Useful when stress-testing whether the nonlinear-propensity angle alone drives downstream differences (without simultaneously cranking the linear angle). Ignored when assignment_interactions = NULL. New in 1.14.1.

(Optional) Integer. Seed for reproducibility. Three deterministic offsets share this seed: the main coefficient draw uses seed; the assignment coefficients use seed + 1L; the Monte Carlo integration in getTes() uses seed + 2L. NA (or NULL) means "draw from the ambient random-number generator" — no set.seed() is called, so any preceding set.seed() is respected and the result varies across calls.

Logical. If TRUE, emit a message() when assignment_interactions canonicalization removes duplicate or unordered pairs (e.g., when the user passes both c(1, 2) and c(2, 1)). Default FALSE (silent — users can verify the final canonical list via coefs$assignment_coefs$interactions).

Deprecated. The former name for G; still accepted with a deprecation warning, and will be removed in a future release. Use G.

Integer. The number of treated cohorts (treatment is assumed to start in periods 2 to G + 1). Defaults to NULL; supply either G or the deprecated alias R (described below).

Integer. The total number of time periods.

Integer. The number of time-invariant covariates. If d > 0, additional terms corresponding to covariate main effects and interactions are included in beta.

Numeric in (0,1]. The probability that any given entry in the initial coefficient vector theta is nonzero. density = 1 gives a fully dense (non-sparse) coefficient vector.

Numeric. The magnitude used to scale nonzero entries in theta. Each nonzero entry is set to eff_size or -eff_size (with a 60 percent chance for a positive value).

Character. One of "cohort" (default) or "event_study". Selects the inverse fusion transform applied to the treatment-effect block, controlling the basis in which the true treatment effects are sparse. "cohort" is byte-identical to previous behavior; "event_study" fuses effects at the same time since treatment across cohorts. See genCoefs() for details.

(Optional) Integer. Seed for reproducibility. NA (or NULL) means "draw from the ambient random-number generator" — no set.seed() is called.

Deprecated. The former name for G; still accepted with a deprecation warning, and will be removed in a future release. Use G.

An object of class "FETWFE_coefs" containing the coefficient vector and simulation parameters.

An object of class "betwfe".

Unused.

An object of class "etwfe".

Unused.

An object of class "fetwfe".

Unused.

An object of class "twfeCovs".

Unused.

A fitted object from fetwfe(), etwfe(), or betwfe(). (twfeCovs is not currently supported – see GitHub issue #58 for the broader treatment of twfeCovs class methods.)

Character; either "event_study" (default; event-time pooled coefficients from eventStudy()) or "catt" (per-cohort ATTs from result$catt_df).

Logical; if TRUE (default), include confidence interval error bars.

Numeric; overrides the fit's alpha for CI computation. NULL (default) uses the fit's alpha (so 95% CIs when the fit's alpha is 0.05). With the default NULL, both views show the fit's ci_type band (simultaneous by default): the "catt" view reads the bounds stored in catt_df, and the "event_study" view re-derives them via eventStudy() (which inherits the fit's ci_type). Asymmetry under an explicit alpha: for the "event_study" view, the explicit alpha is forwarded to eventStudy(), which re-runs the joint machinery and so still produces a simultaneous band at that alpha (when the fit's ci_type is "simultaneous"); for the "catt" view, an explicit alpha recomputes ci_low / ci_high from ⁠estimate +/- qnorm(1 - alpha/2) * se⁠, i.e. a pointwise band at that alpha (the stored simultaneous bounds are at the fit's alpha and are not re-derived at a new alpha for the catt view). To plot simultaneous catt bands at a different alpha, refit at that alpha or call simultaneousCIs() directly.

Currently unused; reserved for future arguments.

A fitted object from fetwfe(), etwfe(), or betwfe(). (twfeCovs is not currently supported – see GitHub issue #58 for the broader treatment of twfeCovs class methods.)

Character; either "event_study" (default; event-time pooled coefficients from eventStudy()) or "catt" (per-cohort ATTs from result$catt_df).

Logical; if TRUE (default), include confidence interval error bars.

Numeric; overrides the fit's alpha for CI computation. NULL (default) uses the fit's alpha (so 95% CIs when the fit's alpha is 0.05). With the default NULL, both views show the fit's ci_type band (simultaneous by default): the "catt" view reads the bounds stored in catt_df, and the "event_study" view re-derives them via eventStudy() (which inherits the fit's ci_type). Asymmetry under an explicit alpha: for the "event_study" view, the explicit alpha is forwarded to eventStudy(), which re-runs the joint machinery and so still produces a simultaneous band at that alpha (when the fit's ci_type is "simultaneous"); for the "catt" view, an explicit alpha recomputes ci_low / ci_high from ⁠estimate +/- qnorm(1 - alpha/2) * se⁠, i.e. a pointwise band at that alpha (the stored simultaneous bounds are at the fit's alpha and are not re-derived at a new alpha for the catt view). To plot simultaneous catt bands at a different alpha, refit at that alpha or call simultaneousCIs() directly.

Currently unused; reserved for future arguments.

A fitted object from fetwfe(), etwfe(), or betwfe(). (twfeCovs is not currently supported – see GitHub issue #58 for the broader treatment of twfeCovs class methods.)

Character; either "event_study" (default; event-time pooled coefficients from eventStudy()) or "catt" (per-cohort ATTs from result$catt_df).