Package {NonlinearDiD}

Type:	Package
Title:	Staggered Difference-in-Differences with Nonlinear Outcomes
Version:	0.2.0
Description:	Supports staggered difference-in-differences designs with nonlinear outcomes for both panel and repeated cross-section data. Implements estimators for staggered treatment adoption with binary, count, and other nonlinear outcomes, extending Callaway and Sant'Anna (2021) <doi:10.1016/j.jeconom.2020.12.001> to settings with nonlinear outcome models such as logit, probit, and Poisson. For panel data, units are followed over time and 'idname' identifies repeated observations. For repeated cross-section data, observations are independent within each time period; 'idname' is optional and may identify survey records or households, but the estimator does not require the same units to appear across periods. Repeated cross-section estimation includes pooled quasi-maximum likelihood approaches motivated by Wooldridge (2023) <doi:10.1093/ectj/utad016>, with optional weighting and clustered inference. Methods also draw on Roth and Sant'Anna (2023) <doi:10.3982/ECTA19402> and Sant'Anna and Zhao (2020) <doi:10.1016/j.jeconom.2020.06.003>.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.0.0)
Imports:	stats, utils, MASS, sandwich, lmtest, ggplot2
Suggests:	did, dplyr, knitr, rmarkdown, testthat (≥ 3.0.0), covr
Config/testthat/edition:	3
URL:	https://github.com/causalfragility-lab/NonlinearDiD
BugReports:	https://github.com/causalfragility-lab/NonlinearDiD/issues
NeedsCompilation:	no
Packaged:	2026-05-20 14:10:49 UTC; Subir
Author:	Subir Hait [aut, cre]
Maintainer:	Subir Hait <haitsubi@msu.edu>
Repository:	CRAN
Date/Publication:	2026-05-20 14:40:14 UTC

NonlinearDiD: Staggered DiD with Nonlinear Outcomes

Description

NonlinearDiD supports staggered difference-in-differences designs with nonlinear outcomes for both panel and repeated cross-section data.

For panel data, units are followed over time and idname identifies repeated observations. For repeated cross-section data, observations are independent within each time period; idname is optional and may identify survey records or households, but the estimator does not require the same units to appear across periods.

The package extends the Callaway and Sant'Anna (2021) framework to nonlinear outcome models, including binary (logit/probit), count (Poisson/NegBin), and odds-ratio estimands.

The Core Problem

The canonical CS2021 framework assumes parallel trends on the mean scale of a continuous outcome. For binary and count outcomes, this assumption is not scale-invariant: parallel trends in P(Y=1) does NOT imply parallel trends in log-odds, pre-trend tests depend on which scale is used, and treatment effect estimates conflate true effects with Jensen's inequality.

Main Functions

• nonlinear_attgt() – Estimate ATT(g,t) under nonlinear outcome models; supports panel and repeated cross-sections, with optional sampling weights (weightsname) and clustered inference (cluster_var).

• nonlinear_aggte() – Aggregate: event-study, group, calendar, overall.

• nonlinear_pretest() – Pre-treatment parallel trends test.

• binary_did_logit() – 2x2 DiD with logit outcome.

• binary_did_probit() – 2x2 DiD with probit outcome.

• binary_did_dr() – Doubly-robust binary DiD.

• count_did_poisson() – Poisson QMLE DiD for count outcomes.

• odds_ratio_did() – Odds-ratio DiD (scale-free).

• nonlinear_bounds() – Nonparametric Manski / PT bounds.

• sim_binary_panel() – Simulate binary staggered panel data.

• sim_count_panel() – Simulate count staggered panel data.

• sim_binary_rcs() – Simulate binary repeated cross-section data.

Quick Start: Panel

library(NonlinearDiD)
dat <- sim_binary_panel(n = 500, nperiods = 8, seed = 42)
res <- nonlinear_attgt(dat, yname = "y", tname = "period",
                        idname = "id", gname = "g",
                        outcome_model = "logit")
agg <- nonlinear_aggte(res, type = "dynamic")
plot(agg)
nonlinear_pretest(res)

Quick Start: Repeated Cross-Section

library(NonlinearDiD)
rcs <- sim_binary_rcs(n_per_period = 500, nperiods = 8, seed = 7)
res <- nonlinear_attgt(rcs, yname = "y", tname = "period",
                        gname = "g", outcome_model = "logit",
                        data_type = "repeated_cross_section",
                        estimand = "ape",
                        control_group = "notyetreated")
plot(nonlinear_aggte(res, type = "dynamic"))

Survey-Weighted Repeated Cross-Section Example

# Example: CPS-FSS-style data with survey weights and state clustering
# res <- nonlinear_attgt(
#   data          = my_survey_data,
#   yname         = "food_insecure",
#   tname         = "year",
#   gname         = "policy_end_year",
#   idname        = "household_id",
#   data_type     = "repeated_cross_section",
#   outcome_model = "logit",
#   estimand      = "ape",
#   weightsname   = "survey_weight",
#   cluster_var   = "state",
#   control_group = "notyetreated"
# )

Author(s)

Maintainer: Subir Hait haitsubi@msu.edu (ORCID)

References

Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2), 200-230.

Roth, J., & Sant'Anna, P. H. C. (2023). When is parallel trends sensitive to functional form? Econometrica, 91(2), 737-747.

Wooldridge, J. M. (2023). Simple approaches to nonlinear difference-in-differences with panel data. The Econometrics Journal, 26(3).

Sant'Anna, P. H. C., & Zhao, J. (2020). Doubly robust difference-in-differences estimators. Journal of Econometrics, 219(1), 101-122.

See Also

Useful links:

• https://github.com/causalfragility-lab/NonlinearDiD

• Report bugs at https://github.com/causalfragility-lab/NonlinearDiD/issues

Inference for Nonlinear DiD

Description

Internal functions for bootstrap and delta-method standard errors in nonlinear staggered DiD, for both panel and repeated cross-section designs, with optional clustering and sampling weights.

Usage

.bootstrap_inference(
  attgt_df,
  data,
  yname,
  tname,
  idname,
  gname,
  xformla,
  outcome_model,
  estimand,
  control_group,
  doubly_robust,
  nboot,
  boot_type,
  alpha,
  anticipation,
  parallel,
  pl_cores,
  data_type = "panel",
  cluster_var = NULL
)

Doubly-Robust Binary DiD

Description

Doubly-robust estimator for binary outcomes combining a nonlinear outcome regression model with inverse probability weighting via propensity score. Consistent if EITHER the outcome model OR the propensity score is correctly specified.

Usage

binary_did_dr(
  data,
  yname,
  tname,
  idname,
  treat_period,
  control_period,
  dname = NULL,
  gname = NULL,
  xformla = ~1,
  outcome_model = c("logit", "probit"),
  se_type = c("robust", "cluster", "analytical"),
  cluster_var = NULL
)

Arguments

Value

A list of class binary_did_dr.

Examples

dat <- sim_binary_panel(n = 500, nperiods = 4, prop_treated = 0.5)
dat2 <- dat[dat$period %in% c(2, 3), ]
res <- binary_did_dr(dat2, "y", "period", "id", 3, 2, gname = "g",
                      outcome_model = "logit")
print(res)

Binary Outcome DiD: Logit Estimator

Description

Estimates a 2x2 difference-in-differences model with a binary outcome using logistic regression on the log-odds scale, reporting both the log-odds DiD coefficient and the average partial effect (APE) on the probability scale.

Usage

binary_did_logit(
  data,
  yname,
  tname,
  idname,
  treat_period,
  control_period,
  dname = NULL,
  gname = NULL,
  xformla = ~1,
  se_type = c("robust", "cluster", "analytical"),
  cluster_var = NULL
)

Arguments

Value

A list of class binary_did_logit.

Examples

dat <- sim_binary_panel(n = 500, nperiods = 4, prop_treated = 0.5)
dat2 <- dat[dat$period %in% c(2, 3), ]
res <- binary_did_logit(dat2, yname = "y", tname = "period",
                         idname = "id", treat_period = 3,
                         control_period = 2, gname = "g")
print(res)

Binary Outcome DiD: Probit Estimator

Description

Estimates 2x2 DiD with binary outcome using probit regression. Parallel trends assumed on the probit (inverse-normal) scale.

Usage

binary_did_probit(
  data,
  yname,
  tname,
  idname,
  treat_period,
  control_period,
  dname = NULL,
  gname = NULL,
  xformla = ~1,
  se_type = c("robust", "cluster", "analytical"),
  cluster_var = NULL
)

Arguments

Value

A list of class binary_did_probit.

Examples

dat <- sim_binary_panel(n = 500, nperiods = 4, prop_treated = 0.5)
dat2 <- dat[dat$period %in% c(2, 3), ]
res <- binary_did_probit(dat2, "y", "period", "id", 3, 2, gname = "g")
print(res)

Count Outcome DiD: Poisson Estimator

Description

Estimates DiD for count outcomes using a Poisson quasi-maximum likelihood (QMLE) estimator with a log-linear parallel trends assumption. The treatment effect is a multiplicative rate ratio.

Usage

count_did_poisson(
  data,
  yname,
  tname,
  idname,
  treat_period,
  control_period,
  dname = NULL,
  gname = NULL,
  xformla = ~1,
  offset = NULL,
  se_type = c("robust", "cluster", "analytical"),
  cluster_var = NULL
)

Arguments

Value

A list of class count_did_poisson.

Examples

dat <- sim_count_panel(n = 400, nperiods = 6, prop_treated = 0.4)
dat2 <- dat[dat$period %in% c(2, 4), ]
res <- count_did_poisson(dat2, "y", "period", "id", 4, 2, gname = "g")
print(res)

Aggregate ATT(g,t) Estimates for Nonlinear DiD

Description

Aggregates the group-time average treatment effects from nonlinear_attgt into interpretable summary parameters. Provides event-study (dynamic), group-level, calendar-time, and overall ATT aggregations - each appropriate for nonlinear settings.

Usage

nonlinear_aggte(
  obj,
  type = c("dynamic", "group", "calendar", "simple"),
  na.rm = TRUE,
  min_periods = 1L,
  weights = c("equal", "sample")
)

Arguments

Value

An object of class nonlinear_aggte with slots:

agg

Data frame with aggregated ATT, SE, and CI.

type

The aggregation type used.

overall_att

Scalar overall ATT estimate.

overall_se

SE for overall ATT.

Examples

set.seed(1)
dat  <- sim_binary_panel(n = 400, nperiods = 8, prop_treated = 0.5)
res  <- nonlinear_attgt(dat, yname = "y", tname = "period",
                         idname = "id", gname = "g",
                         outcome_model = "logit")
agg  <- nonlinear_aggte(res, type = "dynamic")
plot(agg)

Nonlinear Staggered DiD: Group-Time ATT Estimation

Description

Computes group-time average treatment effects on the treated (ATT(g,t)) for staggered difference-in-differences designs with nonlinear outcomes. Supports both panel data (same units across periods) and repeated cross-section (RCS) data (independent samples per period).

For panel data the package follows Callaway & Sant'Anna (2021) and uses within-unit outcome changes to estimate counterfactual trends. For repeated cross-sections it uses the Wooldridge (2023) pooled QMLE with a treatment-by-period interaction (non-DR) or an IPW-augmented version (doubly-robust). Both modes optionally accept sampling weights and a clustering variable.

Usage

nonlinear_attgt(
  data,
  yname,
  tname,
  gname,
  idname = NULL,
  data_type = c("panel", "repeated_cross_section"),
  weightsname = NULL,
  cluster_var = NULL,
  xformla = ~1,
  outcome_model = c("logit", "probit", "poisson", "negbin", "linear"),
  estimand = c("att", "ape", "odds_ratio"),
  control_group = c("nevertreated", "notyetreated"),
  doubly_robust = TRUE,
  boot = FALSE,
  nboot = 999,
  boot_type = c("multiplier", "empirical"),
  alpha = 0.05,
  parallel = FALSE,
  pl_cores = 2L,
  anticipation = 0L
)

Arguments

Value

An object of class nonlinear_attgt.

References

Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2), 200-230.

Wooldridge, J. M. (2023). Simple approaches to nonlinear difference-in-differences with panel data. The Econometrics Journal, 26(3).

Roth, J., & Sant'Anna, P. H. C. (2023). When is parallel trends sensitive to functional form? Econometrica, 91(2), 737-747.

Sant'Anna, P. H. C., & Zhao, J. (2020). Doubly robust difference-in-differences estimators. Journal of Econometrics, 219(1), 101-122.

Examples

# ---- Panel example (v0.1.0 syntax — unchanged) ----
set.seed(42)
dat <- sim_binary_panel(n = 500, nperiods = 6, prop_treated = 0.4)
result <- nonlinear_attgt(
  data = dat, yname = "y", tname = "period",
  idname = "id", gname = "g",
  outcome_model = "logit"
)
summary(result)

# ---- Repeated cross-section example ----
set.seed(7)
rcs <- sim_binary_rcs(n_per_period = 400, nperiods = 6, prop_treated = 0.4)
res_rcs <- nonlinear_attgt(
  data = rcs, yname = "y", tname = "period", gname = "g",
  outcome_model = "logit",
  data_type = "repeated_cross_section"
)
summary(res_rcs)

Nonparametric Bounds for Binary Outcomes in Staggered DiD

Description

Computes sharp nonparametric bounds on the ATT for binary outcomes in staggered difference-in-differences designs, following the partial identification approach. These bounds require NO functional form assumptions on the outcome model - only an assumption about the direction or magnitude of selection.

The key insight for binary outcomes: Since Y is binary (0 or 1), the ATT is bounded by: - Lower bound: counterfactual never exceeds observed (pessimistic) - Upper bound: counterfactual never falls below observed (optimistic)

Under a Manski-style no-assumptions bound, plus refinements using the parallel trends assumption as a restriction.

Usage

nonlinear_bounds(
  data,
  yname,
  tname,
  idname,
  gname,
  xformla = ~1,
  control_group = c("nevertreated", "notyetreated"),
  bound_type = c("pt_only", "manski", "pt_monotone"),
  alpha = 0.05
)

Arguments

Value

A data frame of sharp bounds (lb, ub) for ATT(g,t), with bootstrap confidence intervals.

References

Manski, C. F. (1990). Nonparametric bounds on treatment effects. *American Economic Review*, 80(2), 319-323.

Callaway, B. (2021). Bounds on distributional treatment effect parameters. *Journal of Econometrics*, 222(2), 1084-1111.

Examples

set.seed(5)
dat    <- sim_binary_panel(n = 300, nperiods = 6)
bounds <- nonlinear_bounds(dat, "y", "period", "id", "g")
print(bounds)

Pre-Treatment Parallel Trends Test for Nonlinear DiD

Description

Tests for pre-treatment violations of the parallel trends assumption in nonlinear staggered DiD settings. This is fundamentally different from the linear case because:

1. **Scale dependence**: Parallel trends on the probability scale does NOT imply parallel trends on the latent index scale (and vice versa). Tests are performed on the scale specified in 'outcome_model'.

2. **Roth-Sant'Anna sensitivity**: Computes sensitivity of post-treatment estimates to violations of magnitude delta in pre-period, following Roth & Sant'Anna (2023).

3. **Joint test**: Provides a joint chi-squared test of all pre-period ATT(g,t) = 0, accounting for correlation across (g,t) cells.

Usage

nonlinear_pretest(
  obj,
  plot = TRUE,
  alpha = 0.05,
  type = c("joint", "individual", "honestdid")
)

Arguments

Value

A list with:

pretest_results

Data frame of pre-period ATT(g,t) with p-values.

joint_stat

Joint test statistic.

joint_pval

P-value for joint test.

conclusion

Interpretive conclusion string.

References

Roth, J. (2022). Pretest with caution: Event-study estimates after testing for parallel trends. *American Economic Review: Insights*, 4(3), 305-322.

Roth, J., & Sant'Anna, P. H. C. (2023). When is parallel trends sensitive to functional form? *Econometrica*, 91(2), 737-747.

Examples

set.seed(99)
dat <- sim_binary_panel(n = 600, nperiods = 8, prop_treated = 0.5)
res <- nonlinear_attgt(dat, "y", "period", "id", "g",
                        outcome_model = "logit")
pt  <- nonlinear_pretest(res)
print(pt)

S3 Methods for NonlinearDiD Objects

Description

Print, summary, and plot methods for nonlinear_attgt and nonlinear_aggte objects.

Odds-Ratio DiD for Binary Outcomes

Description

Estimates the odds-ratio difference-in-differences (OR-DiD) for binary outcomes. OR-DiD equals 1 under no treatment effect and is invariant to which group is labelled treatment.

Usage

odds_ratio_did(
  data,
  yname,
  tname,
  idname,
  treat_period,
  control_period,
  dname = NULL,
  gname = NULL,
  xformla = ~1
)

Arguments

Value

A list of class odds_ratio_did.

Examples

dat <- sim_binary_panel(n = 500, nperiods = 4, prop_treated = 0.5)
dat2 <- dat[dat$period %in% c(2, 3), ]
res <- odds_ratio_did(dat2, "y", "period", "id", 3, 2, gname = "g")
print(res)

Plot Aggregated DiD Estimates

Description

Plots event-study, group-level, calendar, or overall aggregated ATT estimates from nonlinear_aggte.

Usage

## S3 method for class 'nonlinear_aggte'
plot(x, ...)

Arguments

Value

A ggplot2 object.

Plot ATT(g,t) Estimates

Description

Produces a faceted scatter plot of ATT(g,t) estimates with confidence intervals, one panel per treatment cohort.

Usage

## S3 method for class 'nonlinear_attgt'
plot(x, ..., alpha = 0.05, point_size = 2)

Arguments

Value

A ggplot2 object.

Simulate Binary Panel Data with Staggered Treatment

Description

Generates a simulated panel dataset with staggered treatment adoption and a binary outcome. Useful for testing and illustrating nonlinear DiD methods.

The data-generating process is:

Y_{it} = \mathbf{1}\{ \alpha_i + \lambda_t + \delta_{it} \cdot D_{it} + \epsilon_{it} > 0 \}

where \alpha_i is a unit fixed effect, \lambda_t is a time fixed effect, \delta_{it} is the treatment effect (heterogeneous across cohorts), and \epsilon_{it} is logistic noise.

Usage

sim_binary_panel(
  n = 500L,
  nperiods = 6L,
  prop_treated = 0.5,
  n_cohorts = 3L,
  true_att = 0.3,
  base_prob = 0.3,
  unit_fe_sd = 0.5,
  add_covariates = TRUE,
  seed = NULL
)

Arguments

Value

A data frame in long format. Columns: id (unit identifier), period (time period 1 to nperiods), y (binary outcome 0/1), g (treatment cohort; 0 = never treated), D (treatment indicator), x1 and x2 (covariates, if add_covariates = TRUE), and alpha_i (true unit fixed effect, for validation).

Examples

dat <- sim_binary_panel(n = 1000, nperiods = 8, prop_treated = 0.6,
                         n_cohorts = 4, true_att = c(0.2, 0.4, 0.3, 0.5))
head(dat)
table(dat$g)

Simulate Binary Repeated Cross-Section Data with Staggered Treatment

Description

Generates a simulated repeated cross-section (RCS) dataset with staggered treatment adoption and a binary outcome. At each time period an independent random sample is drawn from the population; no unit is observed more than once. This mirrors settings such as repeated population health surveys (e.g. BRFSS, NHIS) or administrative records linked by group membership rather than individual identifiers.

The data-generating process at period t for individual i belonging to treatment cohort g:

Y_{it} = \mathbf{1}\{ \mu_0 + \lambda_t + \delta_g \cdot D_{gt} + \beta x_{1i} + \epsilon_{it} > 0 \}

where \mu_0 = \text{logit}(\text{base\_prob}), \lambda_t is a common time trend, \delta_g is the cohort-specific treatment effect (on the log-odds scale), and \epsilon_{it} \sim \text{Logistic}(0,1) is i.i.d. noise. No unit-level fixed effect is included because individuals are not re-observed.

Usage

sim_binary_rcs(
  n_per_period = 500L,
  nperiods = 6L,
  prop_treated = 0.5,
  n_cohorts = 3L,
  true_att = 0.3,
  base_prob = 0.3,
  add_covariates = TRUE,
  seed = NULL
)

Arguments

Details

There is no id column that repeats across periods. Use nonlinear_attgt(..., data_type = "repeated_cross_section") to analyse data of this type.

Value

A data frame in long format. One row per observation. Columns:

obs_id

Unique observation identifier.

period

Time period (1 to nperiods).

y

Binary outcome (0/1).

g

Treatment cohort of the observation's group (0 = never treated).

D

Treatment indicator: 1 if the group is treated in this period.

x1, x2

Individual-level covariates (if add_covariates = TRUE).

Examples

dat <- sim_binary_rcs(n_per_period = 500, nperiods = 6,
                       prop_treated = 0.5, true_att = 0.3, seed = 42)
head(dat)
table(dat$g, dat$period)  # each cell is an independent sample

# Estimate ATT(g,t) under repeated cross-section design

res <- nonlinear_attgt(
  data = dat, yname = "y", tname = "period", gname = "g",
  outcome_model = "logit", data_type = "repeated_cross_section"
)
summary(res)

Simulate Count Panel Data with Staggered Treatment

Description

Generates simulated panel data with a count outcome (Poisson-distributed) and staggered treatment adoption. Treatment effect is multiplicative (rate ratio) on the count scale.

Usage

sim_count_panel(
  n = 500L,
  nperiods = 6L,
  prop_treated = 0.5,
  n_cohorts = 3L,
  true_rr = 1.5,
  base_rate = 5,
  overdispersion = FALSE,
  seed = NULL
)

Arguments

Value

Long-format data frame with columns: id, period, y, g, D, x1.

Examples

dat <- sim_count_panel(n = 400, nperiods = 6, true_rr = 1.8)
summary(dat$y)