Staggered Difference-in-Differences with Nonlinear Outcomes.
NonlinearDiD
Staggered Difference-in-Differences with Nonlinear Outcomes — panel and repeated cross-section data
The Problem
The Callaway & Sant'Anna (2021) framework for staggered DiD is hugely influential — but it assumes continuous outcomes with linear parallel trends.
For binary outcomes (employed/not, hospitalized/not, defaulted/not), this creates fundamental problems:
| Problem | Why it matters |
|---|---|
| Scale sensitivity | Parallel trends in P(Y=1) ≠ parallel trends in log-odds. Pre-trends can appear flat or steep depending on the scale. |
| Jensen's inequality | Treatment effects on the probability scale mix the "real" effect with curvature of the CDF. |
| Heterogeneous baseline rates | Units with different baseline probabilities will show "spurious" violations of parallel trends even under no treatment effect. |
NonlinearDiD extends the CS2021 framework to properly handle logit, probit, Poisson, and negative binomial outcome models — for both panel and repeated cross-section data.
What's New in 0.2.0
- Repeated cross-section support — different individuals each period (e.g. BRFSS, NHIS, CPS supplements). Set
data_type = "repeated_cross_section";idnamebecomes optional. - Sampling weights — pass
weightsname = "wt"and the weight is threaded through the outcome regression, propensity score, and pooled QMLE. - Clustered inference — pass
cluster_var = "state"forsandwich::vcovCL()analytical SEs and cluster-resampling bootstrap. - No more compilation — the Rcpp helpers from 0.1.0 are now pure R, so installation is one step on every platform.
- All v0.1.0 functions and arguments preserved — existing scripts using named arguments continue to work unchanged.
Installation
# CRAN
install.packages("NonlinearDiD")
# GitHub (development version)
remotes::install_github("causalfragility-lab/NonlinearDiD")
Quick Start: Panel Data
library(NonlinearDiD)
# 1. Simulate staggered binary panel data
dat <- sim_binary_panel(n = 500, nperiods = 8, n_cohorts = 3,
prop_treated = 0.5, true_att = 0.25, seed = 42)
# 2. Estimate ATT(g,t) with logistic outcome model
res <- nonlinear_attgt(
data = dat,
yname = "y",
tname = "period",
idname = "id",
gname = "g",
xformla = ~ x1 + x2,
outcome_model = "logit",
estimand = "att",
control_group = "nevertreated",
doubly_robust = TRUE
)
# 3. Aggregate into event-study
agg <- nonlinear_aggte(res, type = "dynamic")
plot(agg)
# 4. Pre-treatment parallel trends test
nonlinear_pretest(res)
Quick Start: Repeated Cross-Section Data
library(NonlinearDiD)
# 1. Simulate repeated cross-section binary data
rcs <- sim_binary_rcs(n_per_period = 500, nperiods = 8,
prop_treated = 0.5, true_att = 0.3, seed = 7)
# 2. Estimate ATT(g,t) — note the new data_type argument
res <- nonlinear_attgt(
data = rcs,
yname = "y",
tname = "period",
gname = "g",
outcome_model = "logit",
estimand = "ape",
data_type = "repeated_cross_section",
control_group = "notyetreated"
)
plot(nonlinear_aggte(res, type = "dynamic"))
Survey-Weighted Real-World Example
Repeated cross-section survey data (e.g. CPS Food Security Supplement) with sampling weights and state-level clustering:
res <- nonlinear_attgt(
data = snap_data,
yname = "food_insecure",
tname = "year",
gname = "policy_end_year",
idname = "household_id", # optional — used only as a record ID
data_type = "repeated_cross_section",
outcome_model = "logit",
estimand = "ape",
weightsname = "survey_weight",
cluster_var = "state",
control_group = "notyetreated"
)
summary(res)
nonlinear_aggte(res, type = "dynamic")
Key Functions
| Function | Description |
|---|---|
nonlinear_attgt() | Main engine: estimates ATT(g,t) for all cohort × time cells. Panel and repeated cross-section. |
nonlinear_aggte() | Aggregates ATT(g,t) into event-study, group, calendar, or overall ATT |
nonlinear_pretest() | Tests pre-treatment parallel trends (joint + individual + HonestDiD) |
binary_did_logit() | Simple 2×2 DiD with logistic outcome |
binary_did_probit() | Simple 2×2 DiD with probit outcome |
binary_did_dr() | Doubly-robust binary DiD |
count_did_poisson() | Poisson QMLE DiD for count outcomes (Wooldridge 2023) |
odds_ratio_did() | Odds-ratio DiD estimator |
nonlinear_bounds() | Nonparametric Manski / PT bounds |
sim_binary_panel() | Simulate binary panel data for testing |
sim_binary_rcs() | Simulate binary repeated cross-section data (new in 0.2.0) |
sim_count_panel() | Simulate count panel data for testing |
Estimands
| Estimand | Scale | When to use |
|---|---|---|
"att" | Link scale (log-odds / probit index / log-count) | Compare with linear DiD coefficient |
"ape" | Probability scale | What practitioners usually report |
"odds_ratio" | Multiplicative | Scale-free; natural for 2×2 tables |
Panel vs Repeated Cross-Section
NonlinearDiD supports staggered difference-in-differences designs with nonlinear outcomes for both panel and repeated cross-section data.
Panel data (
data_type = "panel", default): units are followed over time andidnameidentifies repeated observations. Estimation uses within-unit outcome changes following Callaway & Sant'Anna (2021).Repeated cross-section data (
data_type = "repeated_cross_section"): observations are independent within each time period.idnameis optional and may identify survey records or households, but the estimator does not require the same units to appear across periods. Estimation uses pooled quasi-maximum likelihood approaches motivated by Wooldridge (2023), with an optional IPW-augmented doubly-robust variant.
Outcome Models
outcome_model | Parallel Trends Assumption | Outcome Type |
|---|---|---|
"logit" | Parallel in log-odds | Binary (0/1) |
"probit" | Parallel in probit index | Binary (0/1) |
"poisson" | Parallel in log-count | Count (≥ 0) |
"negbin" | Parallel in log-count | Overdispersed count |
"linear" | Parallel in mean (LPM) | Continuous / binary |
References
- Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2), 200–230. https://doi.org/10.1016/j.jeconom.2020.12.001
- Roth, J., & Sant'Anna, P. H. C. (2023). When is parallel trends sensitive to functional form? Econometrica, 91(2), 737–747. https://doi.org/10.3982/ECTA19402
- Wooldridge, J. M. (2023). Simple approaches to nonlinear difference-in-differences with panel data. The Econometrics Journal, 26(3), C31–C66. https://doi.org/10.1093/ectj/utad016
- Sant'Anna, P. H. C., & Zhao, J. (2020). Doubly robust difference-in-differences estimators. Journal of Econometrics, 219(1), 101–122. https://doi.org/10.1016/j.jeconom.2020.06.003
- Manski, C. F. (1990). Nonparametric bounds on treatment effects. American Economic Review, 80(2), 319–323.
Contributing
This package addresses an active research frontier. Contributions, bug reports, and methodological suggestions are welcome — please open an issue or pull request on GitHub.
License
MIT © 2026 Subir Hait.