library(endoSwitch)
data("ImpactData", package = "endoSwitch")
d <- as.data.frame(ImpactData)
d$Output <- log10(d$Output) # optional log transformation
adopt <- "CA" # adoption (0/1)
yvar <- "Output" # outcome
instr <- c("Distance_to_market", "Association") # instruments
sel_cov <- unique(c("Age", "Education", "Farm_size", "Access_to_credit",
"Perception", instr)) # instruments added to selection
out_cov <- c("Age", "Education", "Farm_size", "Fertilizer_ha", "Access_to_credit")
d <- na.omit(d[, unique(c(adopt, yvar, sel_cov, out_cov))])
Computational Provenance & Reproducibility Record Endogenous Switching Regression · 1.0.0 · DOI 10.5281/zenodo.23114309
This Computational Provenance Record documents the statistical computing environment, software dependencies, computational provenance, and bibliographic references associated with the RAISINS Endogenous Switching Regression module. It is intended to support computational reproducibility and software transparency. Detailed statistical methodology, mathematical derivations, and user guidance are provided separately in the official module documentation.
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1 Module Metadata
| Parameter | Specification |
|---|---|
| Module | Endogenous Switching Regression |
| Module Version | 1.0.0 |
| DOI | 10.5281/zenodo.23114309 |
| Document Type | Computational workflow |
| Statistical Engine | R |
| R Version | 4.5.2 |
| Reproducibility | Execution Environment: Posit Connect · GCR · renv-locked |
2 Statistical Dependency Manifest
| Package | Version | Repository | Core Statistical Functions |
|---|---|---|---|
| endoSwitch | 1.0.0 |
GitHub (cbw1243/endoSwitch@d572d57) |
endoSwitch2Stage(), endoSwitch(), summary.endoSwitch(), treatmentEffect() |
| maxLik | 1.5-2.2 |
CRAN | maxLik(method = "BFGS"), the optimiser called by endoSwitch() |
| msm | 1.8.2 |
CRAN | deltamethod(), standard errors of the back-transformed σ and ρ |
| data.table | 1.18.6.1 |
CRAN | as.data.table(), the data structure required by endoSwitch |
| ivreg | 0.6-8 |
CRAN | ivreg(), summary(diagnostics = TRUE) |
| car | 3.1-5 |
CRAN | vif(), leveneTest() |
| stats | 4.5.2 |
Base R | glm(), lm(), logLik(), pchisq(), pnorm(), dnorm(), qnorm(), t.test(), prop.test(), shapiro.test() |
3 Statistical Function Registry
| Analytical Role | Primary Function(s) |
|---|---|
| Instrument falsification test | stats::glm(family = binomial("probit")), stats::lm() on non-adopters |
| Endogeneity test (weak instruments, Wu-Hausman, Sargan) | ivreg::ivreg() + summary(diagnostics = TRUE) |
| Adopter vs non-adopter characteristics | stats::prop.test(), car::leveneTest(center = median), stats::t.test() |
| Multicollinearity | car::vif() on stats::lm() of adoption on all covariates |
| Two-stage estimation (probit + OLS with inverse Mills ratio) | endoSwitch::endoSwitch2Stage() |
| Probit average marginal effects | stats::pnorm(), stats::dnorm(), stats::vcov(); delta-method standard errors |
| Full information maximum likelihood | endoSwitch::endoSwitch() → maxLik::maxLik() |
| σ and ρ with standard errors | endoSwitch:::calcPar() → msm::deltamethod() |
| LR test of independent equations | stats::logLik(), stats::pchisq(df = 2) |
| Treatment effects (ATT, ATU, heterogeneity) | summary(fit)$treatmentEffect; household-level values from endoSwitch:::treatmentEffect(treatEffect = FALSE) |
| Residual normality | stats::shapiro.test() on the second-stage OLS residuals |
4 Default Methods & Parameters
| Analysis | Step / Parameter | Default Method / Value |
|---|---|---|
| Model Specification |
Adoption variable | Binary, coded 0 (did not adopt) / 1 (adopted); both values must be present |
| Instrument(s) | Chosen separately; added automatically to the selection equation and never to the outcome equation (exclusion restriction) | |
| Covariates | Selection equation = selection covariates + instruments; outcome equation = outcome covariates, identical in both regimes | |
| Text covariates | Trimmed, converted to upper case and expanded into 0/1 dummy columns with model.matrix(); the first category is the reference |
|
| Sample | Files with a completely blank row or column are rejected before analysis; remaining rows with a missing value in any selected column are dropped (stats::na.omit() inside endoSwitch()). A warning is shown below 200 complete observations, because two-step estimates become unstable in small samples (Bascle, 2008) |
|
| Transformation | Log transform (optional, off by default) | Base-10 log transformation of the selected numeric columns, used to reduce skewness so that effects on the outcome can be read as percentage changes. Columns with any zero or negative value are first shifted so that their smallest value becomes 1. All later steps use the transformed values |
| Pre-estimation Tests |
Falsification test | An instrument is valid when it is significant (p < 0.05) in the adoption probit on all selection covariates, and not significant (p ≥ 0.05) in the OLS of the outcome for non-adopters on all instruments jointly plus the outcome covariates (Di Falco, Veronesi & Yesuf, 2011) |
| Endogeneity test | IV regression of the outcome on adoption + outcome covariates, adoption instrumented by the instruments. Reports the weak-instrument F-test, the Wu-Hausman test and the Sargan test (Sargan requires two or more instruments) | |
| Group differences | 0/1 variables: two-sample test of proportions (prop.test(), continuity-corrected; reported as "Chi-square test"). Continuous variables: Student's t-test if the median-centred Levene's test gives p ≥ 0.05, otherwise Welch's t-test |
|
| Multicollinearity | VIF from an OLS of adoption on all selection and outcome covariates; < 5 acceptable, 5–10 moderate, ≥ 10 high. Perfectly collinear (aliased) covariates stop the analysis | |
| Two-Stage Estimation |
First stage | Probit (binomial(link = "probit")) of adoption on the selection covariates |
| Second stage | Separate OLS regressions of the outcome for adopters and for non-adopters on the outcome covariates. Each regression also includes a selection-correction term (the inverse Mills ratio) from the first-stage probit, which captures unobserved factors that affect both the decision to adopt and the outcome. The OLS standard errors are not adjusted for the fact that this term is itself an estimate | |
| Marginal effects | Average marginal effects of the probit, which express each coefficient as a change in the probability of adoption. For a continuous variable, this is the average effect of a one-unit increase. For a 0/1 variable, it is the average change in probability when the variable switches from 0 to 1. Standard errors use the delta method | |
| Full MLE | Optimiser | maxLik() with method = "BFGS" (package default), unweighted (Weight = NA); return code 0 = converged |
| Starting values | The coefficients, error standard deviations (σ) and correlations (ρ) from the two-stage estimation (endoSwitch2Stage()) are used as starting values. A negative two-stage error variance is replaced by 0.1 |
|
| σ and ρ | σ is the standard deviation of the outcome-equation error in each regime. ρ is the correlation between the adoption-equation error and each outcome-equation error, and its sign shows the direction of self-selection. Both are estimated on an unrestricted scale, which keeps σ positive and ρ between −1 and 1, and are then converted back. Standard errors use the delta method | |
| LR test | Likelihood-ratio test of whether the adoption and outcome equations are independent, i.e. whether both correlations are zero. It compares the full ESR model with separate probit and OLS models fitted to the same observations, using a chi-square test with 2 degrees of freedom. p < 0.05 is reported as selection bias present | |
| Treatment Effects |
Conditional expectations | Four expected outcomes are predicted for every household from the full MLE estimates: adopters' actual outcome, adopters' counterfactual outcome had they not adopted, non-adopters' actual outcome, and non-adopters' counterfactual outcome had they adopted. Each prediction combines the household's own characteristics, the coefficients of the relevant regime and a selection-correction term (Lokshin & Sajaia, 2004) |
| ATT, ATU | ATT is the average difference between adopters' actual and counterfactual outcomes, i.e. the gain adopters obtained from adopting. ATU is the same average difference for non-adopters, i.e. the gain they would have obtained had they adopted. Standard errors come from a paired t-test of the two sets of household-level predictions | |
| Heterogeneity | Base heterogeneity (Y1 and Y0 columns) shows whether adopters and non-adopters differ systematically in outcome under the same adoption status, i.e. whether adopters are inherently better or worse off. Transitional heterogeneity shows whether adoption benefits adopters more or less than it would benefit non-adopters. Standard errors come from Welch two-sample t-tests. Values in parentheses under Y1 / Y0 are standard deviations of the household-level predictions |
5 R Code for Key Analytical Steps
The code blocks below demonstrate the computation behind each reported result using the ImpactData dataset supplied with the endoSwitch package (adoption of conservation agriculture by 408 farm households in Zambia).
5.1 Data and Model Specification
5.2 Instrument Falsification and Endogeneity Tests
# relevance: instruments in the adoption probit (valid if p < 0.05)
f1 <- glm(reformulate(sel_cov, adopt), family = binomial("probit"), data = d)
coef(summary(f1))[instr, ]
# exclusion: instruments in the outcome OLS of non-adopters (valid if p >= 0.05)
f2 <- lm(reformulate(c(instr, out_cov), yvar), data = d[d[[adopt]] == 0, ])
coef(summary(f2))[instr, ]
# IV diagnostics: weak instruments, Wu-Hausman, Sargan
iv <- ivreg::ivreg(as.formula(paste(yvar, "~", paste(c(adopt, out_cov), collapse = " + "), "|",
paste(c(instr, out_cov), collapse = " + "))), data = d)
summary(iv, diagnostics = TRUE)$diagnostics5.3 Group Differences and Multicollinearity
grp <- factor(d[[adopt]] == 1)
x <- d$Age # continuous variable
eq <- car::leveneTest(x ~ grp, center = median)$`Pr(>F)`[1] >= 0.05
t.test(x[grp == "TRUE"], x[grp == "FALSE"], var.equal = eq) # Student's or Welch's
b <- d$Access_to_credit # 0/1 variable
prop.test(c(sum(b[grp == "TRUE"]), sum(b[grp == "FALSE"])),
c(sum(grp == "TRUE"), sum(grp == "FALSE")))
car::vif(lm(reformulate(unique(c(sel_cov, out_cov)), adopt), data = d))5.4 Two-Stage Estimation and Marginal Effects
ts <- endoSwitch2Stage(d, yvar, adopt, out_cov, sel_cov)
summary(ts$FirstStageReg) # probit selection equation
summary(ts$SecondStageReg.0) # non-adopters + Mills ratio
summary(ts$SecondStageReg.1) # adopters + Mills ratio
ts$distParEst # sigma0, sigma1, rho0, rho1
# average marginal effect of a continuous regressor, delta-method SE
X <- model.matrix(ts$FirstStageReg); b <- coef(ts$FirstStageReg); V <- vcov(ts$FirstStageReg)
xb <- as.vector(X %*% b); k <- "Farm_size"
me <- mean(dnorm(xb)) * b[[k]]
grad <- -b[[k]] * colMeans(xb * dnorm(xb) * X); grad[k] <- grad[k] + mean(dnorm(xb))
c(me = me, se = sqrt(as.numeric(t(grad) %*% V %*% grad)))5.5 Full Information Maximum Likelihood and LR Test
fit <- endoSwitch(d, yvar, adopt, out_cov, sel_cov, Weight = NA, treatEffect = TRUE)
s <- summary(fit)
s$estimate # Select.*, Outcome.0.*, Outcome.1.*, Sigma, Rho
c(s$maxinType, s$loglik, s$returnCode) # BFGS; return code 0 = converged
ll_ind <- as.numeric(logLik(f1) +
logLik(lm(reformulate(out_cov, yvar), data = d[d[[adopt]] == 0, ])) +
logLik(lm(reformulate(out_cov, yvar), data = d[d[[adopt]] == 1, ])))
lr <- 2 * (s$loglik - ll_ind)
pchisq(lr, df = 2, lower.tail = FALSE) # H0: rho0 = rho1 = 05.6 Treatment Effects and Residual Normality
s$treatmentEffect # ATT, ATU, heterogeneity
hp <- endoSwitch:::treatmentEffect(fit$MLE.Results, data.table::as.data.table(d),
yvar, adopt, out_cov, sel_cov, FALSE)
mean(hp$EYA1$EY1.A1 - hp$EYA1$EY0.A1) # ATT
mean(hp$EYA0$EY1.A0 - hp$EYA0$EY0.A0) # ATU
t.test(hp$EYA1$EY1.A1, hp$EYA1$EY0.A1, paired = TRUE)$stderr # SE of ATT
shapiro.test(residuals(ts$SecondStageReg.0)) # non-adopters
shapiro.test(residuals(ts$SecondStageReg.1)) # adoptersExplore the entire Endogenous Switching Regression module in preview mode using our demo datasets. To submit suggestions or report a workflow issue, please use the discussion section below, or visit the official RAISINS website.
6 RAISINS Native Statistical Framework
RAISINS uses R for all its statistical computations. Every package used to generate major results is listed and demonstrated with examples, so results can be reproduced independently. These results are then organized and formatted on the RAISINS website along with visualisation to make them easier to use and interpret. RAISINS also has its own custom-built statistical tools for managing workflows, validating results, and generating reports. Details of these are not fully covered here, they’re shared with outside researchers only on request, and are subject to licensing terms.
7 Package References
R Core Team. (2025). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/
Chen, B., Yun, S., & Gramig, B. (n.d.). endoSwitch: Endogenous Switching Regression Models (R package version 1.0.0, GitHub commit d572d57). https://github.com/cbw1243/endoSwitch
Henningsen, A., & Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3), 443-458. https://doi.org/10.1007/s00180-010-0217-1
Jackson, C. H. (2011). Multi-State Models for Panel Data: The msm Package for R. Journal of Statistical Software, 38(8), 1-29. https://doi.org/10.18637/jss.v038.i08
Barrett, T., Dowle, M., Srinivasan, A., Gorecki, J., Chirico, M., Hocking, T., Schwendinger, B., & Krylov, I. (2025). data.table: Extension of ‘data.frame’ (R package version 1.18.6.1). https://doi.org/10.32614/CRAN.package.data.table
Fox, J., Kleiber, C., & Zeileis, A. (2025). ivreg: Instrumental-Variables Regression by ‘2SLS’, ‘2SM’, or ‘2SMM’, with Diagnostics (R package version 0.6-8). https://doi.org/10.32614/CRAN.package.ivreg
Fox, J., & Weisberg, S. (2019). An R Companion to Applied Regression (3rd ed.). Sage, Thousand Oaks, CA. https://www.john-fox.ca/Companion/
Heckman, J. J. (1979). Sample Selection Bias as a Specification Error. Econometrica, 47(1), 153-161. https://doi.org/10.2307/1912352
Lokshin, M., & Sajaia, Z. (2004). Maximum likelihood estimation of endogenous switching regression models. The Stata Journal, 4(3), 282-289. https://doi.org/10.1177/1536867X0400400306
Di Falco, S., Veronesi, M., & Yesuf, M. (2011). Does Adaptation to Climate Change Provide Food Security? A Micro-Perspective from Ethiopia. American Journal of Agricultural Economics, 93(3), 829-846. https://doi.org/10.1093/ajae/aar006
Bascle, G. (2008). Controlling for endogeneity with instrumental variables in strategic management research. Strategic Organization, 6(3), 285-327. https://doi.org/10.1177/1476127008094339
Allaire, J. J., Xie, Y., Dervieux, C., McPherson, J., Luraschi, J., Ushey, K., Atkins, A., Wickham, H., Cheng, J., Chang, W., & Iannone, R. (2025). rmarkdown: Dynamic Documents for R (R package version 2.30). https://github.com/rstudio/rmarkdown