Estimate Heterogeneous Effects in Factorial Experiments Using Grouping and Sparsity

Estimates heterogeneous effects in factorial (and conjoint) models. The methodology employs a Bayesian finite mixture of regularized logistic regressions, where moderators can affect each observation's probability of group membership and a sparsity-inducing prior fuses together levels of each factor while respecting ANOVA-style sum-to-zero constraints. Goplerud, Imai, and Pashley (2024) provide further details.

FactorHet

This package estimates heterogeneous effects in factorial and conjoint experiments. Its details are fully described in Goplerud, Imai, and Pashley (2025): "Estimating Heterogeneous Causal Effects of High-Dimensional Treatments: Application to Conjoint Analysis".

The core method is a Bayesian regularized finite mixture-of-experts where moderators can affect an individual's probability of cluster membership and a sparsity-inducing prior fuses together levels of each factor in each cluster while respecting ANOVA-style sum-to-zero constraints described in Egami and Imai (2019). The posterior mode is found using an AECM algorithm with a number of techniques to accelerate convergence. Approximate quantification of uncertainty is provided by examining the Hessian of the log-posterior. Additional details are explained in the paper and (briefly) in the package documentation.

It can be installed from CRAN or the most-to-update version can be installed using devtools. Note, macOS users may need to ensure that XQuartz is installed; please see information from CRAN (here) for more details.

# CRAN
install.packages("FactorHet")
# Up-to-Date GitHub Version
library(devtools)
devtools::install_github('mgoplerud/FactorHet')

There are two key functions for estimating the model: In most cases, one will prefer to use the FactorHet_mbo function to jointly (i) estimate the amount of regularization by minimizing a criterion such as the BIC using model-based optimization and (ii) estimate the final model. However, if one has a specific value of lambda of interest, one can fit the model for a fixed amount of regularization using FactorHet. A simple example is shown below:

fit_FH <- FactorHet_mbo(
  formula = y ~ factor_1 + factor_2 + factor_1 : factor_2, 
  design = design,
  moderator = ~ moderator_1 + moderator_2)

In the case of repeated observations, the individual is specified via group and the task identifier is specified via task. In the case of a conjoint experiment, the profile identifier (i.e. "left" or "right") is specified via choice_order. An example is shown below:

fit_FH <- FactorHet_mbo(
  formula = y ~ factor_1 + factor_2 + factor_1 : factor_2, 
  design = design, moderator = ~ moderator_1 + moderator_2, 
  group = ~ id, task = ~ task, choice_order = ~ choice_left)

Finally, after fitting the model, there are functions to calculate the Average Marginal Effect (AME) and related concepts (e.g. ACE, AMIE). A simple example is shown below:

AME(fit_FH)

The effects of moderators on cluster membership can be analyzed using two key functions; first, posterior_by_moderators shows the estimated distribution of (posterior) cluster membership probabilities by covariates. Second, margeff_moderators shows the change in the prior cluster membership as one moderator changes, averaging across all other moderators. This is similar to a marginal effect in a multinomial logistic regression. Example code is shown below:

posterior_by_moderators(fit_FH)
margeff_moderators(fit_FH)

Some function names (e.g., AME and margeff_moderators) have been changed for clarity from an older verison of those package. Those functions should still run but will throw a warning and should be updated in existing code.