arXiv subjects

Max Goplerud

Publications and source records attributed to Max Goplerud.

7 recordsLinked to original sources

arXiv2026

Disentangling Causal Mechanisms in Conjoint Experiments Using Mediation

Conjoint experiments provide an attractive way to assess the role of multiple attributes simultaneously on decision-making. However, the randomization of multiple attributes prevents understanding the causal mechanisms that, critically, depend on the relationship between attributes -- e.g., how one attribute affects the respondent's belief as to another attribute. This is because conjoint experiments recover controlled effects whereas a substantively important estimand may be the total or indirect effect of one attribute. Unfortunately, existing experimental designs for conjoint experiments cannot estimate these effects. We provide an alternative framework that requires one additional, simple experiment to learn the relationship between attributes among respondents alongside the standard assumptions for causal mediation. Estimation of the relevant effects can be done in a doubly robust fashion using machine learning methods. We illustrate this by conducting a pre-registered experiment on candidate choice and disentangle the effect of different attributes by understanding their mediation through the candidate's party.

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arXiv2025

Multivariate MRP

Measuring public opinion at subnational geographies is critical to many theories in political science. Multilevel regression and post-stratification (MRP) is a popular tool for doing so, although existing work is limited to measuring opinion on a single survey question. We provide a framework for estimating the joint distribution of opinion on multiple questions ("Multivariate MRP"). To do so, we derive a novel method for variational inference in multinomial logistic regression with many random effects. This requires performing variational inference with high-dimensional fixed effects, but we show that this can be done at a low computational cost. We validate this procedure by estimating public opinion by party in the United States and show that existing methods can be improved considerably by adding contextual covariates on the prior levels of party identification. Substantively, we show how the output of multivariate MRP can be used to study representation across multiple policy issues simultaneously.

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arXiv2023

Partially factorized variational inference for high-dimensional mixed models

While generalized linear mixed models are a fundamental tool in applied statistics, many specifications, such as those involving categorical factors with many levels or interaction terms, can be computationally challenging to estimate due to the need to compute or approximate high-dimensional integrals. Variational inference is a popular way to perform such computations, especially in the Bayesian context. However, naive use of such methods can provide unreliable uncertainty quantification. We show that this is indeed the case for mixed models, proving that standard mean-field variational inference dramatically underestimates posterior uncertainty in high-dimensions. We then show how appropriately relaxing the mean-field assumption leads to methods whose uncertainty quantification does not deteriorate in high-dimensions, and whose total computational cost scales linearly with the number of parameters and observations. Our theoretical and numerical results focus on mixed models with Gaussian or binomial likelihoods, and rely on connections to random graph theory to obtain sharp high-dimensional asymptotic analysis. We also provide generic results, which are of independent interest, relating the accuracy of variational inference to the convergence rate of the corresponding coordinate ascent algorithm that is used to find it. Our proposed methodology is implemented in the R package, see https://github.com/mgoplerud/vglmer . Numerical results with simulated and real data examples illustrate the favourable computation cost versus accuracy trade-off of our approach compared to various alternatives.

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arXiv2023

Generalized Kernel Regularized Least Squares

Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing approaches are inflexible and do not allow KRLS to be combined with theoretically-motivated extensions such as random effects, unregularized fixed effects, or non-Gaussian outcomes. Second, estimation is extremely computationally intensive for even modestly sized datasets. Our paper addresses both concerns by introducing generalized KRLS (gKRLS). We note that KRLS can be re-formulated as a hierarchical model thereby allowing easy inference and modular model construction where KRLS can be used alongside random effects, splines, and unregularized fixed effects. Computationally, we also implement random sketching to dramatically accelerate estimation while incurring a limited penalty in estimation quality. We demonstrate that gKRLS can be fit on datasets with tens of thousands of observations in under one minute. Further, state-of-the-art techniques that require fitting the model over a dozen times (e.g. meta-learners) can be estimated quickly.

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arXiv2022

Estimating Heterogeneous Causal Effects of High-Dimensional Treatments: Application to Conjoint Analysis

Estimation of heterogeneous treatment effects is an active area of research. Most of the existing methods, however, focus on estimating the conditional average treatment effects of a single, binary treatment given a set of pre-treatment covariates. In this paper, we propose a method to estimate the heterogeneous causal effects of high-dimensional treatments, which poses unique challenges in terms of estimation and interpretation. The proposed approach finds maximally heterogeneous groups and uses a Bayesian mixture of regularized logistic regressions to identify groups of units who exhibit similar patterns of treatment effects. By directly modeling group membership with covariates, the proposed methodology allows one to explore the unit characteristics that are associated with different patterns of treatment effects. Our motivating application is conjoint analysis, which is a popular type of survey experiment in social science and marketing research and is based on a high-dimensional factorial design. We apply the proposed methodology to the conjoint data, where survey respondents are asked to select one of two immigrant profiles with randomly selected attributes. We find that a group of respondents with a relatively high degree of prejudice appears to discriminate against immigrants from non-European countries like Iraq. An open-source software package is available for implementing the proposed methodology.

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arXiv2021

Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference

Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to scalable and accurate inference. First, I derive a new mean-field variational algorithm for estimating binomial logistic hierarchical models with an arbitrary number of non-nested random effects. Second, I propose "marginally augmented variational Bayes" (MAVB) that further improves the initial approximation through a step of Bayesian post-processing. I prove that MAVB provides a guaranteed improvement in the approximation quality at low computational cost and induces dependencies that were assumed away by the initial factorization assumptions. I apply these techniques to a study of voter behavior using a high-dimensional application of the popular approach of multilevel regression and post-stratification (MRP). Existing estimation took hours whereas the algorithms proposed run in minutes. The posterior means are well-recovered even under strong factorization assumptions. Applying MAVB further improves the approximation by partially correcting the under-estimated variance. The proposed methodology is implemented in an open source software package.

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arXiv2021

Modelling Heterogeneity Using Bayesian Structured Sparsity

How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to draw reliable inferences. This paper allows a common way of simplifying complex phenomenon (placing observations with similar effects into discrete groups) to be integrated into regression analysis. The framework allows researchers to (i) use their prior knowledge to guide which groups are permissible and (ii) appropriately quantify uncertainty. The paper does this by extending work on "structured sparsity" from a traditional penalized likelihood approach to a Bayesian one by deriving new theoretical results and inferential techniques. It shows that this method outperforms state-of-the-art methods for estimating heterogeneous effects when the underlying heterogeneity is grouped and more effectively identifies groups of observations with different effects in observational data.

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