Causal Effect Analysis in Nonrandomized Data With Latent Variables and Categorical Indicators: The Implementation and Benefits of EffectLiteR

Translational Abstract When assessing psychological constructs, like competencies, preferences, personality attributes, and so forth, measurement error typically occurs in the observed scores. Latent variable models can control for the measurement error, but do not provide estimates of the person's true scores on the latent construct. Thus, for using the latent variables in subsequent analysis, the analysis method has to be combined somehow with the latent variable model. One option is the implementation of two-step procedures that obtain score estimates from latent variable models, which are then used as manifest variables in the analysis model. Yet, score estimates are not always error-free. As an alternative the R package EffectLiteR directly incorporates latent variable models for estimating various covariate adjusted effects in nonrandomized group comparisons. We extend this approach for latent covariates and latent outcome variables that are modeled in the tradition of item response theory with categorical indicators. For implementing the complex models (i.e., a moderated regression with latent variables that is implemented as a multidimensional multigroup structural equation model for ordered categorical indicators), we describe the EffectLiteR syntax and the model specification through a graphical user interface. In addition, we regard the benefit of latent variables for causal effect estimation in comparison to using score estimates (i.e., individual score estimates or plausible values). For this we review the assumptions of the different analysis strategies and present a hands-on example with large scale assessment data. Instead of using manifest proxies for a latent outcome or latent covariates in a causal effect analysis, the R package EffectLiteR facilitates a direct integration of latent variables based on structural equation models (SEM). The corresponding framework considers latent interactions and provides various effect estimates for evaluating the differential effectiveness of treatments. In addition, a user-friendly graphical interface customizes the implementation of the complex models. We aim to enable applications of EffectLiteR in more contexts, and therefore generalize the framework for incorporating latent variables measured with categorical indicators. This refers, for instance, to achievement tests in educational large-scale assessments (LSAs), which are typically constructed in the tradition of item response theory (IRT). We review different modeling strategies for incorporating latent variables from IRT models in an effect analysis (i.e., individual score estimates, plausible values, SEM for categorical indicators). The strategies differ in the handling of measurement error and, thus, have different implications for the accuracy and efficiency of causal effect estimates. We describe our extensions of EffectLiteR based on SEM for categorical indicators and illustrate the model specification step-by-step. In addition, we present a hands-on example, where we apply EffectLiteR in LSA data. The practical benefit of using latent variables in comparison to proficiency scores is of special interest in the application and discussion.