Predicting Differences in Model Parameters with Individual Parameter Contribution Regression Using the R Package ipcr

Abstract

Unmodeled differences between individuals or groups can bias parameter estimates and may lead to false-positive or false-negative findings. Such instances of heterogeneity can often be detected and predicted with additional covariates. However, predicting differences with covariates can be challenging or even infeasible, depending on the modeling framework and type of parameter. Here, we demonstrate how the individual parameter contribution (IPC) regression framework, as implemented in the R package ipcr, can be leveraged to predict differences in any parameter across a wide range of parametric models. First and foremost, IPC regression is an exploratory analysis technique to determine if and how the parameters of a fitted model vary as a linear function of covariates. After introducing the theoretical foundation of IPC regression, we use an empirical data set to demonstrate how parameter differences in a structural equation model can be predicted with the ipcr package. Then, we analyze the performance of IPC regression in comparison to alternative methods for modeling parameter heterogeneity in a Monte Carlo simulation.

Politics speak louder than skills: Political similarity effects in hireability judgments in multiparty contexts and the role of political interest.

“…To assess the influence of control variables (age, gender, prior selection experience), we conducted individual parameter contribution regression analyses. That is, an SEM parameter was regressed on a covariate, after which one can test whether the magnitude of the parameter is predicted by a control variable (Arnold et al, 2021). Control variables had no substantial influence (see Supplemental Material 06).…”

Editorial of the Psych Special Issue “Computational Aspects, Statistical Algorithms and Software in Psychometrics”

“…The article of Arnold et al [8] investigates parameter heterogeneity with respect to covariates in structural equation models. The authors demonstrate how the individual parameter contribution regression framework could be used to predict differences in any parameter of a structural equation model.…”

“…The authors demonstrate how the individual parameter contribution regression framework could be used to predict differences in any parameter of a structural equation model. Arnold et al [8] implement the individual parameter regression framework in the R package ipcr. Furthermore, they compare the performance of individual parameter regression with alternative methods for dealing with parameter heterogeneity (e.g., regularization methods, structural equation models with interaction effects) in a simulation study.…”

Estimating Local Structural Equation Models

“…A tutorial on how to apply MNFA using the R package OpenMx ( Boker et al 2011 ) was given by Kolbe et al ( 2022 ). LSEM also bears a similarity to the approach of individual parameter change ( Oberski 2013 ; Arnold et al ( 2020 , 2021 ). Variation in SEM model parameters can also be tested with score-based invariance tests ( Huth et al 2022 ; Merkle and Zeileis 2013 ; Wang et al 2014 ).…”