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.
Highlights
RobitzschA fundamental assumption of parametric modeling is that the model parameters represent all individuals in the sample
We expanded upon earlier research about predicting parameter differences in structural equation modeling (SEM) and demonstrated that individual parameter contribution (IPC) regression can predict parameter differences in linear regression models
IPC regression offers some advantages compared to other procedures for exploring heterogeneity with covariates
Summary
A fundamental assumption of parametric modeling is that the model parameters represent all individuals in the sample. Psych 2021, 3 neither the built-in function lm (for fitting linear regression models) or the functions of the widely used lme package (for fitting mixed models; [6]) allow for ways to explain individual and group differences in the variance parameters in the model with covariates. Other modeling frameworks, such as structural equation modeling (SEM; [7,8]), offer the user more flexibility to incorporate covariates and investigate their effects on all model parameters.
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