Identifying Heterogeneity in Dynamic Panel Models with Individual Parameter Contribution Regression

Arnold, Manuel; Oberski, Daniel L.; Brandmaier, Andreas M.; Voelkle, Manuel C.

doi:10.1080/10705511.2019.1667240

Cited by 8 publications

(13 citation statements)

References 46 publications

(42 reference statements)

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“…Another disadvantage of SEM trees is that they provide only sparse information about how a parameter changes with respect to a covariate. Recently, Arnold et al (2019) suggested a framework called individual parameter contribution regression that allows modeling SEM parameter estimates as a linear function of covariates.…”

Section: Discussionmentioning

confidence: 99%

Score-Guided Structural Equation Model Trees

2021

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Structural equation model (SEM) trees are data-driven tools for finding variables that predict group differences in SEM parameters. SEM trees build upon the decision tree paradigm by growing tree structures that divide a data set recursively into homogeneous subsets. In past research, SEM trees have been estimated predominantly with the R package semtree. The original algorithm in the semtree package selects split variables among covariates by calculating a likelihood ratio for each possible split of each covariate. Obtaining these likelihood ratios is computationally demanding. As a remedy, we propose to guide the construction of SEM trees by a family of score-based tests that have recently been popularized in psychometrics (Merkle and Zeileis, 2013; Merkle et al., 2014). These score-based tests monitor fluctuations in case-wise derivatives of the likelihood function to detect parameter differences between groups. Compared to the likelihood-ratio approach, score-based tests are computationally efficient because they do not require refitting the model for every possible split. In this paper, we introduce score-guided SEM trees, implement them in semtree, and evaluate their performance by means of a Monte Carlo simulation.

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Section: Discussionmentioning

confidence: 99%

Score-Guided Structural Equation Model Trees

2021

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“…In the following, we will first derive the IPCs in very general terms and then give more specific results for linear regression models. Further derivations for SEMs are provided by Arnold et al [12]. Readers uninterested in technical details may skip this section.…”

Section: Derivation and Properties Of Individual Parameter Contributionsmentioning

confidence: 99%

“…These insights also apply to other model classes. Generally speaking, the bias of the IPCs increases with the amount of heterogeneity in the data [12]. In homogeneous samples, the IPCs are guaranteed to be unbiased.…”

Section: Calculation Of the Individual Parameter Contributionsmentioning

confidence: 99%

“…Arnold et al [12] suggested a correction procedure termed iterated IPC regression that removes bias in the IPCs in a stepwise fashion. Iterated IPC regression proceeds as follows: first, the model is fitted, and standard IPC regression is performed.…”

Section: Bias Correction Proceduresmentioning

confidence: 99%

“…As an alternative procedure to exploring the effects of covariates by adding them to the model, we introduced individual parameter contribution (IPC) regression [11,12]. IPC regression allows determining whether and how the parameters of a model vary as functions of covariates.…”

Section: Introductionmentioning

confidence: 99%

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

Arnold

Brandmaier

Voelkle

2021

Psych

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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.

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An Illustration of Local Structural Equation Modeling for Longitudinal Data: Examining Differences in Competence Development in Secondary Schools

Olaru

Robitzsch

Hildebrandt

et al. 2023

Methodology of Educational Measurement and Assessment

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In this chapter, we discuss how a combination of longitudinal modeling and local structural equation modeling (LSEM) can be used to study how students’ context influence their growth in educational achievement. LSEM is a nonparametric approach that allows for the moderation of a structural equation model over a continuous variable (e.g., socio-economic status; cultural identity; age). Thus, it does not require the categorization of continuous moderators as applied in multi-group approaches. In contrast to regression-based approaches, it does not impose a particular functional form (e.g., linear) on the mean-level differences and can spot differences in the variance-covariance structure. LSEM can be used to detect nonlinear moderation effects, to examine sources of measurement invariance violations, and to study moderation effects on all parameters in the model. We showcase how LSEM can be implemented with longitudinal of the National Educational Panel Study (NEPS) using the R-package sirt. In more detail, we examine the effect of parental education on math and reading competence in secondary school across three measurement occasions, comparing LSEM to regression based approaches and multi-group confirmatory factor analysis. Results provide further evidence of the strong influence of the educational background of the family. This chapter offers a new approach to study inter-individual differences in educational development.

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Identifying Heterogeneity in Dynamic Panel Models with Individual Parameter Contribution Regression

Cited by 8 publications

References 46 publications

Score-Guided Structural Equation Model Trees

Score-Guided Structural Equation Model Trees

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

An Illustration of Local Structural Equation Modeling for Longitudinal Data: Examining Differences in Competence Development in Secondary Schools

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