Using recursive partitioning to account for parameter heterogeneity in multinomial processing tree models

Wickelmaier, Florian; Zeileis, Achim

doi:10.3758/s13428-017-0937-z

Cited by 16 publications

(10 citation statements)

References 40 publications

(57 reference statements)

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“…The papers of Strobl et al (2015) and Komboz et al (2018) also describe an application of model-based trees to detect subpopulations that show measurement invariance. Related approaches were presented for a variety of other models that are commonly used in psychology and related fields, like multinomial processing tree models (Wickelmaier & Zeileis, 2018), several extensions of generalized linear models (Fokkema, Smits, Zeileis, Hothorn, & Kelderman, 2018;Seibold, Hothorn, & Zeileis, 2019) and network models (Jones, Mair, Simon, & Zeileis, 2019).…”

Section: An Overviewmentioning

confidence: 99%

An R Toolbox for Score-Based Measurement Invariance Tests in IRT Models

Schneider¹,

Strobl²,

Zeileis³

et al. 2020

Preprint

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The detection of differential item functioning (DIF) is a central topic in psychometrics and educational measurement. In the past few years, a new family of score-based tests of measurement invariance has been proposed that allows the detection of DIF along arbitrary person covariates in a variety of item response theory (IRT) models. This paper illustrates the application of these tests within the R system for statistical computing, making them accessible to a broad range of users. This presentation also includes IRT models for which these tests have not previously been investigated, such as the generalized partial credit model. The paper has three goals: First, we review the ideas behind score-based tests of measurement invariance. Second, we describe the implementation of these tests within the R system for statistical computing, which is based on the interaction of the R packages mirt, psychotools and strucchange. Third, we illustrate the application of this software and the interpretation of its output in two empirical datasets, and show how to conduct simulation studies, such as IRT-based power analyses, in the context of DIF investigations. The complete R code for reproducing our results is reported in the paper and its appendix.

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Section: An Overviewmentioning

confidence: 99%

An R Toolbox for Score-Based Measurement Invariance Tests in IRT Models

Schneider¹,

Strobl²,

Zeileis³

et al. 2020

Preprint

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“…Unlike semtree, partykit is not limited to a specific model class such as SEMs but provides the infrastructure for general recursive partitioning across various model classes. Among other features, partykit provides the generic MOB algorithm for model-based recursive partitioning that has been used to study heterogeneity in M-estimators (Zeileis et al, 2008), Bradley-Terry models (Strobl et al, 2011), Rasch models (Strobl et al, 2015;Komboz et al, 2018), multinomial processing trees (Wickelmaier and Zeileis, 2018), generalized linear mixed-effects models (Fokkema et al, 2018), network models (Jones et al, 2020), and circular regression models (Lang et al, 2020). Moreover, MOB is also used in more specialized recursive partitioning packages such as psychotree (Zeileis et al, 2020).…”

Section: Introductionmentioning

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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“…Other model-based recursive partitioning methods suggested for general M-estimators (Zeileis et al, 2008), Bradley-Terry models (Strobl, Wickelmaier, & Zeileis, 2011), Rasch models (Strobl, Kopf, & Zeileis, 2015), multinomial processing trees (Wickelmaier & Zeileis, 2018), network models (Jones, Mair, Simon, & Zeileis, 2019), or for circular data (Lang et al, 2020) (Merkle, Fan, & Zeileis, 2014;Merkle & Zeileis, 2013;Wang, Merkle, & Zeileis, 2014;Wang, Strobl, Zeileis, & Merkle, 2018). Score-based tests are computationally lightweight as they do not require the estimation of group-specific SEMs for each split.…”

Section: Introductionmentioning

confidence: 99%

Score-Guided Structural Equation Model Trees

Arnold¹,

Voelkle²,

Brandmaier³

2020

Preprint

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Structural equation model (SEM) trees are data-driven tools for finding covariates that predict group differences in the parameters of an SEM. SEM trees build upon the decision tree paradigm by growing tree structures that divide a data set recursively into homogeneous subsets. Currently, the selection of split variables among covariates involves the calculation of a likelihood ratio for each possible split of each covariate. Obtaining these likelihood ratios is computationally intensive. Moreover, comparing maximum likelihood ratios biases the selection process by favoring covariates with many different values. Several correction procedures for this selection bias have been proposed. Unfortunately, these procedures either reduce statistical power to detect group differences or impose an additional computational burden. As a remedy, we propose to guide the construction of SEM trees by a family of score-based tests instead of using likelihood ratios. These score-based tests monitor fluctuations in the case-wise derivatives of the likelihood function, also called scores, to detect parameter differences between groups. In contrast to the likelihood-ratio approach, score-based tests are computationally efficient because they do not require refitting the model for every possible split, they offer an unbiased selection of covariates, and have high statistical power. In this paper, we introduce score-guided SEM trees and its implementation in the R package semtree and evaluate their performance by means of a Monte Carlo simulation.

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Using recursive partitioning to account for parameter heterogeneity in multinomial processing tree models

Cited by 16 publications

References 40 publications

An R Toolbox for Score-Based Measurement Invariance Tests in IRT Models

An R Toolbox for Score-Based Measurement Invariance Tests in IRT Models

Score-Guided Structural Equation Model Trees

Score-Guided Structural Equation Model Trees

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