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Multilevel SEM with random slopes in discrete data using the pairwise maximum likelihood

Maria T. Barendse and Yves Rosseel (UGent)
(2023) BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY. 76(2). p.327-352
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Abstract
Pairwise maximum likelihood (PML) estimation is a promising method for multilevel models with discrete responses. Multilevel models take into account that units within a cluster tend to be more alike than units from different clusters. The pairwise likelihood is then obtained as the product of bivariate likelihoods for all within-cluster pairs of units and items. In this study, we investigate the PML estimation method with computationally intensive multilevel random intercept and random slope structural equation models (SEM) in discrete data. In pursuing this, we first reconsidered the general 'wide format' (WF) approach for SEM models and then extend the WF approach with random slopes. In a small simulation study we the determine accuracy and efficiency of the PML estimation method by varying the sample size (250, 500, 1000, 2000), response scales (two-point, four-point), and data-generating model (mediation model with three random slopes, factor model with one and two random slopes). Overall, results show that the PML estimation method is capable of estimating computationally intensive random intercept and random slopes multilevel models in the SEM framework with discrete data and many (six or more) latent variables with satisfactory accuracy and efficiency. However, the condition with 250 clusters combined with a two-point response scale shows more bias.
Keywords
discrete data, multilevel models, pairwise maximum likelihood, random slopes, STRUCTURAL EQUATION MODELS, LINEAR-MODELS, GROWTH-CURVES, VARIABLES

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MLA
Barendse, Maria T., and Yves Rosseel. “Multilevel SEM with Random Slopes in Discrete Data Using the Pairwise Maximum Likelihood.” BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY, vol. 76, no. 2, 2023, pp. 327–52, doi:10.1111/bmsp.12294.
APA
Barendse, M. T., & Rosseel, Y. (2023). Multilevel SEM with random slopes in discrete data using the pairwise maximum likelihood. BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY, 76(2), 327–352. https://doi.org/10.1111/bmsp.12294
Chicago author-date
Barendse, Maria T., and Yves Rosseel. 2023. “Multilevel SEM with Random Slopes in Discrete Data Using the Pairwise Maximum Likelihood.” BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY 76 (2): 327–52. https://doi.org/10.1111/bmsp.12294.
Chicago author-date (all authors)
Barendse, Maria T., and Yves Rosseel. 2023. “Multilevel SEM with Random Slopes in Discrete Data Using the Pairwise Maximum Likelihood.” BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY 76 (2): 327–352. doi:10.1111/bmsp.12294.
Vancouver
1.
Barendse MT, Rosseel Y. Multilevel SEM with random slopes in discrete data using the pairwise maximum likelihood. BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY. 2023;76(2):327–52.
IEEE
[1]
M. T. Barendse and Y. Rosseel, “Multilevel SEM with random slopes in discrete data using the pairwise maximum likelihood,” BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY, vol. 76, no. 2, pp. 327–352, 2023.
@article{01HMVEFTQ57P1NBCA7R2DSPC4G,
  abstract     = {{Pairwise maximum likelihood (PML) estimation is a promising method for multilevel models with discrete responses. Multilevel models take into account that units within a cluster tend to be more alike than units from different clusters. The pairwise likelihood is then obtained as the product of bivariate likelihoods for all within-cluster pairs of units and items. In this study, we investigate the PML estimation method with computationally intensive multilevel random intercept and random slope structural equation models (SEM) in discrete data. In pursuing this, we first reconsidered the general 'wide format' (WF) approach for SEM models and then extend the WF approach with random slopes. In a small simulation study we the determine accuracy and efficiency of the PML estimation method by varying the sample size (250, 500, 1000, 2000), response scales (two-point, four-point), and data-generating model (mediation model with three random slopes, factor model with one and two random slopes). Overall, results show that the PML estimation method is capable of estimating computationally intensive random intercept and random slopes multilevel models in the SEM framework with discrete data and many (six or more) latent variables with satisfactory accuracy and efficiency. However, the condition with 250 clusters combined with a two-point response scale shows more bias.}},
  author       = {{Barendse, Maria T. and Rosseel, Yves}},
  issn         = {{0007-1102}},
  journal      = {{BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY}},
  keywords     = {{discrete data,multilevel models,pairwise maximum likelihood,random slopes,STRUCTURAL EQUATION MODELS,LINEAR-MODELS,GROWTH-CURVES,VARIABLES}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{327--352}},
  title        = {{Multilevel SEM with random slopes in discrete data using the pairwise maximum likelihood}},
  url          = {{http://doi.org/10.1111/bmsp.12294}},
  volume       = {{76}},
  year         = {{2023}},
}
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