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

Maria T Barendse1,2, Yves Rosseel3

  • 1Oral Public Health Department, Academic Centre for Dentistry, Amsterdam, Netherlands.

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Summary
This summary is machine-generated.

Pairwise maximum likelihood (PML) estimation accurately estimates complex multilevel models with discrete data. This method shows good performance for random intercept and slope structural equation models, even with many latent variables.

Keywords:
discrete datamultilevel modelspairwise maximum likelihoodrandom slopes

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Area of Science:

  • Statistics
  • Psychometrics
  • Econometrics

Background:

  • Multilevel models account for clustered data, where units within a cluster are more similar than those from different clusters.
  • Discrete response variables are common in many fields, posing unique challenges for statistical modeling.
  • Pairwise maximum likelihood (PML) estimation offers a potential solution for complex multilevel models with discrete outcomes.

Purpose of the Study:

  • To investigate the accuracy and efficiency of Pairwise maximum likelihood (PML) estimation for computationally intensive multilevel random intercept and random slope structural equation models (SEM) with discrete data.
  • To extend the 'wide format' (WF) approach for SEM to accommodate random slopes in multilevel models.
  • To evaluate the performance of PML under varying conditions, including sample size, response scale, and model complexity.

Main Methods:

  • A simulation study was conducted to assess the Pairwise maximum likelihood (PML) estimation method.
  • The study manipulated sample size (250, 500, 1000, 2000), response scales (two-point, four-point), and data-generating models (mediation and factor models with varying numbers of random slopes).
  • The 'wide format' (WF) approach for SEM was reconsidered and extended to include random slopes.

Main Results:

  • Pairwise maximum likelihood (PML) estimation demonstrated satisfactory accuracy and efficiency for estimating complex multilevel random intercept and random slope SEMs with discrete data and numerous latent variables (six or more).
  • The method performed well across various sample sizes and model types.
  • A slight increase in bias was observed under conditions with a small number of clusters (250) and a dichotomous (two-point) response scale.

Conclusions:

  • Pairwise maximum likelihood (PML) estimation is a viable and effective method for analyzing computationally demanding multilevel structural equation models with discrete outcomes.
  • The findings support the use of PML for complex models, particularly when dealing with many latent variables.
  • Researchers should be mindful of potential bias when using PML with very small sample sizes and dichotomous response scales.