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2 results

  • Maximum Likelihood Estimation of Multilevel Structural Equation Models with Random Slopes for Latent Covariates

  • Nicholas J. Rockwood
  • Journal:
    Psychometrika / Volume 85 / Issue 2 / June 2020
    Published online by Cambridge University Press:
    01 January 2025, pp. 275-300

  • A maximum likelihood estimation routine for two-level structural equation models with random slopes for latent covariates is presented. Because the likelihood function does not typically have a closed-form solution, numerical integration over the random effects is required. The routine relies upon a method proposed by du Toit and Cudeck (Psychometrika 74(1):65–82, 2009) for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically, reducing the computational burden of high-dimensional numerical integration. The method is demonstrated and assessed using a small-scale simulation study and an empirical example.

Article has an altmetric score of 2
Article has an altmetric score of 2

  • 12 - Repeated Measures Designs

  • Gerry P. Quinn, Deakin University, Victoria, Michael J. Keough, University of Melbourne
  • Book:
    Experimental Design and Data Analysis for Biologists
    Published online:
    04 September 2023
    Print publication:
    07 September 2023, pp 242-256

  • Summary

    Making repeated observations through time adds complications, but it’s a common way to deal with limited research resources and reduce the use of experimental animals. A consequence of this design is that observations fall into clusters, often corresponding to individual organisms or “subjects.” We need to incorporate these relationships into statistical models and consider the additional complication where observations closer together in time may be more similar than those further apart. These designs were traditionally analyzed with repeated measures ANOVA, fitted by OLS. We illustrate this traditional approach but recommend the alternative linear mixed models approach. Mixed models offer better ways to deal with correlations within the data by specifying the clusters as random effects and modeling the correlations explicitly. When the repeated measures form a sequence (e.g. time), mixed models also offer a way to deal with occasional missing observations without omitting the whole subject from the model.