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A Newton procedure for conditionally linear mixed-effects models

Abstract

This article reviews Newton procedures for the analysis of mean and covariance structures that may be functions of parameters that enter a model nonlinearly. The kind of model considered is a mixed-effects model that is conditionally linear with regard to its parameters. This means parameters entering the model nonlinearly must be fixed, whereas those entering linearly may vary across individuals. This framework encompasses several models, including hierarchical linear models, linear and nonlinear factor analysis models, and nonlinear latent curve models. A full maximum-likelihood estimation procedure is described. Mx, a statistical software package often used to estimate structural equation models, is considered for estimation of these models. An example with Mx syntax is provided.

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Correspondence to Shelley A. Blozis.

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Blozis, S.A. A Newton procedure for conditionally linear mixed-effects models. Behavior Research Methods 39, 695–708 (2007). https://doi.org/10.3758/BF03192960

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  • DOI: https://doi.org/10.3758/BF03192960

Keywords

  • Gradient Vector
  • Hierarchical Linear Model
  • Reading Score
  • Factor Analysis Model
  • Exponential Growth Model