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Fast estimation of generalized linear latent variable models for performance and process data with ordinal,

Maoxin Zhang1, Björn Andersson1,2, Shaobo Jin3

  • 1Center for Educational Measurement, University of Oslo, Oslo, Norway.

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|February 12, 2024
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Summary

This study introduces an efficient method for analyzing mixed data types in psychological and educational measurements. The second-order Laplace approximation improves convergence and parameter accuracy for ordinal, continuous, and count data.

Keywords:
Laplace approximationestimation efficiencyhigh dimensionalitymixed data types

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Psychological and educational assessments generate diverse data types (e.g., response times, counts).
  • Modeling these mixed data types, including complex dependencies, requires specialized statistical approaches.
  • Generalized linear latent variable models (GLLVMs) can handle mixed data but face computational challenges during estimation.

Purpose of the Study:

  • To develop an efficient estimation method for simultaneously modeling ordinal, continuous, and count data within GLLVMs.
  • To extend existing Laplace approximation methods for joint modeling of mixed data types.
  • To evaluate the performance of the proposed method through simulations and empirical examples.

Main Methods:

  • Derivation of an estimation method using first- or second-order Laplace approximations for joint modeling of ordinal, continuous, and count data.
  • Application of the method to analyze mixed data from computer-based assessments.
  • Conducting simulation studies to assess estimation efficiency, convergence rates, and parameter recovery.

Main Results:

  • The second-order Laplace approximation demonstrated superior convergence rates and parameter accuracy compared to the first-order approximation.
  • The proposed method provides fast and accurate parameter estimates for complex GLLVMs.
  • Models incorporating stimulus-level dependencies significantly improved empirical data fit.

Conclusions:

  • The developed Laplace approximation method offers an efficient solution for joint modeling of mixed data types in psychological and educational research.
  • Second-order Laplace approximation is recommended for its balance of accuracy and computational efficiency.
  • Accounting for variable dependencies within stimuli enhances model performance and data interpretation.