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Multivariate normal maximum likelihood with both ordinal and continuous variables, and data missing at random.

Joshua N Pritikin1, Timothy R Brick2, Michael C Neale3

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Summary
This summary is machine-generated.

A new method estimates structural equation models (SEM) with mixed ordinal and continuous data using a multivariate probit model. This approach handles missing data and efficiently includes up to 13 ordinal variables.

Keywords:
Continuous latent variablesJoint ordinal continuousMaximum likelihoodMultivariate probitStructural equation modeling

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Structural Equation Models (SEM) are widely used in social sciences.
  • Estimating SEM with mixed indicator types (ordinal and continuous) presents computational challenges.
  • Existing methods often struggle with a large number of ordinal variables.

Purpose of the Study:

  • Introduce a novel maximum likelihood estimation method for SEM with both ordinal and continuous indicators.
  • Address limitations of current methods in handling mixed data types and computational efficiency.
  • Provide an open-source implementation for broader accessibility.

Main Methods:

  • Utilize a flexible multivariate probit model for ordinal indicators within a full information maximum likelihood framework.
  • Employ the axiom of conditional probability to decouple the distributions of continuous and ordinal variables.
  • Implement the method in OpenMx, a free and open-source statistical software package.

Main Results:

  • The novel method provides unbiased estimates for data missing at random.
  • It can accommodate up to 13 ordinal variables with manageable computation times (under 1s per row).
  • Simulation studies confirm the accuracy of the proposed approach and demonstrate the effectiveness of a heuristic for selecting the most efficient computational method.

Conclusions:

  • The developed method offers a robust and computationally efficient solution for estimating SEM with mixed ordinal and continuous indicators.
  • The implementation in OpenMx facilitates its application in research.
  • This advancement expands the capabilities for analyzing complex data structures in various scientific fields.