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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Marginal and Random Intercepts Models for Longitudinal Binary Data With Examples From Criminology.

Jeffrey D Long1, Rolf Loeber, David P Farrington

  • 1University of Minnesota.

Multivariate Behavioral Research
|July 2, 2010
PubMed
Summary
This summary is machine-generated.

This study compares two models for longitudinal binary data: marginal and random intercepts models. Numerical averaging with the random intercepts model approximates group-level insights, similar to the marginal model for criminal offending data.

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Criminal Justice Research

Background:

  • Longitudinal binary data analysis requires appropriate statistical models.
  • Existing models like marginal and random intercepts models offer different perspectives (group vs. individual level).
  • Linear mixed models (LMM) provide a unified framework for continuous data, but not directly for binary data.

Purpose of the Study:

  • To compare the marginal model and the random intercepts model for analyzing longitudinal binary data.
  • To explore how numerical averaging can bridge the gap between individual and group-level inferences in the random intercepts model.
  • To illustrate model-based inferences using real-world criminal offending data.

Main Methods:

  • Utilized two distinct models: the marginal model (via generalized estimating equations) and the random intercepts model (via maximum likelihood).
  • Applied numerical averaging techniques to the random intercepts model to derive group-level information.
  • Analyzed longitudinal criminal offending data (N=506 males, 22-year period) including official records and self-report.

Main Results:

  • The random intercepts model, when combined with numerical averaging, produced prediction curves nearly identical to those from the marginal model.
  • Both models provided valuable, yet distinct, types of information (group-level vs. individual-level heterogeneity).
  • The study demonstrated the practical application of these models in analyzing complex behavioral data.

Conclusions:

  • Numerical averaging offers a viable method to approximate marginal model outputs using random intercepts model parameters.
  • The choice between marginal and random intercepts models depends on the specific research question regarding group-level trends versus individual variability.
  • Understanding the estimation procedures and key features aids in selecting the most appropriate model for empirical analysis of longitudinal binary data.