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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Antedependence models for nonstationary categorical longitudinal data with ignorable missingness: likelihood-based

Yunlong Xie¹, Dale L Zimmerman

¹Biostatistics and Bioinformatics Branch, Division of Epidemiology Statistics and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892, USA. yunlong.xie@nih.gov

Statistics in Medicine

|February 26, 2013

Summary

This study introduces new statistical methods for analyzing categorical longitudinal data using antedependence (AD) models. The developed likelihood-based procedures effectively determine the order of antedependence and assess model fit for complex datasets.

Keywords:

Markov models likelihood ratio test missing data transition models

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Area of Science:

Statistics
Biostatistics
Longitudinal Data Analysis

Background:

Antedependence (AD) models are established for continuous longitudinal data.
Inference for categorical longitudinal data using AD models is underdeveloped.

Purpose of the Study:

To develop likelihood-based inferential procedures for unstructured antedependence models for categorical longitudinal data.
To provide methods for model selection, parameter estimation, and hypothesis testing in these models.

Main Methods:

Derivation of maximum likelihood estimators (MLEs) for model parameters.
Development of penalized likelihood criteria and likelihood ratio tests for determining antedependence order.
Formulation of likelihood ratio tests for homogeneity, time invariance, and strict stationarity.
Implementation of a restricted expectation-maximization algorithm for arbitrary missing data patterns.

Main Results:

Closed-form expressions for MLEs and test statistics are provided for most cases, accommodating empty cells and monotone missing data.
Simulation studies evaluate the performance of the proposed tests.
Application to toenail infection and Alzheimer's disease severity data demonstrates practical utility.

Conclusions:

The developed methods offer robust inference for categorical longitudinal data under antedependence models.
Analysis of real-world data revealed nonstationary behavior and identified optimal model orders, outperforming existing models.
The findings suggest specific autoregressive models for different disease severity data structures.