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Semiparametric count data regression for self-reported mental health.

Daniel R Kowal1, Bohan Wu1

  • 1Department of Statistics, Rice University, Houston, Texas.

Biometrics
|December 29, 2021
PubMed
Summary

This study introduces a new statistical method, star regression, to accurately analyze self-reported mental health data. This method addresses common data challenges, improving the identification of factors affecting mental well-being.

Keywords:
generalized linear modelhealth dataquestionnaire datatransformation

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Area of Science:

  • Statistics
  • Public Health
  • Psychometrics

Background:

  • Self-reported mental health data, often collected in surveys like the National Health and Nutrition Examination Survey (NHANES), present significant statistical challenges.
  • These challenges include overdispersion, zero-inflation, upper bounds (30 days), and data clustering at specific intervals (e.g., 5 and 7 days).

Purpose of the Study:

  • To develop a robust statistical framework for analyzing count data with complex distributional properties, specifically for self-reported mental health.
  • To introduce a semiparametric estimation and inference method, termed 'star regression', to overcome the limitations of existing models for health questionnaire data.

Main Methods:

  • A novel semiparametric regression framework is proposed, modeling the data-generating process via simultaneous transformation and rounding of a latent Gaussian regression model.
  • The transformation is estimated nonparametrically, while a rounding operator ensures the correct data support.
  • Maximum likelihood estimators are computed using an expectation-maximization (EM) algorithm, compatible with least squares estimable models.

Main Results:

  • The star regression framework incorporates hypothesis testing, confidence intervals, variable selection, and diagnostic tools.
  • Simulation studies confirm the framework's utility and effectiveness.
  • Application of star regression identified key factors associated with self-reported mental health, showing improved goodness-of-fit over traditional count data models.

Conclusions:

  • Star regression offers a superior approach for analyzing challenging count data common in health surveys.
  • This method enhances the identification of factors influencing self-reported mental health, leading to more reliable public health insights.