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Robust Bayesian growth curve modelling using conditional medians.

Xin Tong¹, Tonghao Zhang¹, Jianhui Zhou¹

¹University of Virginia, Charlottesville, Virginia, USA.

The British Journal of Mathematical and Statistical Psychology

|September 14, 2020

Summary

This summary is machine-generated.

This study introduces a robust growth curve model using conditional medians for analyzing non-normal longitudinal data. The new Bayesian approach offers more accurate parameter estimates, especially with outliers, improving social and behavioral science research.

Keywords:

asymmetric Laplace distribution conditional medians growth curve modelling robust methods

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Area of Science:

Social and Behavioral Sciences
Statistics

Background:

Growth curve models are standard for longitudinal data analysis.
Normality assumptions in traditional models are often violated in real-world data.
Non-normality can lead to inaccurate estimations and flawed statistical inferences.

Purpose of the Study:

To develop a robust growth curve modeling approach for non-normal longitudinal data.
To enhance the reliability of statistical inference in the presence of outliers and leverage observations.
To provide a more accurate and efficient estimation method compared to traditional approaches.

Main Methods:

Utilized conditional medians, which are less sensitive to extreme values.
Employed Bayesian methods for model estimation and inference.
Leveraged asymmetric Laplace distributions to transform median estimation into a maximum likelihood problem.

Main Results:

Monte Carlo simulations demonstrated superior performance of the proposed method.
The robust approach yielded more accurate and efficient parameter estimates.
The method proved effective even with data containing outliers or leverage points.

Conclusions:

The proposed robust growth curve model effectively handles non-normal longitudinal data.
This Bayesian approach using conditional medians offers a reliable alternative to traditional methods.
The method was successfully applied to real-world data from the Virginia Cognitive Aging Project.