A Simulation Study Using a Mixed Model Framework to Analyze the Impact of Sample Size and Variability on Type I Error
Xiaoxue Gu
Johnson & Johnson, 29B Technology Dr, Irvine, CA 92618, United States.
Curt Doetkott
Information Technology, North Dakota State University, Fargo, North Dakota, 58108, USA.
Rhonda Magel *
Department of Statistics, North Dakota State University, Fargo, North Dakota, 58108, USA.
*Author to whom correspondence should be addressed.
Abstract
Aims: This simulation study was conducted to check the validity of a MIXED model’s statistical inference when violating the underlying assumptions – normality of random errors when there are unbalanced group sizes and inequality of variance of errors [Scheffe, 1959].
Study Design: Monte Carlo Simulation Study.
Place and Duration of Study: North Dakota State University 2020-2021.
Methodology: Repeated measures designs (or longitudinal studies) are commonly seen in many research fields, especially in pharmaceutical clinical trials, agricultural research, and psychology. PROC MIXED (SAS Inc.) is a well-known standard tool for analyzing repeated measures data nowadays. The MIXED procedure is based on the standard linear MIXED model, which estimates parameters by maximizing the restricted likelihood. The usual assumption for a standard linear MIXED model is normality. However, the character of data in the real world may be non- smoothed, or non-symmetric, or having heavy tails. We estimate the Type I error rates in different combinations of settings and compare them with the stated Type I error.
Conclusion: The main results in this study show us that the MIXED model is reasonably robust to modest violations of the normal distribution. However, when a small sample size associated with a treatment was combined with the effects of that treatment having a large variance, a severe inflation problem on Type I error rates could occur when using the MIXED model procedure. When the Type I errors were found to be inflated, the Group= option was found to often help with this problem. A Sub-Sampling procedure was also found to help with this problem.
Keywords: Repeated measures, covariance structures, behrens-fischer problem, unbalanced group sizes, non-normal distributions