Abstract
Researchers often collect proportion data that cannot be interpreted as arising from a set of Bernoulli trials. Analyses based on the beta distribution may be appropriate for such data. The SAS® GLIMMIX procedure provides a tool for these analyses using a likelihood based approach in the context of generalized linear mixed models. Since the t and F-distribution based inference employed in this approach relies on asymptotic properties, it is important to understand the sample sizes required to obtain reasonable approximate answers to inference questions. In addition, the complexity of the likelihood functions can lead to numerical issues for optimization algorithms that may or may not be related to sample size issues. This simulation study is based on a simple intercept-only model for known beta distributed responses. Convergence and estimation issues are investigated over a range of beta distributions and sample sizes.
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Recommended Citation
Thompson, Kevin and Gbur, Edward
(2013).
"A SIMULATION STUDY OF THE SMALL SAMPLE PROPERTIES OF LIKELIHOOD BASED INFERENCE FOR THE BETA DISTRIBUTION,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1019
A SIMULATION STUDY OF THE SMALL SAMPLE PROPERTIES OF LIKELIHOOD BASED INFERENCE FOR THE BETA DISTRIBUTION
Researchers often collect proportion data that cannot be interpreted as arising from a set of Bernoulli trials. Analyses based on the beta distribution may be appropriate for such data. The SAS® GLIMMIX procedure provides a tool for these analyses using a likelihood based approach in the context of generalized linear mixed models. Since the t and F-distribution based inference employed in this approach relies on asymptotic properties, it is important to understand the sample sizes required to obtain reasonable approximate answers to inference questions. In addition, the complexity of the likelihood functions can lead to numerical issues for optimization algorithms that may or may not be related to sample size issues. This simulation study is based on a simple intercept-only model for known beta distributed responses. Convergence and estimation issues are investigated over a range of beta distributions and sample sizes.
