Models for Counts and Particle Size Distributions of Subvisible Particle Data

Abstract

Traditional statistical analyses of subvisible particle data are usually based on either descriptive statistics, normal-based methods, or standard Poisson models. These methods often do not adequately describe the counts or particle size distribution. They usually ignore relevant information represented in the data, such as count correlation. Therefore, any meaningful analyses of subvisible particle data require a reasonable representation of counts and particle size distribution and the correlation in the data. Such comprehensive approaches are not widely available or used when analyzing subvisible particle data. In this article, we propose the use of generalized linear mixed models to analyze the counts and the particle size distribution of subvisible particle data. These models make optimal use of the information in the data and allow flexible approaches for the analyses of a wide range of data structures. They are readily accessible to practitioners through the use of modern statistical software. These models are demonstrated with two numerical examples using two different data structures.

Keywords: Generalized linear mixed models; Ordinal logistic regression with normal random effects models; Overdispersion; Poisson regression with normal random effects.