Analyzing Data from a Split-Plot Experiment When the Observations Have Overdispersed Poisson Distributions

• Activity Number: 127
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Jia Liu*+ and Philip Michael Dixon
• Companies: Iowa State University and Iowa State University
• Keywords: overdipersed Poisson distribution ; split-plot ; generalized linear mixed model

Abstract

Counts of weeds in agricultural fields often follow overdispersed Poisson distributions with moderate to large overdispersion. We consider the split-plot experiments with two factors and two sizes of experimental units. Such data can be analyzed by log transforming the counts then assuming normal distributions for the random effects, or using a generalized linear mixed model assuming an overdispersed Poisson distribution with an additional normally distributed random component. We find the split-plot analysis of transformed data has empirical rejection rates close to the nominal 5% rate for all tests. The overdispersed Poisson model gives conservative tests of the main plot effects and very liberal tests of the split plot main and interaction effects. When the overdispersion is moderate, the empirical rejection rate can exceed 60% for a nominal 5% test.