A case study on cumulative logit models with low frequency and mixed effects

Abstract

Data with ordinal responses may be encountered in many research fields, such as social, medical, agriculture or financial sciences. In this paper, we present a case study on cumulative logit models with low frequency and mixed effects and discuss some strengths and limitations of the current methodology. Two plant pathologists requested our statistical advice to fit a cumulative logit mixed model seeking for the effect of six commercial products on the control of a seed and seedling disease in soybeans in vitro. In their attempt to estimate the model parameters using a generalized linear mixed model approach with PROC GLIMMIX, the model failed to converge. Three alternative approaches to solve the problem were examined: 1) stratifying the data searching for the random effect; 2) assuming the random effect would be small and reducing the model to a fixed model; and 3) combining the original categories of the response variable to a lower number of categories. In addition, we conducted a power analysis to evaluate the required sample size to detect treatment differences. The results of all the proposed solutions were similar. Collapsing categories for a cumulative/proportional odds model has little effect on estimation. The sample size used in the case study is enough to detect a large shift of frequencies between categories, but not for moderated changes. Moreover, we do not have enough information to estimate a random effect. Even when it is present, the results regarding the fixed factors: pathogen, evaluation day, and treatment effects are the same as the obtained by the fixed model alternatives. All six products had a significant effect in slowing the effect of the pathogen, but the effects vary between pathogen species and assessment timing or date.