Extra-binominal variation in logistic multilevel models

Abstract

"The objective of this study was to investigate the effects of Sample size and model misspecification on estimating the level 1 variance for binary responses. The Small simulation study Shows that: (1) in small samples, estimates around 0.8 can appear although the model is correctly specified under the binomial assumption, and (2) estimates dose to 1.0 do not allow us to conclude correct model specification. Estimating the level 1 variance in logistic multilevel models cannot be treated as a simple indication to test the assumed binomial distribution. In large sample sizes, the estimate is usually dose to 1.0, but it cannot be used as an assessment of the distribution by statistical testing. Model mis-specification leads to "itnproved" estimates, because overdispersion reduces the downward bias. The estimation procedure PQL2 gives downwardly biased results, so that "too close" estimates are rather an indication of an incorrect model. A variance larger than 1.0 emerges only when duster effects are neglected. Then, at least, overdispersion can be used to detect model mis-specifications. A further analysis of more complex models including more predictors, varying the level 2 variance and several random effects is necessary, to be sure if underdispersion is always found under a given binomial distribution." (Author's abstract, IAB-Doku) ((en))

Cite article

Jacob, M. (2000): Extra-binominal variation in logistic multilevel models. A simulation. In: Multilevel modelling newsletter, Vol. 12, No. 1, p. 8-14.