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The standard linear models approach (ANOVA) is inappropriate for binary response data since
Bernoulli random variables have heteroscedastic errors and the mean response is typically nonlinear.
Generally, binary response data is modeled with a linear logistic regression model, and
this approach works well for a completely randomized design (CRD). However, the standard
logistic regression model is inappropriate for designs having randomization restrictions, such as
randomized complete block designs (RCBD), latin square design and split-plot designs.
Generalized linear mixed models (GLMMs), such as the logistic/normal model, have been used
for analyzing binary data collected under a randomized complete block design (matched pairs
design), but do not seem to be used for more complex design structures. So, where does this
leave the researcher? The purpose of this talk is to provide some insight into the analysis of
binary response data for a variety of experimental designs.
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