Growth curve models of repeated binary response

Experimental designs that include repeated measures of binary response variables over time and under different conditions are common in biology. In such settings, it is often desirable to characterize the response pattern over time. When response variables are continuous, this characterization can be made in terms of a growth model such as the Potthoff-Roy growth curve model. We illustrate how a similar growth curve modeling strategy can be implemented using weighted least squares (WLS) methods for binary response data. The growth models are constructed in terms of polynomial functions across marginal response. However, when growth models are fit to repeated binary response, the nonsignificant higher-order polynomial functions are dropped from the model, rather than used as covariates. Dropping the nonsignificant polynomials from the model will reduce the number of response functions, and help avoid small-sample problems that can occur when the number of correlated response functions is large and sample sizes are small. The reduced set of response functions are then modeled using WLS methods. We illustrate such models with an example of binary fly oviposition response (accept or reject) exhibited by two populations of flies at four ages to two types of fruit.