Accommodating Missing Data in Mixture Models for Classification by Opinion-Changing Behavior

Abstract

Popular theories in political science regarding opinion-changing behavior postulate the existence of one or both of two broad categories of people: those with stable opinions over time; and those who appear to hold no solid opinion and, when asked to make a choice, do so seemingly at random. The model presented here explores evidence for a third category: durable changers. People in this group will change their opinions in a rational, informed manner, after being exposed to new information. Survey data collected at four time points over nearly two years track Swiss citizens' readiness to support pollution-reduction policies. We analyzed the data using finite mixture models that allow estimation of the percentage in the poluation falling in each category for each question as well as the frequency of certain types of relevant behaviors within each category. These models extend the finite mixture model structure used in Hill and Kriesi (2001a,b) to accommodate missing response data. This extension increases the sample size by nearly 60% and weakens the missing-data assumptions required. We describe augmented models and fitting algorithms corresponding to different assumptions about the missing-data mechanism as well as the differences in results obtained.