Beta prime regression with application to risky behavior frequency screening

Our aim is to model the frequency of certain behavioral acts, especially those that are likely to transmit communicable diseases between persons. We develop a generalized linear model on the basis of the beta prime distribution to model the responses to a survey question of the form, 'When was the last time that you engaged in this behavior?' Intuitively, individuals reporting more recent events are more likely to have greater frequency of the risky behavior. The beta prime distribution is especially suited to this application because of its long tail. We adjust for length-biased sampling. We show how to use this distribution as the basis of a linear regression model that accounts for differences in demographic and psychological characteristics of the respondents. We discuss estimation of parameters, residuals, tests for heterogeneity of these parameters, and jackknife measures of influence. We apply the methods to a survey of alcohol abuse use among individuals who are at high risk for spreading HIV and other communicable diseases in a study conducted in Saint Petersburg, Russia.