Because our dependent variables were categorical indicators, we used both logistic and probit regression models to estimate the relative odds or relative risk of a past-year alcohol or drug use disorder or cross-state migration among ‘exposed’ and ‘unexposed’ subjects (Breslow and Day 1980; Hosmer and Lemeshow 1989), and to investigate the possibility of differences in effect estimates across demographic groups. In most of these models, the response variable was an indicator of past-year alcohol or drug use disorder, and the predictor of interest was MLDA exposure; indicators for each state controlled for factors that vary across states but not over time, and indicators for single year of birth controlled for factors that vary across birth years but not across states. Although estimates from logistic models can be biased when strata are sparse (Kalbfleisch and Sprott, 1970), our pooled sample sizes are large enough that nearly identical estimates and standard errors were generated by ordinary fixed effect logistic models with state indicators, and by conditional logistic models stratified by state. However, ordinary logistic models gave better convergence and the ability to
