This paper considers nonlinear panel data models with random intercepts and random slopes. Existing implementations of such models always assume joint normality for random intercepts and slopes. This paper demonstrates that, in certain situations, linking the intercepts and slopes via copula functions potentially offers improved fits and more accurate estimates of treatment effects. To demonstrate, a case study investigates the effect of mental health problems on visits to outpatient departments. Normal-based and copula-based models both find positive effects. But results also show that, at the 85th percentile, a better-fitting copula-based model uncovers an effect more than 30 percent larger than its normal-based counterpart.
JEL Codes: C23; C51; I12