When multiple durations are generated by a single unit, they may be related in a way that is not fully captured by the regressors. The omitted unit-specific variables might vary over the durations. They might also be correlated with the variables in the regression component. The authors propose an estimator that responds to these concerns and develop a specification test for detecting unobserved unit-specific effects. Data from Malaysia reveal that concentration of child mortality in some families is imperfectly explained by observed explanatory variables, and that failure to control for unobserved heterogeneity seriously biases the parameter estimates.