Conditional decomposition diagnostics for regression analysis of zero-inflated and left-censored data

Health and safety studies that entail both incidence and magnitude of effects produce semi-continuous outcomes, in which the response is either zero or a continuous positive value. Zero-inflated left-censored models typically employ latent mixture constructions to allow different covariate processes to impact the incidence versus the magnitude. Assessment of the model, however, requires a focus on the observable characteristics. We employ a conditional decomposition approach, in which the model assessment is partitioned into two observable components: the adequacy of the marginal probability model for the boundary value and the adequacy of the conditional model for values strictly above the boundary. A conditional likelihood decomposition facilitates the statistical assessment. For corresponding residual and graphical analysis, the conditional mean and quantile functions for events above the boundary and the marginal probabilities of boundary events are investigated. Large sample standard errors for these quantities are derived for enhanced graphical assessment, and simulation is conducted to investigate the finite-sample behaviour. The methods are illustrated with data from two health-related safety studies. In each case, the conditional assessments identify the source for lack of fit of the previously considered model and thus lead to an improved model.