Reconciling Recalled Dates of Developmental Milestones, Events and Transitions: A Mixed Generalized Linear Model with Random Mean and Variance Functions

Reconciliation of conflicting reports on the dating of events has typically been approached as ‘data cleaning’. We present an alternative approach of modelling discrepancies by a statistical measurement model. The model combines two explanations of ‘telescoping’, systematic compression of the timescale and heteroscedastic random measurement error. The model can be viewed as a mixed generalized linear model with random effects within both mean and variance functions, or alternatively as involving multiplicative random effects. We illustrate the model in the context of multiple mothers' reports of the onset of puberty in their daughters. Estimated by penalized or predictive quasi‐likelihood, the model correctly distinguished the different mechanisms for telescoping and provided much improved estimates of the true age‐of‐onset distribution.