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Assessment of model fit based on incomplete data

The talk discusses a general framework for the analysis of survey data with missing observations. The approach presented here considers missing data an unavoidable feature of any survey of the human population and aims at taking the unobserved part of the data into account when assessing model fit. To handle coverage error and unit nonresponse, the true distribution is modeled as a mixture of an observable and of an unobservable component. To assess model fit in this context, the mixture index of fit is used. The mixture index of fit does not postulate that the model of interest may account for the entire population, rather it considers the true distribution as a mixture of a component where the model fits and of another one where the model does not fit. The fit of the model with missing data taken into account is assessed by equating these two mixtures, one describing the observational process and the other one representing model fit, and asking, for different rates of missing observations, what is the largest fraction of the population where the model may hold true. In this framework the talk proposes a diagnostic procedure and illustrates its application to survey data.