Dealing with non-ignorable nonresponse in survey sampling: A latent modeling approach

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Alina Matei and M. Giovanna RanalliNote 1

Abstract

Nonresponse is present in almost all surveys and can severely bias estimates. It is usually distinguished between unit and item nonresponse. By noting that for a particular survey variable, we just have observed and unobserved values, in this work we exploit the connection between unit and item nonresponse. In particular, we assume that the factors that drive unit response are the same as those that drive item response on selected variables of interest. Response probabilities are then estimated using a latent covariate that measures the will to respond to the survey and that can explain a part of the unknown behavior of a unit to participate in the survey. This latent covariate is estimated using latent trait models. This approach is particularly relevant for sensitive items and, therefore, can handle non-ignorable nonresponse. Auxiliary information known for both respondents and nonrespondents can be included either in the latent variable model or in the response probability estimation process. The approach can also be used when auxiliary information is not available, and we focus here on this case. We propose an estimator using a reweighting system based on the previous latent covariate when no other observed auxiliary information is available. Results on its performance are encouraging from simulation studies on both real and simulated data.

Key Words: Unit nonresponse; Item nonresponse; Latent trait models; Response propensity; Rasch models.

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