We review three alternative approaches to modelling survey non-contact and refusal: multinomial, sequential, and sample selection (bivariate probit) models. We then propose a multilevel extension of the sample selection model to allow for both interviewer effects and dependency between non-contact and refusal rates at the household and interviewer level. All methods are applied and compared in an analysis of household non-response in the United Kingdom, using a data set with unusually rich information on both respondents and non-respondents from six major surveys. After controlling for household characteristics, there is little evidence of residual correlation between the unobserved characteristics affecting non-contact and refusal propensities at either the household or the interviewer level. We also find that the estimated coefficients of the multinomial and sequential models are surprisingly similar, which further investigation via a simulation study suggests is due to non-contact and refusal having largely different predictor
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