Adjusting for Nonignorable Nonresponse Using a Latent Modeling Approach
Alina Matei1, Giovanna Ranalli2
1Institute of Statistics, University of Neuchatel, Switzerland; 2Dipartimento di Economia, Finanza e Statistica, University of Perugia, Italy

Nonignorable nonresponse occurs when the probability of response in surveys depends upon the variable of interest observed only for respondents. This type of nonresponse is typical for surveys with sensitive questions (concerning drug abuse, sexual attitudes, politics, income etc). In such cases, ignoring the nonresponse can generate significant bias in estimation. A method based on latent variable modeling is developed for weighting the respondent units. The proposed weighting system seeks to reduce the non-response bias. We suppose that the survey item indicators (1 if an unit answers the item, and 0 otherwise) are related to an underlying latent continuous scale which indicates a unit degree of support for an attitude. This is called here the 'will-to-respond to the survey'. By linking unit and item nonresponse and using a latent trait model, we compute a latent variable for willingness to answer the survey for each unit in the sample, not only for respondents. Estimates of the response probabilities are provided using a logistic regression with this latent variable as covariate. No information about the nonrespondents and no auxiliary information are required. For this reason, we apply the proposed method in cases where no observed auxiliary information is available. The proposed weighting system is used in two estimators, a Hajek type estimator and a Horvitz-Thompson type estimator (using imputation or reweighting methods to deal with item nonresponse). The asymptotic properties of these estimators are studied and variance estimation methods that account for the effect of using such estimated response probabilities are discussed. In the absence of any observed auxiliary information, we show that the previous estimators perform well in several simulation studies comparing to the naive estimator computed without this latent covariate, and the gain in efficiency is substantial in certain cases.

Keywords: survey sampling; unit and item nonresponse; non-ignorable nonresponse; latent models

Biography: Alina Matei is PhD in statistics (2005, University of Neuchatel, Switzerland). Her research interests are in: survey sampling (sample co-ordination/integration of surveys, unequal probability sampling designs, variance estimation, longitudinal analysis, calibration estimation, nonresponse, inferential methods in finite populations), statistical computing and computational methods for sample surveys, latent variables modeling.