U.S. flag

An official website of the United States government

Department of Labor Logo United States Department of Labor
Dot gov

The .gov means it's official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you're on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Bureau of Labor Statistics > Office of Survey Methods Research > Publications > Browse Research Papers

Testing Bias of Mean Estimates Due to Not Missing and Random Nonresponse With Application to the Consumer Expenditure Survey

Michael Sverchkov

Abstract

In practice most survey methods that adjust for nonresponse assume either explicitly or implicitly that the missing data are ‘missing at random’ (MAR). That is, they assume response does not depend on the variable of interest (the outcome variable) given some auxiliary information known for the whole population. However, in many practical situations, this assumption is not valid, since the probability of responding often depends on the outcome value, even after conditioning on available covariate information. In such cases, the use of methods that assume nonresponse is MAR can lead to large bias of parameter estimators and distort subsequent inference.

The case where the missing data are not MAR (NMAR) can be treated by postulating a parametric model for the distribution of the outcomes before nonresponse and a model for the response mechanism. These two models define a parametric model for the observed outcomes, so that the parameters of these models can be estimated from the observed data. Once the parameters are estimated, the first model can be used for inference.

Modeling the distribution of the outcomes before nonresponse is difficult since only the observed data are available. Sverchkov (2008) proposes an alternative approach, which allows the parameters of the response model to be estimated without postulating a parametric model for the distribution of the outcomes before nonresponse. To account for the nonresponse, Sverchkov (2008) assumes a response model and estimates the response probabilities by applying the missing information principle (MIP), which consists of defining the likelihood as if there was complete response, and then integrating out the unobserved outcomes from the likelihood, employing the relationship between the distributions of the observed and unobserved data.