Regression Diagnostics to Detect Nonrandom Missingness in Linear Regression

Abstract

Missing data is a common problem in regression analysis. The usual estimation strategies require that the data values be missing completely at random (MCAR); if this is not the case, estimates can be severely biased. In this article it is shown that tests can be constructed based on common regression diagnostics to detect non-MCAR behavior. The construction of these tests and their properties when data are missing in one explanatory variable are detailed. Computer simulations indicate good power to detect various non-MCAR processes. Three examples are presented. Extensions to missing data in more than one explanatory variable and to arbitrary regression models are discussed.

KEY WORDS:

• Missing data
• Missing completely at random
• Outlier/leverage point diagnostics
• Regression fill-in