By Sik-Yum Lee

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Ileus, R. (2003). Beyond alpha: An empirical examination of the effects of different sources of measurement error on reliability estimates for measures of individual-differences constructs. Psychological Methods 8, 206–224. Schmitt, N. (1996). Uses and abuses of coefficient alpha. Psychological Assessment 8, 350–353. Shapiro, A. (1982a). Rank reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis. Psychometrika 47, 187–199. Shapiro, A. (1982b). Weighted minimum trace factor analysis.

The effects of sampling model on inference with coefficient alpha. Educational & Psychological Measurement 57, 893–905. Becker, G. (2000). Coefficient alpha: Some terminological ambiguities and related misconceptions. Psychological Reports 86, 365–372. M. (1968). Alpha-maximized factor analysis (Alphamax): Its relation to alpha and canonical factor analysis. Psychometrika 33, 335–345. M. (1972). A lower-bound method for the dimension-free measurement of internal consistency. Social Science Research 1, 343–357.

Returning to the survey example, data missing not at random would include questions that are left unanswered because they relate to a sensitive topic to the respondent such as domestic life, income, or substance abuse. Since there are not any clues as to why the data are missing, the analysis of MNAR data is challenging in the sense that one may never know the validity of the final inferences made based on the data. Values are not always missing from a collection of data because of a failure by the respondent or omissions in the recording of the data.