User:Econterms/Pattern-mixture models

Pattern-mixture models (PMM)


 * X is matrix of independent variables, observed in every case
 * Y is a vector of observed outcomes, sometimes observed
 * Binary M is 1 if Y is observed, 0 if not

Selection models and pattern-mixture models are different models of this situation, applying to different cases.

Pattern-mixture cases: we have survey data and some of the survey respndents can be matched to administrative data (Medicare payments, Census, unemployment receipt) or big data on credit card use, receipt of food stamps, Internet use. . and whether a match is found is of their own X's (age, location, sex) and also the Y's (health, poverty, education). (is that definitely not a "selection" case? yes, it's a function of whether the Y value exists at all, too)

Missingness concepts
sources: Rubin 1976; Little and Rubin 1987


 * Missing completely at random (MCAR): Missingness in Y depends on neither Y nor X
 * Missing at random (MAR): Missingness in Y depends on X, but not Y
 * Ex: Survey respondents under age 65 won't have health care expenses paid by Medicare, so we don't observe whether they had health care expenses nor how large they were
 * Missing not at random (MNAR): Missingness in Y depends on Y
 * Ex: Survey respondents with high health care expenses may be less likely to report those expenses, so missingess is confounded with their level