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Missing Data

Missing data involve the same considerations as conditional families. If x is missing and y is observed and the joint density is tex2html_wrap_inline2443 , then the likelihood is the marginal density tex2html_wrap_inline2481 considered a function of tex2html_wrap_inline2411 for y fixed at the observed value.

As we observed in the preceding section tex2html_wrap_inline2481 is the normalizing constant for the joint density considered as an unnormalized conditional density (1.4). Thus the family of unnormalized densities is involved in both conditional likelihood inference and likelihood inference with missing data.

Latent variables, random effects, and ordinary (non-Bayes) empirical Bayes models all involve missing data of some form, and all give rise to the same considerations.



Charles Geyer
Fri Jul 5 15:26:21 CDT 1996