By J.L. Schafer
Offers a unified, Bayesian method of the research of incomplete multivariate info, protecting datasets within which the variables are non-stop, express or either. comprises actual info examples and functional recommendation.
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21) will not precisely hold, but it may still be approximately true provided that the amount of information missing on the predictors is not large. 1) show the weight gains of two groups of female rats, one fed a low-protein diet and the other fed a high-protein diet. The low-protein group has 7 rats and the high-protein group has 12. Snedecor and Cochran perform a classical analysis assuming that the observations are independent and normally distributed and the within-group variances are equal.
If all the variables used in the sampling plan are included in Yobs, then the missing data will be MAR. In most of the above examples, the missing data may be said to be missing by design, because it was never the intention of the investigator to record all potential variables for all subjects. When missing data are missing by design, they tend also to be MAR. 2 Examples where ignorability is not known to hold In many other missing-data contexts, however, it is not known whether or not the MAR condition is satisfied.
18) where β = ( β 0 , β1 ) , T 1 1 X = M 1 ( βˆ = X T X ) −1 y11 y12 y y21 , y = 22 , M M yn1 ,1 yn1 , 2 X T y and εˆ = y − Xβˆ . Details of the calculations leading to these posteriors may be found in standard texts on Bayesian analysis and will be reviewed in Chapters 5-6. In the above example, a particular factorization of the observed data likelihood enabled us to express the posterior in a tractable form. This will not always be the case. One cannot always factor the observed-data likelihood into complete-data likelihoods whose parameters are distinct.