By J.L. Schafer
Offers a unified, Bayesian method of the research of incomplete multivariate facts, overlaying datasets within which the variables are non-stop, express or either. comprises genuine info examples and sensible suggestion.
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Extra resources for Analysis of Incomplete Multivariate Data
The relative sizes of the subdomains in the population are assumed to be known and are not estimated from the sample. Similarly, with data from planned experiments, the relevant analysis is usually a comparison of mean responses across two or more treatment groups; the manner in which experimental units are allocated to treatments is determined by the experimenter and does not need to be modeled. In discussing situations like these, we will refer to variables in a generic sense as either response variables or design variables, with the latter being those that the statistical analysis ultimately regards as fixed.
Dempster, Laird and Rubin (1977) formalized the meaning of filling in the missing data at each step and presented the algorithm in its full generality, naming it ExpectationMaximization or EM. In any incomplete-data problem, the distribution of the complete data Y can be factored as P(Y | θ ) = P(Yobs | θ ) P(Ymis | Yobs , θ ). 2) where l(θ | Y ) = logP (Y|θ) denotes the complete-data loglikelihood, l(θ|Yo b s ) = log P ( Y|θ) the observed-data loglikelihood, and c an arbitrary constant. The term P(Ymis|Yobs , θ), which we shall call the predictive distribution of the missing data given θ, plays a central role in EM because it captures the interdependence between Ymis , and θ .
The Expectation or E-step, in which the function Q(θ|θ ) is calculated by averaging the complete-data loglikelihood (t) l(θ|Y) over P(Ymis|Yobs, θ ); and (t) 2. the Maximization or M-step, in which θ (t+1) is found by maximizing Q(θ|θ ). }. Dempster, Laird, and Rubin (1977) and Wu (1983) provide conditions under which this sequence converges reliably to a stationary point of the observed-data loglikelihood. In well-behaved problems this stationary point is a global maximum and EM yields the unique maximumlikelihood estimate (MLE) of θ , the maximizer of l(θ|Y obs).