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Cih Huang, Professor of Political Science, National Churg-Chen University.
Yu-tzung Chang, Assistant Professor of Political Science, National Taiwan University.
On Minimum-Discrimination-Information (MDI) Method of Weighting: an Application to the 2001 Taiwan's Election and Democratization Study(TEDS) (in Chinese) Download
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Goodness-of-fit tests allow us to examine if the sample at hand is representative enough of the population to ensure accurate statistical inferences of parameters. When the sample fails the tests, survey researchers often appeal to reweighting as a remedy. Post-stratification and raking are perhaps the two most popular weighting methods. However, post-stratification requires the knowledge of multivariate joint distribution of the population when more than one post-stratifying variable is considered. Without such detailed information, raking comes as a rescue since it requires only the knowledge of marginal distributions of selected variables. Popular as it may be, raking takes no account of associations among post-stratifying variables. Furthermore, it relies heavily on Chi-squared tests and a pre-selected p-value (usually 0.5) as the stopping rule of iteration, an ad hoc rule justified only by convenience.

This article proposes a third way of Weighting, which we call it the minimum-discrimination-information (MDI) method. MDI approach finds optimal (in terms of minimum cross-entropy) relative weights by treating sample joint distribution as prior and known population marginal distributions as constraints. We first explain the rationale behind this proposed MDI method and then use TEDS 2001 survey data to compare the estimates of raking and MDI weights. We find that nearly 70 percent of the latter indeed replicate the Census 2000 population joint distribution better than the former. We thus conclude that MDI method is an approach worth further theoretical investigation.