Essential properties of Type III* methods

Lynn R. LaMotte

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 15, 4942-4952

Abstract: Type III methods, introduced by SAS in 1976, formulate estimable functions that substitute, somehow, for classical ANOVA effects in multiple linear regression models. They have been controversial since, provoking wide use and satisfied users on the one hand and skepticism and scorn on the other. Their essential mathematical properties have not been established, although some are widely thought to be known. Those include, for example, what those functions are, to what extent they coincide with classical ANOVA effects, and how they are affected by cell sample sizes and empty cells. Those properties are established here.

Date: 2025
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DOI: 10.1080/03610926.2024.2434555

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