arXiv subjects

Lynn Roy LaMotte

Publications and source records attributed to Lynn Roy LaMotte.

3 recordsLinked to original sources

arXiv2024

Essential Properties of Type III* Methods

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 they are widely thought to be known: what those functions are, to what extent they coincide with classical ANOVA effects, and how they are affected by cell sample sizes, empty cells, and covariates. Those properties are established here.

stat.ME↗

arXiv2018

A Formula for Type III Sums of Squares

Type III methods were introduced by SAS to address difficulties in dummy-variable models for effects of multiple factors and covariates. They are widely used in practice; they are the default method in several statistical computing packages. Type III sums of squares (SSs) are defined by a set of instructions; an explicit mathematical formulation does not seem to exist. An explicit formulation is derived in this paper. It is used to illustrate Type III SSs and their properties in the two-factor ANOVA model.

stat.ME↗

arXiv2017

Yates's MWSM SS in the General Linear Model

In 1934, F. Yates described a sum of squares for testing factor main effects in saturated unbalanced models for effects of two factors. He claimed no particular properties of this sum of squares other than that it provided an "efficient estimate of the variance from the A means of the sub-class means... ." Although it became widely regarded as the gold standard in the two-factor model, its fundamental properties and relations to other sums of squares for the same model were not established until decades later. Its method has not been extended to more general settings. This paper shows how Yates's approach can be extended to construct numerator sums of squares for test statistics for linear hypotheses in general linear models. It is shown that Yates's sum of squares is equivalent to the restricted model - full model difference in error sum of squares, which in turn is shown to be the unique sum of squares that tests exactly the hypothesis in question.

stat.ME↗