arXiv subjects

Lynn R. LaMotte

Publications and source records attributed to Lynn R. LaMotte.

3 recordsLinked to original sources

arXiv2022

Three Properties of F-Statistics for Multiple Regression and ANOVA

This paper establishes three properties of F-statistics for inference about the mean vector in multiple regression and analysis of variance. The extra SSE due to imposing a set of linear conditions on the model tests the estimable part of those conditions. All other possible numerator sums of squares that test the same have not-lesser degrees of freedom and not-greater non-centrality parameters. When factor-level combinations are coded by contrasts, the model restricted to eliminate an ANOVA effect is formulated by omitting that effect's columns from the model matrix.

stat.ME↗

arXiv2017

Deconstructing Type III

SAS introduced Type III methods to address difficulties in dummy-variable models for effects of multiple factors and covariates. Type III methods are widely used in practice; they are the default method in many statistical computing packages. Type III sums of squares (SSs) are defined by an algorithm, and an explicit mathematical formulation does not seem to exist. For that reason, their properties have not been rigorously proven. Some that are widely believed to be true are not always true. An explicit formulation is derived in this paper. It is used as a basis to prove fundamental properties of Type III estimable functions and SSs. It is shown that, in any given setting, Type III effects include all estimable ANOVA effects, and that if all of an ANOVA effect is estimable then the Type III SS tests it exactly. The setting for these results is general, comprising linear models for the mean vector of a response that include arbitrary sets of effects of factors and covariates.

stat.ME↗

arXiv2016

Yates's and Other Sums of Squares

It is shown that the sum of squares by Yates's method of weighted squares of means is equivalent to numerator sums of squares formulated by other methods. These relations are established first for hypotheses about fixed effects in a general linear model, in the process showing how Yates's method can be extended. They are then illustrated in the unequal-subclass-numbers model for main effects and interaction effects of two factors.

stat.ME↗