A formula for Type III sums of squares

@article{Lamotte2019AFF,
  title={A formula for Type III sums of squares},
  author={Lynn Roy Lamotte},
  journal={Communications in Statistics - Theory and Methods},
  year={2019}
}
  • L. Lamotte
  • Published 29 March 2018
  • Mathematics
  • Communications in Statistics - Theory and Methods
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… 
GENERAL LINEAR MODEL: AN EFFECTIVE TOOL FOR ANALYSIS OF CLAIM SEVERITY IN MOTOR THIRD PARTY LIABILITY INSURANCE
The paper focuses on the analysis of claim severity in motor third party liability insurance under the general linear model. The general linear model combines the analyses of variance and regression

References

SHOWING 1-10 OF 18 REFERENCES
ANOVA for unbalanced data: Use Type II instead of Type III sums of squares
TLDR
Today, most major statistical programs perform, by default, unbalanced ANOVA based on Type III sums of squares (Yates's weighted squares of means), which is founded on unrealistic models—models with interactions, but without all corresponding main effects.
Factorial ANOVA with unbalanced data: A fresh look at the types of sums of squares
In this paper we endeavour to provide a largely non-technical description of the issues surrounding unbalanced factorial ANOVA and review the arguments made for and against the use of Type I, Type II
Methods of Analysis of Linear Models with Unbalanced Data
Abstract The objective of this article is to review existing methods for analyzing experimental design models with unbalanced data and to relate them to existing computer programs. The methods are
Some Computational and Model Equivalences in Analyses of Variance of Unequal-Subclass-Numbers Data
Abstract Available methodologies for calculating sums of squares in analyses of variance of unequal-subclass-numbers (unbalanced) data include (i) full rank reparameterized models, (ii) “indirect”
Which Sums of Squares Are Best In Unbalanced Analysis of Variance ?
Three fundamental concepts of science and statistics are entities, variables (which are formal representations of properties of entities), and relationships between variables. These concepts help to
Tests of hypotheses in fixed effects linear models
Using the concept of estimability, tests of hypotheses in multifactor fixed effects linear models are developed without resorting to the “usual assumptions.” Three types of estimable functions are
Analysis of Variance Computing Package Output for Unbalanced Data from Fixed-Effects Models with Nested Factors
Abstract Explanations are offered for some of the idiosyncrasies evident in computer output of sums of squares of unbalanced data described by Dallal (1992).
The Gram-Schmidt Construction as a Basis for Linear Models
The Gram-Schmidt construction, with a little extension, can be used to establish results in linear algebra, multiple regression analysis, and the theory of linear models. This article describes and
Hypothesis Testing in Linear Models (Eisenhart Model I)
The results from an analysis of balanced data are frequently summarized in an analysis of variance (AOV) table. Each sum of squares (SS) in the AOV table is uniquely associated with testing a
Linear Models For Unbalanced Data
TLDR
This chapter presents basic results for Cell Means Models and discusses the 2-Way Crossed Classification with All-Cells-Filled Data and Models with Covariables: The General Case and Some Applications.
...
1
2
...