General Linear Models: Univariate GLM, Anova/Ancova, Repeated Measures

by G. David Garson

GLM UNIVARIATE, ANOVA, ANCOVAOverviewUnivariate GLM is the general linear model now often used to implement such long-established statistical procedures as regression and members of the anova family. It is "general" in the sense that one may implement both regression and anova models. One may also have fixed factors, random factors, and covariates as predictors. Also, in GLM one may have multiple dependent variables, as discussed in a separate section on multivariate GLM and one may have linear transformations and/or linear combinations of dependent variables. Moreover, one can apply multivariate tests of significance when modeling correlated dependent variables, not relying on individual univariate tests as in multiple regression. GLM also handles repeated measures designs. Finally, because GLM uses a generalized inverse of the matrix of independent variables' correlations with each other, it can handle redundant independents which would prevent solution in ordinary regression models. The full content is now available from Statistical Associates Publishers. is the unformatted table of contents.GLM UNIVARIATETable of ContentsOverview 4Key Concepts 8Why testing means is related to variance in analysis of variance 8One-way anova 9Simple one-way anova in SPSS 9Simple one-way anova in SAS 13Two-way anova 16Two-way anova in SPSS 17Two-way anova in SAS 20Multivariate or n-way anova 22Regression models 22Parameter estimates (b coefficients) for factor levels 24Parameter estimates for dichotomies 25Significance of parameter estimates 25Research designs 25Between-groups anova design 25Completely randomized design 27Full factorial anova 27Balanced designs 28Latin square designs 29Graeco-Latin square designs 30Randomized Complete Block Design (RCBD anova) 30Split plot designs 32Mixed design models 32Random v. fixed effects models 34In SPSS 34In SAS 35Linear mixed models (LMM) vs. general linear models (GLM) 36Effects 36Treating a random factor as a fixed factor 36Mixed effects models 37Nested designs 37Nested designs 38In SPSS 39In SAS 42Treatment by replication design 42Within-groups (repeated measures) anova designs 42Counterbalancing 43Reliability procedure 44Repeated measures GLM in SPSS 44Repeated measures GLM in SAS 44Interpreting repeated measures output 45Variables 46Types of variables 46Dependent variable 46Fixed and random factors 47Covariates 47WLS weights 47Models and types of effects 48Full factorial models 48Effects 49Main effects 49Interaction effects 49Residual effects 52Effect size measures 53Effect size coefficients based on percent of variance explained 53Partial eta-squared 53Omega-squared 54Herzberg's R2 55Intraclass correlation 55Effect size coefficients based on standardized mean differences 55Cohen's d 55Glass's delta 57Hedge's g 58Significance tests 58F-test 58Reading the F value 58Example 1 59Example 2 59Significance in two-way anova 60Computation of F 60F-test assumptions 60Adjusted means 61Lack of fit test 61Power level and noncentrality parameter 62Hotelling's T-Square 63Planned multip

175 pages, Kindle Edition

First published August 26, 2012