
GLM MULTIVARIATE, MANOVA, & CANONICAL CORRELATION Overview
An illustrated tutorial and introduction to multivariate general linear models, MANOVA, MANCOVA, and linear and nonlinear canonical correlation, using SPSS, SAS, and Stata for examples. Suitable for introductory graduatelevel study.
The 2015 edition is a major update to the 2012 edition. Among the new features are these:
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Below is the unformatted table of contents.
MULTIVARIATE GLM, MANOVA, AND MANCOVA 1 Data examples for MANOVA 10 MANOVA & MANCOVA 10 GLM in statistics packages 12 SPSS 12 SAS 12 Stata 12 Key coefficients in multivariate GLM 13 F tests 13 t tests 13 Partial etasquare 14 RSquare 14 Omegasquare 14 Multivariate GLM in SPSS 15 SPSS input 15 The main multivariate GLM dialog 15 The Model dialog 16 The Options dialog 18 The Contrasts dialog 19 The Plots dialog 20 The Save dialog 21 The Post hoc dialog 22 The Bootstrap dialog 23 SPSS syntax 24 SPSS output 25 Multivariate significance tests 25 Significance tests of betweensubjects effects (F tests) 28 Parameter estimates 30 Differences in statistical inference 32 Lack of fit tests 32 Spreadversuslevel plots 36 Residual plots 38 Outlier diagnostics 40 Analysis of covariance 40 Estimated marginal means 40 Profile plots 43 Pairwise comparison tables 46 Multiple comparison and posthoc tests 48 Contrast tests 50 Multivariate GLM in SAS 53 SAS input 53 SAS Output 55 Multivariate significance tests 55 Significance tests of betweensubjects effects 56 Parameter Estimates 60 Lack of fit tests 61 Spreadversuslevel plots 61 Residual plots 63 Outlier diagnostics 68 Analysis of covariance 73 Estimated marginal means 74 Profile Plots 75 Pairwise comparison tables 76 Multiple comparison and posthoc tests 80 Contrast tests 82 Multivariate GLM in Stata 85 Stata input 85 Stata output 87 Multivariate significance tests 87 Significance tests of betweensubjects effects (F tests) 89 Parameter Estimates 91 Lack of fit tests 91 Spreadversuslevel plots 91 Residual plots 95 Outlier diagnostics 101 Analysis of covariance 108 Estimated marginal means 110 Profile Plots 111 Pairwise comparison tables 113 Multiple comparison and posthoc tests 115 Contrast tests 119 GLM multivariate assumptions 123 Measurement level 123 Observations are independent of one another 123 Random sampling 124 Homogeneity of error variances 124 Levene's test 125 SPSS 126 SAS 127 Stata 128 Homogeneity of regressions 130 Overview 130 SPSS 131 SAS 132 Stata 133 Homogeneity of covariances 135 Box's M test 135 SPSS 136 SAS 137 Stata 138 Sphericity 139 Bartlett's test of sphericity 139 SPSS 140 SAS 141 Stata 142 Low measurement error of the covariates 142 Similar group sizes 143 Adequate group sizes 143 Appropriate sums of squares 143 SPSS 144 SAS 144 Stata 144 Random normal residuals 145 Linearity 145 Multivariate normal distribution 145 No outliers 146 GLM frequently asked questions 146 Why can't I just use multiple univariate ANOVA tests rather than MANOVA? 146 How do I write up the results of my MANOVA analysis? 147 How many dependent variables can I have in MANOVA? 148 Can I enter just one dependent variable in MANOVA? 149 Is there a limit on the number of covariates which can be included in a multiple analysis of variance? 149 Explain the syntax for MANOVA in SPSS 149 What is analysis of residuals for in MANOVA 150 What is bootstrapped significance testing? 151 What types of contrasts are available for contrast analysis? 151 Simple contrasts 151 Deviation contrasts 151 Difference contrasts 151 Helmert contrasts 152 Repeated contrasts 152 Polynomial contrasts 152 Explain alternative multiple comparison and posthoc tests 152 Overview 152 Least significant difference (LSD) test 156 Bonferroni adjusted ttests 157 Sidak adjusted ttests 158 Tukey's test 159 TukeyKramer test 161 Tukeyb test 162 Dunnett's test 162 Dunnett's T3 and Dunnett's C tests 163 Tamhane's T2 test 163 GamesHowell test 163 Scheffé test 165 SNK (StudentNewmanKeuls) test 166 Duncan test 166 Hochberg's GT2 test 167 Gabriel test 167 REGWQ (Ryan test) 168 REGWF (Ryan test) 168 Simulation test 169 WallerDuncan test 170 Other tests 171 HSU's unconstrained multiple comparison with the best (UMCB) test 171 Explain SAS syntax for multiple comparison tests 172 What is stepdown MANOVA? 175 SPSS 176 SAS 176 Stata 176 What is the "protected F" or least significant difference (LSD) test in MANOVA? How does it relate to the use of discriminant analysis in MANCOVA? 176 What is the multivariate GLM syntax in SPSS? 177 What is the MANOVA syntax in SPSS? 178 CANONICAL CORRELATION: LINEAR & NONLINEAR 181 Data examples for canonical correlation 181 Overview 182 Key Concepts and Terms 184 Canonical variables (variates) 184 Canonical correlation and canonical dimensions 184 Canonical correlation vs. redundancy 185 Redundancy coefficient 186 Pooled canonical correlation 187 Pooled redundancy coefficients 187 Eigenvalues 187 Canonical weights 188 Canonical scores 189 Structure coefficients/ canonical factor loadings 189 Canonical communality coefficients 190 Canonical variate adequacy coefficients 190 Canonical Correlation in SPSS: MANOVA method 190 SPSS input 190 SPSS output 192 Multivariate significance tests 192 Eigenvalues and canonical correlations 193 Dimension reduction analysis 194 Standardized canonical weights and structure correlations 194 Redundancy analysis 197 Univariate F tests for observed dependent variables 198 Regression ttests of observed covariate effects 199 SPSS CANCORR macro method 201 Overview 201 Input 201 Output 202 Canonical Correlation in SAS 202 SAS input 202 SAS output 203 Multivariate significance tests 203 Eigenvalues and canonical correlations 204 Dimension reduction analysis 204 Standardized canonical weights and structure correlations 205 Redundancy analysis 209 Univariate F tests for observed dependent variables 210 Regression ttests of observed covariate variables 211 Canonical Correlation in Stata 214 Stata input 214 Stata output 214 Multivariate significance tests 215 Eigenvalues and canonical correlations 215 Dimension reduction analysis 216 Standardized canonical weights and structure correlations 217 Redundancy analysis 223 Univariate F tests for observed dependent variables 225 Regression ttests of observed covariate variables 226 Nonlinear canonical correlation in SPSS 227 Data 227 Overview 228 Input 229 Invoking nonlinear canonical correlation 229 Defining nonlinear canonical correlation 230 Selecting output options 231 Syntax 233 Output 233 Model fit and loss values 233 Eigenvalues 234 Canonical correlation 234 Item fit 235 Canonic weights, quantifications, and category coordinate plots 238 Component loadings 240 Transformation plots 243 Multiple category centroid plots 247 Object scores 249 Canonical correlation assumptions 251 Overview 251 Data level 251 Data independence 251 Linearity 251 Multiple significant measured dependent variables 251 Low multicollinearity 252 Multivariate normality 252 Homogeneity of variance 253 Measurement error 253 Unrestricted variance 253 Singularity 253 Sample size 253 Cell count adequacy 254 Random sampling 254 Outliers 254 Crossvalidation 254 Canonical correlation: Frequently asked questions 255 How do I write up canonical correlation research? 255 How is it that some of my variables have high structure correlations even though their canonical weights are near zero? 255 Is the canonical correlation a measure of the percent of variance explained in the original variables? 255 Can the canonical coefficients be used to explain with which original variables a canonical correlation is predominantly associated? 256 Can canonical correlation be used for repeated measures? 256 What is "backward" or "stepwise" canonical correlation? 257 Should the canonical solution be rotated, as in factor analysis, for greater interpretability? 257 How does canonical correlation compare with factor analysis? 258 How is factor analysis used in conjunction with canonical correlation? 258 What are regression alternatives to canonical correlation? 259 How does SPSS MANOVA output differ from SPSS canonical correlation output? 259 One of my variables is a multiresponse item. What do I do? 259 What does the output for the SPSS CANCORR macro method look like? 259 What is a second example of canonical correlation? 262 What is a heliograph for canonical correlation? 263 Acknowledgments 264 Bibliography 265 Pagecount: 270