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Garson, G. D. (2015). GLM Multivariate, MANOVA. & Canonical Correlation. Asheboro, NC: Statistical Associates Publishers.

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Table of Contents
ISBN: 978-1-62638-034-9
ASIN number (e-book counterpart to ISBN): B0092WUSQS .
@c 2015 by G. David Garson and Statistical Associates Publishers. worldwide rights reserved in all languages and on all media. Permission is not granted to copy, distribute, or post e-books or passwords.


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 graduate-level study.

The 2015 edition is a major update to the 2012 edition. Among the new features are these:

The full content is now available from Statistical Associates Publishers. Click here.

Below is the unformatted table of contents.

Data examples for MANOVA	10
GLM in statistics packages	12
SAS	12
Stata	12
Key coefficients in multivariate GLM	13
F tests	13
t tests	13
Partial eta-square	14
R-Square	14
Omega-square	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 between-subjects effects (F tests)	28
Parameter estimates	30
Differences in statistical inference	32
Lack of fit tests	32
Spread-versus-level 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 post-hoc tests	48
Contrast tests	50
Multivariate GLM in SAS	53
SAS input	53
SAS Output	55
Multivariate significance tests	55
Significance tests of between-subjects effects	56
Parameter Estimates	60
Lack of fit tests	61
Spread-versus-level 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 post-hoc tests	80
Contrast tests	82
Multivariate GLM in Stata	85
Stata input	85
Stata output	87
Multivariate significance tests	87
Significance tests of between-subjects effects (F tests)	89
Parameter Estimates	91
Lack of fit tests	91
Spread-versus-level 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 post-hoc 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 post-hoc tests	152
Overview	152
Least significant difference (LSD) test	156
Bonferroni adjusted t-tests	157
Sidak adjusted t-tests	158
Tukey's test	159
Tukey-Kramer test	161
Tukey-b test	162
Dunnett's test	162
Dunnett's T3 and Dunnett's C tests	163
Tamhane's T2 test	163
Games-Howell test	163
Scheffé test	165
S-N-K (Student-Newman-Keuls)  test	166
Duncan test	166
Hochberg's GT2 test	167
Gabriel test	167
REGWQ (Ryan test)	168
REGWF (Ryan test)	168
Simulation test	169
Waller-Duncan 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 step-down 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
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 t-tests 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 t-tests 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 t-tests 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
Cross-validation	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 multi-response 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
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