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Using Multivariate Statistics

ISBN: 9780673994141 | 0673994147
Format: Hardcover
Publisher: Addison-Wesley
Pub. Date: 3/1/1996

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Table of Contents
Prefacexxix
CHAPTER 1 Introduction
1(18)
1.1 MULTIVARIATE STATISTICS: WHY?
1(6)
... MORE
1.1.1 The Domain of Multivariate Statistics: Number of IVs and DVs
2(1)
1.1.2 Experimental and Nonexperimental Research
2(2)
1.1.2.1 Multivariate Statistics in Nonexperimental Research
3(1)
1.1.2.2 Multivariate Statistics in Experimental Research
3(1)
1.1.3 Computers and Multivariate Statistics
4(2)
1.1.3.1 Program Updates
6(1)
1.1.3.2 Garbage In, Roses Out?
6(1)
1.1.4 Why Not?
6(1)
1.2 SOME USEFUL DEFINITIONS
7(4)
1.2.1 Continuous, Discrete, and Dichotomous Data
7(1)
1.2.2 Samples and Populations
8(1)
1.2.3 Descriptive and Inferential Statistics
9(1)
1.2.4 Orthogonality
9(1)
1.2.5 Standard and Sequential Analyses
10(1)
1.3 COMBINING VARIABLES
11(1)
1.4 NUMBER AND NATURE OF VARIABLES TO INCLUDE
12(1)
1.5 DATA APPROPRIATE FOR MULTIVARIATE STATISTICS
13(4)
1.5.1 The Data Matrix
13(1)
1.5.2 The Correlation Matrix
14(1)
1.5.3 The Variance-Covariance Matrix
14(1)
1.5.4 The Sum-of-Squares and Cross-Products Matrix
15(1)
1.5.5 Residuals
16(1)
1.6 ORGANIZATION OF THE BOOK
17(2)
CHAPTER 2 A Guide to Statistical Techniques: Using the Book
19(14)
2.1 RESEARCH QUESTIONS AND ASSOCIATED TECHNIQUES
19(9)
2.1.1 Degree of Relationship among Variables
19(2)
2.1.1.1 Bivariate r
20(1)
2.1.1.2 Multiple R
20(1)
2.1.1.3 Sequential R
20(1)
2.1.1.4 Canonical R
20(1)
2.1.1.5 Multiway Frequency Analysis
21(1)
2.1.2 Significance of Group Differences
21(4)
2.1.2.1 One-Way ANOVA and t Test
21(1)
2.1.2.2 One-Way ANCOVA
21(1)
2.1.2.3 Factorial ANOVA
22(1)
2.1.2.4 Factorial ANCOVA
22(1)
2.1.2.5 Hotelling's T(2)
22(1)
2.1.2.6 One-Way MANOVA
23(1)
2.1.2.7 One-Way MANCOVA
23(1)
2.1.2.8 Factorial MANOVA
24(1)
2.1.2.9 Factorial MANCOVA
24(1)
2.1.2.10 Profile Analysis
24(1)
2.1.3 Prediction of Group Membership
25(2)
2.1.3.1 One-Way Discriminant Function
25(1)
2.1.3.2 Sequential One-Way Discriminant Function
25(1)
2.1.3.3 Multiway Frequency Analysis (Logit)
26(1)
2.1.3.4 Logistic Regression
26(1)
2.1.3.5 Sequential Logistic Regression
26(1)
2.1.3.6 Factorial Discriminant Function
27(1)
2.1.3.7 Sequential Factorial Discriminant Function
27(1)
2.1.4 Structure
27(1)
2.1.4.1 Principle Components
27(1)
2.1.4.2 Factor Analysis
27(1)
2.1.4.3 Structural Equation Modeling
28(1)
2.2 A DECISION TREE
28(1)
2.3 TECHNIQUE CHAPTERS
28(1)
2.4 PRELIMINARY CHECK OF THE DATA
29(4)
CHAPTER 3 Review of Univariate and Bivariate Statistics
33(24)
3.1 HYPOTHESIS TESTING
33(4)
3.1.1 One-Sample z Test
33(3)
3.1.2 Power
36(1)
3.1.3 Extensions of the Model
37(1)
3.2 ANALYSIS OF VARIANCE
37(15)
3.2.1 One-Way Between-Subjects ANOVA
38(2)
3.2.2 Factorial Between-Subjects ANOVA
40(3)
3.2.3 Within-Subjects ANOVA
43(2)
3.2.4 Mixed Between-Within-Subjects ANOVA
45(1)
3.2.5 Design Complexity
46(3)
3.2.5.1 Nesting
46(1)
3.2.5.2 Latin Square Designs
47(1)
3.2.5.3 Unequal n and Nonorthogonality
48(1)
3.2.5.4 Fixed and Random Effects
49(1)
3.2.6 Specific Comparisons
49(3)
3.2.6.1 Weighting Coefficients for Comparisons
49(1)
3.2.6.2 Orthogonality of Weighting Coefficients
50(1)
3.2.6.3 Obtained F for Comparisons
50(1)
3.2.6.4 Critical F for Planned Comparisons
51(1)
3.2.6.5 Critical F for Post Hoc Comparisons
52(1)
3.3 PARAMETER ESTIMATION
52(1)
3.4 STRENGTH OF ASSOCIATION
53(1)
3.5 BIVARIATE STATISTICS; CORRELATION AND REGRESSION
54(2)
3.5.1 Correlation
54(1)
3.5.2 Regression
55(1)
3.6 CHI-SQUARE ANALYSIS
56(1)
CHAPTER 4 Cleaning Up Your Act: Screening Data Prior to Analysis
57(70)
4.1 IMPORTANT ISSUES IN DATA SCREENING
58(30)
4.1.1 Accuracy of Data Files
58(1)
4.1.2 Honest Correlations
58(2)
4.1.2.1 Inflated Correlation
58(1)
4.1.2.2 Deflated Correlation
58(2)
4.1.3 Missing Data
60(5)
4.1.3.1 Deleting Cases or Variables
62(1)
4.1.3.2 Estimating Missing Data
63(1)
4.1.3.3 Using a Missing Data Correlation Matrix
64(1)
4.1.3.4 Treating Missing Data as Data
65(1)
4.1.3.5 Repeating Analyses with and without Missing Data
65(1)
4.1.4 Outliers
65(5)
4.1.4.1 Detecting Univariate and Multivariate Outliers
66(2)
4.1.4.2 Describing Outliers
68(1)
4.1.4.3 Reducing the Influence of Outliers
69(1)
4.1.4.4 Outliers in a Solution
69(1)
4.1.5 Normality, Linearity, and Homoscedasticity
70(11)
4.1.5.1 Normality
71(7)
4.1.5.2 Linearity
78(2)
4.1.5.3 Homoscedasticity, Homogeneity of Variance, Homogeneity of Variance-Covariance Matrices
80(1)
4.1.6 Common Data Transformations
81(3)
4.1.7 Multicollinearity and Singularity
84(3)
4.1.8 A Checklist and Some Practical Recommendations
87(1)
4.2 COMPLETE EXAMPLES OF DATA SCREENING
88(39)
4.2.1 Screening Ungrouped Data
88(16)
4.2.1.1 Accuracy of Input, Missing Data, Distributions, and Univariate Outliers
88(6)
4.2.1.2 Linearity and Homoscedasticity
94(1)
4.2.1.3 Transformation
94(1)
4.2.1.4 Detecting Multivariate Outliers
94(2)
4.2.1.5 Variables Causing Cases to be Outliers
96(8)
4.2.1.6 Multicollinearity
104(1)
4.2.2 Screening Grouped Data
104(23)
4.2.2.1 Accuracy of Input, Missing Data, Distributions, Homogeneity of Variance, and Univariate Outliers
106(1)
4.2.2.2 Linearity
107(2)
4.2.2.3 Multivariate Outliers
109(2)
4.2.2.4 Variables Causing Cases to be Outliers
111(2)
4.2.2.5 Multicollinearity
113(14)
CHAPTER 5 Multiple Regression
127(68)
5.1 GENERAL PURPOSE AND DESCRIPTION
127(1)
5.2 KINDS OF RESEARCH QUESTIONS
128(3)
5.2.1 Degree of Relationship
129(1)
5.2.2 Importance of IVs
129(1)
5.2.3 Adding IVs
129(1)
5.2.4 Changing IVs
129(1)
5.2.5 Contingencies among IVs
130(1)
5.2.6 Comparing Sets of IVs
130(1)
5.2.7 Predicting DV Scores for Members of a New Sample
130(1)
5.2.8 Parameter Estimates
130(1)
5.3 LIMITATIONS TO REGRESSION ANALYSES
131(8)
5.3.1 Theoretical Issues
131(1)
5.3.2 Practical Issues
132(7)
5.3.2.1 Ratio of Cases to IVs
132(1)
5.3.2.2 Outliers Among the IVs and on the DV
133(1)
5.3.2.3 Multicollinearity and Singularity
134(2)
5.3.2.4 Normality, Linearity, Homoscedasticity, and Independence of Residuals
136(3)
5.3.2.5 Outliers in the Solution
139(1)
5.4 FUNDAMENTAL EQUATIONS FOR MULTIPLE REGRESSION
139(7)
5.4.1 General Linear Equation
140(1)
5.4.2 Matrix Equations
141(3)
5.4.3 Computer Analyses of Small Sample Example
144(2)
5.5 MAJOR TYPES OF MULTIPLE REGRESSION
146(10)
5.5.1 Standard Multiple Regression
149(1)
5.5.2 Sequential Multiple Regression
149(1)
5.5.3 Statistical (Stepwise) and Setwise Regression
150(3)
5.5.4 Choosing among Regression Strategies
153(3)
5.6 SOME IMPORTANT ISSUES
156(9)
5.6.1 Importance of IVs
156(3)
5.6.1.1 Standard Multiple and Setwise Regression
158(1)
5.6.1.2 Sequential or Statistical Regression
159(1)
5.6.2 Statistical Inference
159(5)
5.6.2.1 Test for Multiple R
159(2)
5.6.2.2 Test of Regression Components
161(1)
5.6.2.3 Test of Added Subset of IVs
161(1)
5.6.2.4 Confidence Limits around B
162(1)
5.6.2.5 Comparing Two Sets of Predictors
163(1)
5.6.3 Adjustments of R(2)
164(1)
5.6.4 Suppressor Variables
165(1)
5.7 COMPARISON OF PROGRAMS
165(9)
5.7.1 SPSS Package
166(6)
5.7.2 BMDP Series
172(1)
5.7.3 SAS System
173(1)
5.7.4 SYSTAT System
173(1)
5.8 COMPLETE EXAMPLES OF REGRESSION ANALYSIS
174(18)
5.8.1 Evaluation of Assumptions
174(8)
5.8.1.1 Ratio of Cases to IVs
174(1)
5.8.1.2 Normality, Linearity, Homoscedasticity, and Independence of Residuals
174(4)
5.8.1.3 Outliers
178(1)
5.8.1.4 Multicollinearity and Singularity
179(3)
5.8.2 Standard Multiple Regression
182(3)
5.8.3 Sequential Regression
185(7)
5.9 SOME EXAMPLES FOR THE LITERATURE
192(3)
CHAPTER 6 Canonical Correlation
195(44)
6.1 GENERAL PURPOSE AND DESCRIPTION
195(1)
6.2 KINDS OF RESEARCH QUESTIONS
196(1)
6.2.1 Number of Canonical Variate Pairs
196(1)
6.2.2 Interpretations of Canonical Variates
196(1)
6.2.3 Importance of Canonical Variates
197(1)
6.2.4 Canonical Variate Scores
197(1)
6.3 LIMITATIONS
197(2)
6.3.1 Theoretical Limitations
197(1)
6.3.2 Practical Issues
198(1)
6.3.2.1 Ratio of Cases to IVs
198(1)
6.3.2.2 Normality, Linearity, and Homoscedasticity
198(1)
6.3.2.3 Missing Data
199(1)
6.3.2.4 Outliers
199(1)
6.3.2.5 Multicollinearity and Singularity
199(1)
6.4 FUNDAMENTAL EQUATIONS FOR CANONICAL CORRELATION
199(21)
6.4.1 Eigenvalues and Eigenvectors
200(3)
6.4.2 Matrix Equations
203(2)
6.4.3 Proportions of Variance Extracted
205(2)
6.4.4 Computer Analyses of Small Sample Example
207(13)
6.5 SOME IMPORTANT ISSUES
220(2)
6.5.1 Importance of Canonical Variates
220(1)
6.5.2 Interpretation of Canonical Variates
221(1)
6.6 COMPARISON OF PROGRAMS
222(2)
6.6.1 SPSS Package
222(1)
6.6.2 BMDP Series
222(2)
6.6.3 SAS System
224(1)
6.6.4 SYSTAT System
224(1)
6.7 COMPLETE EXAMPLE OF CANONICAL CORRELATION
224(13)
6.7.1 Evaluation of Assumptions
227(3)
6.7.1.1 Missing Data
227(1)
6.7.1.2 Normality, Linearity, and Homoscedasticity
227(3)
6.7.1.3 Outliers
230(1)
6.7.1.4 Multicollinearity and Singularity
230(1)
6.7.2 Canonical Correlation
230(7)
6.8 SOME EXAMPLES FROM THE LITERATURE
237(2)
CHAPTER 7 Multiway Frequency Analysis
239(82)
7.1 GENERAL PURPOSE AND DESCRIPTION
239(1)
7.2 KINDS OF RESEARCH QUESTIONS
240(2)
7.2.1 Associations among Variables
240(1)
7.2.2 Effect on a Dependent Variable
240(1)
7.2.3 Parameter Estimates
241(1)
7.2.4 Importance of Effects
241(1)
7.2.5 Strength of Association
241(1)
7.2.6 Specific Comparisons and Trend Analysis
242(1)
7.3 LIMITATIONS TO MULTIWAY FREQUENCY ANALYSIS
242(2)
7.3.1 Theoretical Issues
242(1)
7.3.2 Practical Issues
242(2)
7.3.2.1 Independence
242(1)
7.3.2.2 Ratio of Cases to Variables
243(1)
7.3.2.3 Adequacy of Expected Frequencies
243(1)
7.3.2.4 Outliers in the Solution
244(1)
7.4 FUNDAMENTAL EQUATIONS FOR MULTIWAY FREQUENCY ANALYSIS
244(35)
7.4.1 Screening for Effects
245(8)
7.4.1.1 Total Effects
246(1)
7.4.1.2 First-Order Effects
247(1)
7.4.1.3 Second-Order Effects
248(5)
7.4.1.4 Third-Order Effects
253(1)
7.4.2 Modeling
253(3)
7.4.3 Evaluation and Interpretation
256(5)
7.4.3.1 Residuals
256(1)
7.4.3.2 Parameter Estimates
256(5)
7.4.4 Computer Analyses of Small Sample Example
261(18)
7.5 SOME IMPORTANT ISSUES
279(6)
7.5.1 Hierarchical and Nonheirarchical Models
279(1)
7.5.2 Statistical Criteria
279(2)
7.5.2.1 Tests of Models
279(1)
7.5.2.2 Tests of Individual Effects
280(1)
7.5.3 One Variable as DV (Logit Analysis)
281(1)
7.5.3.1 Program for Logit Analysis
281(1)
7.5.3.2 Odds Ratios
282(1)
7.5.4 Strategies for Choosing a Model
282(2)
7.5.4.1 BMDP4F (Hierarchical)
283(1)
7.5.4.2 SPSS HILOGLINEAR (Hierarchical)
284(1)
7.5.4.3 SPSS LOGLINEAR and GENLOG (General Loglinear)
284(1)
7.5.4.4 SAS CATMOD and SYSTAT LOGLIN (General Loglinear)
284(1)
7.5.5 Contrasts
284(1)
7.6 COMPARISON OF PROGRAMS
285(6)
7.6.1 SPSS Package
290(1)
7.6.2 BMDP Series
290(1)
7.6.3 SAS System
291(1)
7.6.4 SYSTAT System
291(1)
7.7 COMPLETE EXAMPLE OF MULTIWAY FREQUENCY ANALYSIS
291(26)
7.7.1 Evaluation of Assumptions: Adequacy of Expected Frequencies
291(1)
7.7.2 Hierarchical Loglinear analysis
292(25)
7.7.2.1 Preliminary Model Screening
292(3)
7.7.2.2 Stepwise Model Selection
295(7)
7.7.2.3 Adequacy of Fit
302(1)
7.7.2.4 Interpretation of the Selected Model
302(15)
7.8 SOME EXAMPLES FROM THE LITERATURE
317(4)
CHAPTER 8 Analysis of Covariance
321(54)
8.1 GENERAL PURPOSE AND DESCRIPTION
321(3)
8.2 KINDS OF RESEARCH QUESTIONS
324(2)
8.2.1 Main Effects of IVs
324(1)
8.2.2 Interactions among IVs
325(1)
8.2.3 Specific Comparisons and Trend Analysis
325(1)
8.2.4 Effects of Covariates
325(1)
8.2.5 Strength of Association
325(1)
8.2.6 Adjusted Marginal and Cell Means
326(1)
8.3 LIMITATIONS TO ANALYSIS OF COVARIANCE
326(4)
8.3.1 Theoretical Issues
326(1)
8.3.2 Practical Issues
327(3)
8.3.2.1 Unequal Sample Sizes and Missing Data
327(1)
8.3.2.2 Outliers
327(1)
8.3.2.3 Multicollinearity and Singularity
328(1)
8.3.2.4 Normality
328(1)
8.3.2.5 Homogeneity of Variance
328(1)
8.3.2.6 Linearity
329(1)
8.3.2.7 Homogeneity of Regression
329(1)
8.3.2.8 Reliability of Covariates
330(1)
8.4 FUNDAMENTAL EQUATIONS FOR ANALYSIS OF COVARIANCE
330(8)
8.4.1 Sums of Squares and Cross Products
331(4)
8.4.2 Significance Test and Strength of Association
335(1)
8.4.3 Computer Analyses of Small Sample Example
336(2)
8.5 SOME IMPORTANT ISSUES
338(14)
8.5.1 Test for Homogeneity of Regression
338(4)
8.5.2 Design Complexity
342(7)
8.5.2.1 Within-Subjects and Mixed Within-Between Designs
343(1)
8.5.2.2 Unequal Sample Sizes
344(2)
8.5.2.3 Specific Comparisons and Trend Analysis
346(2)
8.5.2.4 Strength of Association
348(1)
8.5.3 Evaluation of Covariates
349(1)
8.5.4 Choosing Covariates
350(1)
8.5.5 Alternatives to ANCOVA
350(2)
8.6 COMPARISON OF PROGRAMS
352(5)
8.6.1 BMDP Series
352(4)
8.6.2 SPSS Package
356(1)
8.6.3 SYSTAT System
356(1)
8.6.4 SAS System
356(1)
8.7 COMPLETE EXAMPLE OF ANALYSIS OF COVARIANCE
357(16)
8.7.1 Evaluation of Assumptions
357(7)
8.7.1.1 Unequal n and Missing Data
357(1)
8.7.1.2 Normality
357(3)
8.7.1.3 Linearity
360(1)
8.7.1.4 Outliers
360(1)
8.7.1.5 Multicollinearity and Singularity
360(4)
8.7.1.6 Homogeneity of Variance
364(1)
8.7.1.7 Homogeneity of Regression
364(1)
8.7.1.8 Reliability of Covariates
364(1)
8.7.2 Analysis of Covariance
364(9)
8.8 SOME EXAMPLES FROM THE LITERATURE
373(2)
CHAPTER 9 Multivariate Analysis of Variance and Covariance
375(66)
9.1 GENERAL PURPOSE AND DESCRIPTION
375(2)
9.2 KINDS OF RESEARCH QUESTIONS
377(3)
9.2.1 Main Effects of IVs
378(1)
9.2.2 Interactions among IVs
378(1)
9.2.3 Importance of DVs
378(1)
9.2.4 Adjusted Marginal and Cell Means
378(1)
9.2.5 Specific Comparisons and Trend Analysis
379(1)
9.2.6 Strength of Association
379(1)
9.2.7 Effects of Covariates
379(1)
9.2.8 Repeated-Measures Analysis of Variance
379(1)
9.3 LIMITATIONS TO MULTIVARIATE ANALYSIS OF VARIANCE AND COVARIANCE
380(4)
9.3.1 Theoretical Issues
380(1)
9.3.2 Practical Issues
380(4)
9.3.2.1 Unequal Sample Sizes and Missing Data
381(1)
9.3.2.2 Multivariate Normality
381(1)
9.3.2.3 Outliers
381(1)
9.3.2.4 Homogeneity of Variance-Covariance Matrices
382(1)
9.3.2.5 Linearity
382(1)
9.3.2.6 Homogeneity of Regression
383(1)
9.3.2.7 Reliability of Covariates
383(1)
9.3.2.8 Multicollinearity and Singularity
383(1)
9.4 FUNDAMENTAL EQUATIONS FOR MULTIVARIATE ANALYSIS OF VARIANCE AND COVARIANCE
384(16)
9.4.1 Multivariate Analysis of Variance
384(7)
9.4.2 Computer Analyses of Small Sample Example
391(3)
9.4.3 Multivariate Analysis of Covariance
394(6)
9.5 SOME IMPORTANT ISSUES
400(7)
9.5.1 Criteria for Statistical Inference
400(2)
9.5.2 Assessing DVs
402(3)
9.5.2.1 Univariate F
402(1)
9.5.2.2 Roy-Bargmann Stepdown Analysis
403(1)
9.5.2.3 Choosing among Strategies for Assessing DVs
404(1)
9.5.3 Specific Comparisons and Trend Analysis
405(1)
9.5.4 Design Complexity
405(1)
9.5.4.1 Within-Subjects and Between-Within Designs
405(1)
9.5.4.2 Unequal Sample Sizes
406(1)
9.5.5 MANOVA vs. ANOVAs
406(1)
9.6 COMPARISON OF PROGRAMS
407(4)
9.6.1 SPSS Package
407(2)
9.6.2 BMDP Series
409(1)
9.6.3 SYSTAT System
410(1)
9.6.4 SAS System
410(1)
9.7 COMPLETE EXAMPLES OF MULTIVARIATE ANALYSIS OF VARIANCE AND COVARIANCE
411(27)
9.7.1 Evaluation of Assumptions
412(3)
9.7.1.1 Unequal Sample Sizes and Missing Data
412(1)
9.7.1.2 Multivariate Normality
413(1)
9.7.1.3 Linearity
413(1)
9.7.1.4 Outliers
413(1)
9.7.1.5 Homogeneity of Variance-Covariance Matrices
413(1)
9.7.1.6 Homogeneity of Regression
413(2)
9.7.1.7 Reliability of Covariates
415(1)
9.7.1.8 Multicollinearity and Singularity
415(1)
9.7.2 Multivariate Analysis of Variance
415(13)
9.7.3 Multivariate Analysis of Covariance
428(10)
9.7.3.1 Assessing Covariates
428(3)
9.7.3.2 Assessing DVs
431(7)
9.8 SOME EXAMPLES FROM THE LITERATURE
438(3)
9.8.1 Examples of MANOVA
438(1)
9.8.2 Examples of MANCOVA
439(2)
CHAPTER 10 Profile Analysis of Repeated Measures
441(66)
10.1 GENERAL PURPOSE AND DESCRIPTION
441(1)
10.2 KINDS OF RESEARCH QUESTIONS
442(1)
10.2.1 Parallelism of Profiles
442(1)
10.2.2 Overall Difference among Groups
442(1)
10.2.3 Flatness of Profiles
442(1)
10.2.4 Contrasts Following Profile Analysis
443(1)
10.2.5 Marginal/Cell Means and Plots
443(1)
10.2.6 Strength of Association
443(1)
10.2.7 Treatment Effects in Multiple Time-Series Designs
443(1)
10.3 LIMITATIONS TO PROFILE ANALYSIS
443(2)
10.3.1 Theoretical Issues
443(1)
10.3.2 Practical Issues
444(1)
10.3.2.1 Sample Size and Missing Data
444(1)
10.3.2.2 Multivariate Normality
444(1)
10.3.2.3 Outliers
445(1)
10.3.2.4 Homogeneity of Variance-Covariance Matrices
445(1)
10.3.2.5 Linearity
445(1)
10.3.2.6 Multicollinearity and Singularity
445(1)
10.4 FUNDAMENTAL EQUATIONS FOR PROFILE ANALYSIS
445(14)
10.4.1 Differences in Levels
447(1)
10.4.2 Parallelism
448(2)
10.4.3 Flatness
450(1)
10.4.4 Computer Analyses of Small Sample Example
451(8)
10.5 SOME IMPORTANT ISSUES
459(29)
10.5.1 Contrasts in Profile Analysis
459(15)
10.5.1.1 Parallelism and Flatness Significant, Levels Not Significant (Simple Effects Analysis)
462(4)
10.5.1.2 Parallelism and Levels Significant, Flatness Not Significant (Simple Effects Analysis)
466(8)
10.5.1.3 Parallelism, Levels, and Flatness Significant (Interaction Contrast)
470(4)
10.5.1.4 Only Parallelism Significant
474(1)
10.5.2 Multivariate Approach to Repeated Measures
474(2)
10.5.3 Doubly Multivariate Designs
476(7)
10.5.3.1 Kinds of Doubly Multivariate Analysis
476(1)
10.5.3.2 Example of Doubly Multivariate Analysis of Variance
477(6)
10.5.4 Classifying Profiles
483(5)
10.6 COMPARISON OF PROGRAMS
488(2)
10.6.1 SPSS Package
488(1)
10.6.2 BMDP Series
488(1)
10.6.3 SAS System
490(1)
10.6.4 SYSTAT System
490(1)
10.7 COMPLETE EXAMPLE OF PROFILE ANALYSIS
490(14)
10.7.1 Evaluation of Assumptions
491(4)
10.7.1.1 Unequal Sample Sizes and Missing Data
491(1)
10.7.1.2 Multivariate Normality
491(4)
10.7.1.3 Linearity
495(1)
10.7.1.4 Outliers
495(1)
10.7.1.5 Homogeneity of Variance-Covariance Matrices
495(1)
10.7.1.6 Multicollinearity and Singularity
495(1)
10.7.2 Profile Analysis
495(9)
10.8 SOME EXAMPLES FROM THE LITERATURE
504(3)
CHAPTER 11 Discriminant Function Analysis
507(68)
11.1 GENERAL PURPOSE AND DESCRIPTION
507(2)
11.2 KINDS OF RESEARCH QUESTIONS
509(2)
11.2.1 Significance of Prediction
509(1)
11.2.2 Number of Significant Discriminant Functions
509(1)
11.2.3 Dimensions of Discrimination
509(1)
11.2.4 Classification of Functions
510(1)
11.2.5 Adequacy of Classification
510(1)
11.2.6 Strength of Association
510(1)
11.2.7 Importance of Predictor Variables
510(1)
11.2.8 Significance of Prediction with Covariates
511(1)
11.2.9 Estimation of Group Means
511(1)
11.3 LIMITATIONS TO DISCRIMINANT FUNCTION ANALYSIS
511(3)
11.3.1 Theoretical Issues
511(1)
11.3.2 Practical Issues
512(2)
11.3.2.1 Unequal Sample Sizes and Missing Data
512(1)
11.3.2.2 Multivariate Normality
512(1)
11.3.2.3 Outliers
513(1)
11.3.2.4 Homogeneity of Variance-Covariance Matrices
513(1)
11.3.2.5 Linearity
514(1)
11.3.2.6 Multicollinearity and Singularity
514(1)
11.4 FUNDAMENTAL EQUATIONS FOR DISCRIMINANT FUNCTION ANALYSIS
514(14)
11.4.1 Derivation and Test of Discriminant Functions
514(3)
11.4.2 Classification
517(3)
11.4.3 Computer Analyses of Small Sample Example
520(8)
11.5 TYPES OF DISCRIMINANT FUNCTION ANALYSIS
528(5)
11.5.1 Direct Discriminant Function Analysis
528(1)
11.5.2 Sequential Discriminant Function Analysis
529(3)
11.5.3 Stepwise (Statistical) Discriminant Function Analysis
532(1)
11.6 SOME IMPORTANT ISSUES
533(13)
11.6.1 Statistical Inference
533(3)
11.6.1.1 Criteria for Overall Statistical Significance
533(1)
11.6.1.2 Stepping Methods
533(3)
11.6.2 Number of Discriminant Functions
536(1)
11.6.3 Interpreting Discriminant Functions
536(4)
11.6.3.1 Discriminant Function Plots
538(1)
11.6.3.2 Loading Matrices
539(1)
11.6.4 Evaluating Predictor Variables
540(2)
11.6.5 Design Complexity: Factorial Designs
542(1)
11.6.6 Use of Classification Procedures
543(3)
11.6.6.1 Cross-Validation and New Cases
544(1)
11.6.6.2 Jackknifed Classification
545(1)
11.6.6.3 Evaluating Improvement in Classification
545(1)
11.7 COMPARISON OF PROGRAMS
546(8)
11.7.1 SPSS Package
553(1)
11.7.2 BMDP Series
553(1)
11.7.3 SYSTAT System
554(1)
11.7.4 SAS System
554(1)
11.8 COMPLETE EXAMPLE OF DISCRIMINANT FUNCTION ANALYSIS
554(19)
11.8.1 Evaluation of Assumptions
555(1)
11.8.1.1 Unequal Sample Sizes and Missing Data
555(1)
11.8.1.2 Multivariate Normality
555(1)
11.8.1.3 Linearity
555(1)
11.8.1.4 Outliers
556(1)
11.8.1.5 Homogeneity of Variance-Covariance Matrices
556(1)
11.8.1.6 Multicollinearity and Singularity
556(1)
11.8.2 Direct Discriminant Function Analysis
556(17)
11.9 SOME EXAMPLES FROM THE LITERATURE
573(2)
CHAPTER 12 Logistic Regression
575(60)
12.1 GENERAL PURPOSE AND DESCRIPTION
575(1)
12.2 KINDS OF RESEARCH QUESTIONS
576(2)
12.2.1 Prediction of Group Membership of Outcome
576(1)
12.2.2 Importance of Predictors
577(1)
12.2.3 Interactions among Predictors
577(1)
12.2.4 Parameter Estimates
577(1)
12.2.5 Classification of Cases
577(1)
12.2.6 Significance of Prediction with Covariates
578(1)
12.2.7 Strength of Association
578(1)
12.3 LIMITATIONS TO LOGISTIC REGRESSION ANALYSIS
578(2)
12.3.1 Theoretical Issues
578(1)
12.3.2 Practical Issues
579(1)
12.3.2.1 Ratio of Cases to Variables
579(1)
12.3.2.2 Adequacy of Expected Frequencies
579(1)
12.3.2.3 Multicollinearity
580(1)
12.3.2.4 Outliers in the Solution
580(1)
12.4 FUNDAMENTAL EQUATIONS FOR LOGISTIC REGRESSION
580(7)
12.4.1 Testing and Interpreting Coefficients
581(1)
12.4.2 Goodness-of-fit
582(1)
12.4.3 Comparing Models
583(1)
12.4.4 Interpretation and Analysis of Residuals
584(1)
12.4.5 Computer Analyses of Small Sample Example
585(2)
12.5 TYPES OF LOGISTIC REGRESSION
587(7)
12.5.1 Direct Logistic Regression
587(4)
12.5.2 Sequential Logistic Regression
591(1)
12.5.3 Stepwise (Statistical) Logistic Regression
592(2)
12.6 SOME IMPORTANT ISSUES
594(15)
12.6.1 Statistical Inference
594(5)
12.6.1.1 Assessing Goodness-of-Fit of Models
594(4)
12.6.1.2 Tests of Individual Variables
598(1)
12.6.2 Number and Type of Outcome Categories
599(7)
12.6.2.1 Ordered Response Categories with BMDPPR
600(2)
12.6.2.2 Ordered Response Categories with SAS LOGISTIC
602(3)
12.6.2.3 Coding Outcome and Predictor Categories
605(1)
12.6.3 Classification of Cases
606(1)
12.6.4 Hierarchical and Nonhierarchical Analysis
607(1)
12.6.5 Dosage-Response Relationships
607(1)
12.6.6 Interpretation of Coefficients Using Odds
607(1)
12.6.7 Logistic Regression for Matched Groups
608(1)
12.7 COMPARISON OF PROGRAMS
609(6)
12.7.1 SPSS Package
609(4)
12.7.2 BMDP Series
613(1)
12.7.3 SAS System
614(1)
12.7.4 SYSTAT System
614(1)
12.8 COMPLETE EXAMPLES OF LOGISTIC REGRESSION
615(17)
12.8.1 Evaluation of Limitations
615(3)
12.8.1.1 Adequacy of Expected Frequencies
615(3)
12.8.1.2 Ratio of Cases to Variables
618(1)
12.8.1.3 Multicollinearity
618(1)
12.8.1.4 Outliers in the Solution
618(1)
12.8.2 Direct Logistic Regression with Two-Category Outcome
618(6)
12.8.3 Sequential Logistic Regression with Three Categories of Outcome
624(8)
12.9 SOME EXAMPLES FROM THE LITERATURE
632(3)
CHAPTER 13 Principal Components and Factor Analysis
635(74)
13.1 GENERAL PURPOSE AND DESCRIPTION
635(2)
13.2 KINDS OF RESEARCH QUESTIONS
637(2)
13.2.1 Number of Factors
638(1)
13.2.2 Nature of Factors
638(1)
13.2.3 Importance of Solutions and Factors
638(1)
13.2.4 Testing theory in FA
638(1)
13.2.5 Estimating Scores on Factors
638(1)
13.3 LIMITATIONS
639(3)
13.3.1 Theoretical Issues
639(1)
13.3.2 Practical Issues
640(2)
13.3.2.1 Sample Size and Missing Data
640(1)
13.3.2.2 Normality
640(1)
13.3.2.3 Linearity
641(1)
13.3.2.4 Outliers among Cases
641(1)
13.3.2.5 Multicollinearity and Singularity
641(1)
13.3.2.6 Factorability of R
641(1)
13.3.2.7 Outliers among Variables
642(1)
13.3.2.8 Outlying Cases among the Factors
642(1)
13.4 FUNDAMENTAL EQUATIONS FOR FACTOR ANALYSIS
642(18)
13.4.1 Extraction
644(3)
13.4.2 Orthogonal Rotation
647(1)
13.4.3 Communalities, Variance, and Covariance
648(1)
13.4.4 Factor Scores
649(2)
13.4.5 Oblique Rotation
651(2)
13.4.6 Computer Analyses of Small Sample Example
653(7)
13.5 MAJOR TYPES OF FACTOR ANALYSIS
660(11)
13.5.1 Factor Extraction Techniques
660(6)
13.5.1.1 PCA vs. FA
662(2)
13.5.1.2 Principal Components
664(1)
13.5.1.3 Principal Factors
664(1)
13.5.1.4 Image Factor Extraction
664(1)
13.5.1.5 Maximum Likelihood Factor Extraction
665(1)
13.5.1.6 Unweighted Least Squares Factoring
665(1)
13.5.1.7 Generalized (Weighted) Least Factoring
665(1)
13.5.1.8 Alpha Factoring
666(1)
13.5.2 Rotation
666(4)
13.5.2.1 Orthogonal Rotation
666(2)
13.5.2.2 Oblique Rotation
668(1)
13.5.2.3 Geometric Interpretation
669(1)
13.5.3 Some Practical Recommendations
670(1)
13.6 SOME IMPORTANT ISSUES
671(8)
13.6.1 Estimates of Communalities
671(1)
13.6.2 Adequacy of Extraction and Number of Factors
672(2)
13.6.3 Adequacy of Rotation and Simple Structure
674(1)
13.6.4 Importance and Internal Consistency of Factors
675(2)
13.6.5 Interpretation of Factors
677(1)
13.6.6 Factor Scores
378(1)
13.6.7 Comparisons among Solutions and Groups
679(1)
13.7 COMPARISON OF PROGRAMS
679(5)
13.7.1 SPSS Package
679(4)
13.7.2 BMDP Series
683(1)
13.7.3 SAS System
683(1)
13.7.4 SYSTAT System
683(1)
13.8 COMPLETE EXAMPLE OF FA
684(22)
13.8.1 Evaluation of Limitations
684(5)
13.8.1.1 Sample Size and Missing Data
684(1)
13.8.1.2 Normality
684(1)
13.8.1.3 Linearity
685(1)
13.8.1.4 Outliers among Cases
685(1)
13.8.1.5 Multicollinearity and Singularity
685(1)
13.8.1.6 Factorability of R
685(1)
13.8.1.7 Outliers among Variables
685(4)
13.8.1.8 Outlying Cases among the Factors
689(1)
13.8.2 Principal Factors Extraction with Varimax Rotation
689(17)
13.9 SOME EXAMPLES FROM THE LITERATURE
706(3)
CHAPTER 14 Structural Equation Modeling
709(104)
Jodie B. Ullman
14.1 GENERAL PURPOSE AND DESCRIPTION
709(3)
14.2 KINDS OF RESEARCH QUESTIONS
712(2)
14.2.1 Adequacy of the Model
713(1)
14.2.2 Testing Theory
713(1)
14.2.3 Amount of Variance a Variable Accounted for by a Factor
713(1)
14.2.4 Reliability of the Indicators
713(1)
14.2.5 Parameter Estimated
713(1)
14.2.6 Mediation
714(1)
14.2.7 Group Differences
714(1)
14.2.8 Longitudinal Differences
714(1)
14.3 LIMITATIONS TO STRUCTURAL EQUATION MODELING
714(3)
14.3.1 Theoretical Issues
714(1)
14.3.2 Practical Issues
715(2)
14.3.2.1 Sample Size and Missing Data
715(1)
14.3.2.2 Multivariate Normality and Outliers
715(1)
14.3.2.3 Linearity
716(1)
14.3.2.4 Multicollinearity and Singularity
716(1)
14.3.2.5 Analyzability of Covariances
716(1)
14.3.2.6 Residuals
716(1)
14.4 FUNDAMENTAL EQUATIONS FOR STRUCTURAL EQUATIONS MODELING
717(26)
14.4.1 Covariance Algebra
717(2)
14.4.2 Model Hypotheses
719(1)
14.4.3 Model Specifications
720(3)
14.4.4 Model Estimation
723(5)
14.4.5 Model Evaluation
728(1)
14.4.6 Computer Analysis of Small Sample Example
729(14)
14.5 SOME IMPORTANT ISSUES
743(24)
14.5.1 Model Identification
743(3)
14.5.2 Estimation Techniques
746(2)
14.5.2.1 Estimation Methods and Sample Size
747(1)
14.5.2.2 Estimation Methods and Nonnormality
747(1)
14.5.2.3 Estimation Methods and Dependence
748(1)
14.5.2.4 Some Recommendations for Estimation Method
748(1)
14.5.3 Assessing the Fit of the Model
748(4)
14.5.3.1 Comparative Fit Indices
749(1)
14.5.3.2 Absolute Fit Index
750(1)
14.5.3.3 Indices of Proporation of Variance Accounted For
750(1)
14.5.3.4 Degree of Parsimony Fit Indices
751(1)
14.5.3.5 Residual Based Fit Indices
752(1)
14.5.3.6 Choosing among Fit Indices
752(1)
14.5.4 Model Modification
752(11)
14.5.4.1 Chi-Square Difference Test
752(1)
14.5.4.2 Lagrange Multiplier Test (LM)
753(5)
14.5.4.3 Wald Test
758(1)
14.5.4.4 Some Caveats and Hints on Model Modification
758(5)
14.5.5 Reliability and Proporation of Variance
763(1)
14.5.6 Discrete and Ordinal Data
764(1)
14.5.7 Multiple Group Models
765(1)
14.5.8 Mean and Covariance Structure Models
766(1)
14.6 COMPARISON OF PROGRAMS
767(5)
14.6.1 EQS
767(1)
14.6.2 LISREL
767(5)
14.6.3 SAS
772(1)
14.6.4 SYSTAT
772(1)
14.7 COMPLETE EXAMPLES OF STRUCTURAL EQUATION MODELING ANALYSIS
772(38)
14.7.1 Model Specification for CFA
772(2)
14.7.2 Evaluation of Assumptions for CFA
774(1)
14.7.2.1 Sample Size and Missing Data
774(1)
14.7.2.2 Normality and Linearity
774(1)
14.7.2.3 Outliers
774(1)
14.7.2.4 Multicollinearity and Singularity
774(1)
14.7.2.5 Residuals
774(1)
14.7.3 CFA Model Estimation and Preliminary Evaluation
774(9)
14.7.4 Model Modification
783(6)
14.7.5 SEM Model Specification
789(1)
14.7.6 Evaluation of Assumptions for SEM
789(5)
14.7.6.1 Sample Size and Missing Data
789(1)
14.7.6.2 Normality and Linearity
789(4)
14.7.6.3 Outliers
793(1)
14.7.6.4 Multicollinearity and Singularity
793(1)
14.7.6.5 Adequacy of Covariances
793(1)
14.7.6.6 Residuals
794(1)
14.7.7 SEM Model Estimation and Preliminary Evaluation
794(2)
14.7.8 Model Modification
796(14)
14.8 SOME EXAMPLES FROM THE LITERATURE
810(3)
CHAPTER 15 An Overview of the General Linear Model
813(8)
15.1 LINEARITY AND THE GENERAL LINEAR MODEL
813(1)
15.2 BIVARIATE TO MULTIVARIATE STATISTICS AND OVERVIEW OF TECHNIQUES
814(4)
15.2.1 Bivariate Form
814(1)
15.2.2 Simple Multivariate Form
814(2)
15.2.3 Full Multivariate Form
816(2)
15.3 ALTERNATIVE RESEARCH STRATEGIES
818(3)
Appendix A A Skimpy Introduction to Matrix Algebra
821(12)
A.1 THE TRACE OF A MATRIX
822(1)
A.2 ADDITION OF SUBTRACTION OF A CONSTANT TO A MATRIX
822(1)
A.3 MULTIPLICATION OR DIVISION OF A MATRIX BY A CONSTANT
822(1)
A.4 ADDITION AND SUBTRACTION OF TWO MATRICES
823(1)
A.5 MULTIPLICATION, TRANSPOSES, AND SQUARE ROOTS OF MATRICES
824(2)
A.6 MATRIX "DIVISION" (INVERSES AND DETERMINANTS)
826(2)
A.7 EIGENVALUES AND EIGENVECTORS: PROCEDURES FOR CONSOLIDATING VARIANCE FROM A MATRIX
828(5)
Appendix B Research Designs for Complete Examples
833(6)
B.1 WOMEN'S HEALTH AND DRUG STUDY
833(1)
B.2 LEARNING DISABILITIES DATA BANK
834(3)
B.3 SEXUAL ATTRACTION STUDY
837(2)
Appendix C Statistical Tables
839(12)
References851(10)
Index861

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