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Applied Multiple Regression - Correlation Analysis for the Behavioral Sciences

by ;
Edition:
3rd
ISBN13:

9780805822236

ISBN10:
0805822232
Format:
Hardcover
Pub. Date:
8/1/2002
Publisher(s):
Lawrence Erlbau
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Summary

This classic text on multiple regression is noted for its non-mathematical, applied, and data-analytic approach. Readers profit from its verbal-conceptual exposition and frequent use of examples. The applied emphasis provides clear illustrations of the principles and provides worked examples of the types of applications that are possible. Researchers learn how to specify regression models that directly address their research questions. An overview of the fundamental ideas of multiple regression and a review of bivariate correlation and regression and other elementary statistical concepts provide a strong foundation for a solid understanding of the rest of the text. The third edition features an increased emphasis on graphics and the use of confidence intervals and effect size measures and an accompanying CD with data for most of the numerical examples along with the computer code for SPSS, SAS, and SYSTAT. Applied Multiple Regression serves as both a textbook for graduate students and as a reference tool for researchers in psychology, education, health sciences, communications, business, sociology, political science, anthropology, and economics. An introductory knowledge of statistics is required. Self-standing chapters minimize the need for researchers to refer to previous chapters. The book is an ideal text for courses on multiple regression and correlational methods.

Author Biography

Jacob Cohen (deceased) New York University Patricia Cohen New York State Psychiatric Institute and Columbia University College of Physicians and Surgeons Stephen G. West Arizona State University Leona S. Aiken Arizona State University

Table of Contents

Preface xxv
Introduction
1(18)
Multiple Regression/Correlation as a General Data-Analytic System
1(3)
Overview
1(1)
Testing Hypotheses Using Multiple Regression/Correlation: Some Examples
2(1)
Multiple Regression/Correlation in Prediction Models
3(1)
A Comparison of Multiple Regression/Correlation and Analysis of Variance Approaches
4(2)
Historical Background
4(1)
Hypothesis Testing and Effect Sizes
5(1)
Multiple Regression/Correlation and the Complexity of Behavioral Science
6(4)
Multiplicity of Influences
6(1)
Correlation Among Research Factors and Partialing
6(1)
Form of Information
7(1)
Shape of Relationship
8(1)
General and Conditional Relationships
9(1)
Orientation of the Book
10(4)
Nonmathematical
11(1)
Applied
11(1)
Data-Analytic
12(1)
Inference Orientation and Specification Error
13(1)
Computation, the Computer, and Numerical Results
14(2)
Computation
14(1)
Numerical Results: Reporting and Rounding
14(1)
Significance Tests, Confidence Intervals, and Appendix Tables
15(1)
The Spectrum of Behavioral Science
16(1)
Plan for the Book
16(2)
Content
16(1)
Structure: Numbering of Sections, Tables, and Equations
17(1)
Summary
18(1)
Bivariate Correlation and Regression
19(45)
Tabular and Graphic Representations of Relationships
19(4)
The Index of Linear Correlation Between Two Variables: The Pearson Product Moment Correlation Coefficient
23(5)
Standard Scores: Making Units Comparable
23(3)
The Product Moment Correlation as a Function of Differences Between z Scores
26(2)
Alternative Formulas for the Product Moment Correlation Coefficient
28(4)
r as the Average Product of z Scores
28(1)
Raw Score Formulas for r
29(1)
Point Biserial r
29(1)
Phi (φ) Coefficient
30(1)
Rank Correlation
31(1)
Regression Coefficients: Estimating Y From X
32(4)
Regression Toward the Mean
36(1)
The Standard Error of Estimate and Measures of the Strength of Association
37(4)
Summary of Definitions and Interpretations
41(1)
Statistical Inference With Regression and Correlation Coefficients
41(9)
Assumptions Underlying Statistical Inference With Byx, B0, Yi, and rXY
41(1)
Estimation With Confidence Intervals
42(5)
Null Hypothesis Significance Tests (NHSTs)
47(3)
Confidence Limits and Null Hypothesis Significance Testing
50(1)
Precision and Power
50(3)
Precision of Estimation
50(1)
Power of Null Hypothesis Significance Tests
51(2)
Factors Affecting the Size of r
53(9)
The Distributions of X and Y
53(2)
The Reliability of the Variables
55(2)
Restriction of Range
57(2)
Part-Whole Correlations
59(1)
Ratio or Index Variables
60(2)
Curvilinear Relationships
62(1)
Summary
62(2)
Multiple Regression/Correlation With Two or More Independent Variables
64(37)
Introduction: Regression and Causal Models
64(2)
What Is a Cause?
64(1)
Diagrammatic Representation of Causal Models
65(1)
Regression With Two Independent Variables
66(3)
Measures of Association With Two Independent Variables
69(6)
Multiple R and R2
69(3)
Semipartial Correlation Coefficients and Increments to R2
72(2)
Partial Correlation Coefficients
74(1)
Patterns of Association Between Y and Two Independent Variables
75(4)
Direct and Indirect Effects
75(1)
Partial Redundancy
76(1)
Suppression in Regression Models
77(1)
Spurious Effects and Entirely Indirect Effects
78(1)
Multiple Regression/Correlation With k Independent Variables
79(7)
Introduction: Components of the Prediction Equation
79(1)
Partial Regression Coefficients
80(2)
R, R2, and Shrunken R2
82(2)
sr and sr2
84(1)
pr and pr2
85(1)
Example of Interpretation of Partial Coefficients
85(1)
Statistical Inference With k Independent Variables
86(4)
Standard Errors and Confidence Intervals for B and β
86(2)
Confidence Intervals for R2
88(1)
Confidence Intervals for Differences Between Independent R2s
88(1)
Statistical Tests on Multiple and Partial Coefficients
88(2)
Statistical Precision and Power Analysis
90(5)
Introduction: Research Goals and the Null Hypothesis
90(1)
The Precision and Power of R2
91(2)
Precision and Power Analysis for Partial Coefficients
93(2)
Using Multiple Regression Equations in Prediction
95(4)
Prediction of Y for a New Observation
95(1)
Correlation of Individual Variables With Predicted Values
96(1)
Cross-Validation and Unit Weighting
97(1)
Multicollinearity
98(1)
Summary
99(2)
Data Visualization, Exploration, and Assumption Checking: Diagnosing and Solving Regression Problems I
101(50)
Introduction
101(1)
Some Useful Graphical Displays of the Original Data
102(15)
Univariate Displays
103(7)
Bivariate Displays
110(5)
Correlation and Scatterplot Matrices
115(2)
Assumptions and Ordinary Least Squares Regression
117(8)
Assumptions Underlying Multiple Linear Regression
117(7)
Ordinary Least Squares Estimation
124(1)
Detecting Violations of Assumptions
125(16)
Form of the Relationship
125(2)
Omitted Independent Variables
127(2)
Measurement Error
129(1)
Homoscedasticity of Residuals
130(4)
Nonindependence of Residuals
134(3)
Normality of Residuals
137(4)
Remedies: Alternative Approaches When Problems Are Detected
141(9)
Form of the Relationship
141(2)
Inclusion of All Relevant Independent Variables
143(1)
Measurement Error in the Independent Variables
144(1)
Nonconstant Variance
145(2)
Nonindependence of Residuals
147(3)
Summary
150(1)
Data-Analytic Strategies Using Multiple Regression/Correlation
151(42)
Research Questions Answered by Correlations and Their Squares
151(3)
Net Contribution to Prediction
152(1)
Indices of Differential Validity
152(1)
Comparisons of Predictive Utility
152(1)
Attribution of a Fraction of the XY Relationship to a Third Variable
153(1)
Which of Two Variables Accounts for More of the XY Relationship?
153(1)
Are the Various Squared Correlations in One Population Different From Those in Another Given the Same Variables?
154(1)
Research Questions Answered by B or β
154(4)
Regression Coefficients as Reflections of Causal Effects
154(1)
Alternative Approaches to Making BYX Substantively Meaningful
154(3)
Are the Effects of a Set of Independent Variables on Two Different Outcomes in a Sample Different?
157(1)
What Are the Reciprocal Effects of Two Variables on One Another?
157(1)
Hierarchical Analysis Variables in Multiple Regression/Correlation
158(4)
Causal Priority and the Removal of Confounding Variables
158(2)
Research Relevance
160(1)
Examination of Alternative Hierarchical Sequences of Independent Variables Sets
160(1)
Stepwise Regression
161(1)
The Analysis of Sets of Independent Variables
162(9)
Types of Sets
162(2)
The Simultaneous and Hierarchical Analyses of Sets
164(2)
Variance Proportions for Sets and the Ballantine Again
166(3)
B and β Coefficients for Variables Within Sets
169(2)
Significance Testing for Sets
171(5)
Application in Hierarchical Analysis
172(1)
Application in Simultaneous Analysis
173(1)
Using Computer Output to Determine Statistical Significance
174(1)
An Alternative F Test: Using Model 2 Error Estimate From the Final Model
174(2)
Power Analysis for Sets
176(6)
Determining n* for the F Test of sR2B with Model 1 or Model 2 Error
177(2)
Estimating the Population sR2 Values
179(1)
Setting Power for n*
180(1)
Reconciling Different n*s
180(1)
Power as a Function of n
181(1)
Tactics of Power Analysis
182(1)
Statistical Inference Strategy in Multiple Regression/Correlation
182(8)
Controlling and Balancing Type I and Type II Errors in Inference
182(3)
Less Is More
185(1)
Least Is Last
186(1)
Adaptation of Fisher's Protected t Test
187(3)
Statistical Inference and the Stage of Scientific Investigations
190(1)
Summary
190(3)
Quantitative Scales, Curvilinear Relationships, and Transformations
193(62)
Introduction
193(3)
What Do We Mean by Linear Regression?
193(1)
Linearity in the Variables and Linear Multiple Regression
194(1)
Four Approaches to Examining Nonlinear Relationships in Multiple Regression
195(1)
Power Polynomials
196(18)
Method
196(2)
An Example: Quadratic Fit
198(3)
Centering Predictors in Polynomial Equations
201(3)
Relationship of Test of Significance of Highest Order Coefficient and Gain in Prediction
204(1)
Interpreting Polynomial Regression Results
205(2)
Another Example: A Cubic Fit
207(2)
Strategy and Limitations
209(4)
More Complex Equations
213(1)
Orthogonal Polynomials
214(7)
The Cubic Example Revisited
216(3)
Unequal n and Unequal Intervals
219(1)
Applications and Discussion
220(1)
Nonlinear Transformations
221(30)
Purposes of Transformation and the Nature of Transformations
221(2)
The Conceptual Basis of Transformations and Model Checking Before and After Transformation---Is It Always Ideal to Transform?
223(1)
Logarithms and Exponents; Additive and Proportional Relationships
223(2)
Linearizing Relationships
225(2)
Linearizing Relationships Based on Strong Theoretical Models
227(5)
Linearizing Relationships Based on Weak Theoretical Models
232(1)
Empirically Driven Transformations in the Absence of Strong or Weak Models
233(1)
Empirically Driven Transformation for Linearization: The Ladder of Re-expression and the Bulging Rule
233(3)
Empirically Driven Transformation for Linearization in the Absence of Models: Box-Cox Family of Power Transformations on Y
236(3)
Empirically Driven Transformation for Linearization in the Absence of Models: Box-Tidwell Family of Power Transformations on X
239(1)
Linearization of Relationships With Correlations: Fisher z Transform of r
240(1)
Transformations That Linearize Relationships for Counts and Proportions
240(4)
Variance Stabilizing Transformations and Alternatives for Treatment of Heteroscedasticity
244(2)
Transformations to Normalize Variables
246(1)
Diagnostics Following Transformation
247(1)
Measuring and Comparing Model Fit
248(1)
Second-Order Polynomial Numerical Example Revisited
248(1)
When to Transform and the Choice of Transformation
249(2)
Nonlinear Regression
251(1)
Nonparametric Regression
252(1)
Summary
253(2)
Interactions Among Continuous Variables
255(47)
Introduction
255(6)
Interactions Versus Additive Effects
256(3)
Conditional First-Order Effects in Equations Containing Interactions
259(2)
Centering Predictors and the Interpretation of Regression Coefficients in Equations Containing Interactions
261(6)
Regression with Centered Predictors
261(1)
Relationship Between Regression Coefficients in the Uncentered and Centered Equations
262(1)
Centered Equations With No Interaction
262(2)
Essential Versus Nonessential Multicollinearity
264(1)
Centered Equations With Interactions
264(2)
The Highest Order Interaction in the Centered Versus Uncentered Equation
266(1)
Do Not Center Y
266(1)
A Recommendation for Centering
266(1)
Simple Regression Equations and Simple Slopes
267(5)
Plotting Interactions
269(1)
Moderator Variables
269(1)
Simple Regression Equations
269(1)
Overall Regression Coefficient and Simple Slope at the Mean
270(1)
Simple Slopes From Uncentered Versus Centered Equations Are Identical
271(1)
Linear by Linear Interactions
271(1)
Interpreting Interactions in Multiple Regression and Analysis of Variance
272(1)
Post Hoc Probing of Interactions
272(10)
Standard Error of Simple Slopes
272(1)
Equation Dependence of Simple Slopes and Their Standard Errors
273(1)
Tests of Significance of Simple Slopes
273(1)
Confidence Intervals Around Simple Slopes
274(1)
A Numerical Example
275(6)
The Uncentered Regression Equation Revisited
281(1)
First-Order Coefficients in Equations Without and With Interactions
281(1)
Interpretation and the Range of Data
282(1)
Standardized Estimates for Equations Containing Interactions
282(2)
Interactions as Partialed Effects: Building Regression Equations With Interactions
284(1)
Patterns of First-Order and Interactive Effects
285(5)
Three Theoretically Meaningful Patterns of First-Order and Interaction Effects
285(1)
Ordinal Versus Disordinal Interactions
286(4)
Three-Predictor Interactions in Multiple Regression
290(2)
Curvilinear by Linear Interactions
292(3)
Interactions Among Sets of Variables
295(2)
Issues in the Detection of Interactions: Reliability, Predictor Distributions, Model Specification
297(3)
Variable Reliability and Power to Detect Interactions
297(1)
Sampling Designs to Enhance Power to Detect Interactions---Optimal Design
298(1)
Difficulty in Distinguishing Interactions Versus Curvilinear Effects
299(1)
Summary
300(2)
Categorical or Nominal Independent Variables
302(52)
Introduction
302(1)
Categories as a Set of Independent Variables
302(1)
The Representation of Categories or Nominal Scales
302(1)
Dummy-Variable Coding
303(17)
Coding the Groups
303(5)
Pearson Correlations of Dummy Variables With Y
308(3)
Correlations Among Dummy-Coded Variables
311(1)
Multiple Correlation of the Dummy-Variable Set With Y
311(1)
Regression Coefficients for Dummy Variables
312(4)
Partial and Semipartial Correlations for Dummy Variables
316(1)
Dummy-Variable Multiple Regression/Correlation and One-Way Analysis of Variance
317(2)
A Cautionary Note: Dummy-Variable-Like Coding Systems
319(1)
Dummy-Variable Coding When Groups Are Not Mutually Exclusive
320(1)
Unweighted Effects Coding
320(8)
Introduction: Unweighted and Weighted Effects Coding
320(1)
Constructing Unweighted Effects Codes
321(3)
The R2 and the ryiS for Unweighted Effects Codes
324(1)
Regression Coefficients and Other Partial Effects in Unweighted Code Sets
325(3)
Weighted Effects Coding
328(4)
Selection Considerations for Weighted Effects Coding
328(1)
Constructing Weighted Effects
328(2)
The R2 and R2 for Weighted Effects Codes
330(1)
Interpretation and Testing of B With Unweighted Codes
331(1)
Contrast Coding
332(9)
Considerations in the Selection of a Contrast Coding Scheme
332(1)
Constructing Contrast Codes
333(4)
The R2 and R2
337(1)
Partial Regression Coefficients
337(3)
Statistical Power and the Choice of Contrast Codes
340(1)
Nonsense Coding
341(1)
Coding Schemes in the Context of Other Independent Variables
342(9)
Combining Nominal and Continuous Independent Variables
342(1)
Calculating Adjusted Means for Nominal Independent Variables
343(1)
Adjusted Means for Combinations of Nominal and Quantitative Independent Variables
344(4)
Adjusted Means for More Than Two Groups and Alternative Coding Methods
348(2)
Multiple Regression/Correlation With Nominal Independent Variables and the Analysis of Covariance
350(1)
Summary
351(3)
Interactions With Categorical Variables
354(36)
Nominal Scale by Nominal Scale Interactions
354(12)
The 2 by 2 Design
354(7)
Regression Analyses of Multiple Sets of Nominal Variables With More Than Two Categories
361(5)
Interactions Involving More Than Two Nominal Scales
366(9)
An Example of Three Nominal Scales Coded by Alternative Methods
367(5)
Interactions Among Nominal Scales in Which Not All Combinations Are Considered
372(1)
What If the Categories for One or More Nominal ``Scales'' Are Not Mutually Exclusive?
373(1)
Consideration of pr, β, and Variance Proportions for Nominal Scale Interaction Variables
374(1)
Summary of Issues and Recommendations for Interactions Among Nominal Scales
374(1)
Nominal Scale by Continuous Variable Interactions
375(13)
A Reminder on Centering
375(1)
Interactions of a Continuous Variable With Dummy-Variable Coded Groups
375(3)
Interactions Using Weighted or Unweighted Effects Codes
378(1)
Interactions With a Contrast-Coded Nominal Scale
379(1)
Interactions Coded to Estimate Simple Slopes of Groups
380(3)
Categorical Variable Interactions With Nonlinear Effects of Scaled Independent Variables
383(3)
Interactions of a Scale With Two or More Categorical Variables
386(2)
Summary
388(2)
Outliers and Multicollinearity: Diagnosing and Solving Regression Problems II
390(41)
Introduction
390(1)
Outliers: Introduction and Illustration
391(3)
Detecting Outliers: Regression Diagnostics
394(17)
Extremity on the Independent Variables: Leverage
394(4)
Extremity on Y: Discrepancy
398(4)
Influence on the Regression Estimates
402(4)
Location of Outlying Points and Diagnostic Statistics
406(3)
Summary and Suggestions
409(2)
Sources of Outliers and Possible Remedial Actions
411(8)
Sources of Outliers
411(4)
Remedial Actions
415(4)
Multicollinearity
419(6)
Exact Collinearity
419(1)
Multicollinearity: A Numerical Illustration
420(2)
Measures of the Degree of Multicollinearity
422(3)
Remedies for Multicollinearity
425(5)
Model Respecification
426(1)
Collection of Additional Data
427(1)
Ridge Regression
427(1)
Principal Components Regression
428(1)
Summary of Multicollinearity Considerations
429(1)
Summary
430(1)
Missing Data
431(21)
Basic Issues in Handling Missing Data
431(4)
Minimize Missing Data
431(1)
Types of Missing Data
432(1)
Traditional Approaches to Missing Data
433(2)
Missing Data in Nominal Scales
435(7)
Coding Nominal Scale X for Missing Data
435(4)
Missing Data on Two Dichotomies
439(1)
Estimation Using the EM Algorithm
440(2)
Missing Data in Quantitative Scales
442(8)
Available Alternatives
442(2)
Imputation of Values for Missing Cases
444(3)
Modeling Solutions to Missing Data in Scaled Variables
447(1)
An Illustrative Comparison of Alternative Methods
447(3)
Rules of Thumb
450(1)
Summary
450(2)
Multiple Regression/Correlation and Causal Models
452(27)
Introduction
452(8)
Limits on the Current Discussion and the Relationship Between Causal Analysis and Analysis of Covariance
452(2)
Theories and Multiple Regression/Correlation Models That Estimate and Test Them
454(3)
Kinds of Variables in Causal Models
457(2)
Regression Models as Causal Models
459(1)
Models Without Reciprocal Causation
460(7)
Direct and Indirect Effects
460(4)
Path Analysis and Path Coefficients
464(1)
Hierarchical Analysis and Reduced Form Equations
465(1)
Partial Causal Models and the Hierarchical Analysis of Sets
466(1)
Testing Model Elements
467(1)
Models With Reciprocal Causation
467(1)
Identification and Overidentification
468(1)
Just Identified Models
468(1)
Overidentification
468(1)
Underidentification
469(1)
Latent Variable Models
469(6)
An Example of a Latent Variable Model
469(2)
How Latent Variables Are Estimated
471(1)
Fixed and Free Estimates in Latent Variable Models
472(1)
Goodness-of-Fit Tests of Latent Variable Models
472(1)
Latent Variable Models and the Correction for Attenuation
473(1)
Characteristics of Data Sets That Make Latent Variable Analysis the Method of Choice
474(1)
A Review of Causal Model and Statistical Assumptions
475(1)
Specification Error
475(1)
Identification Error
475(1)
Comparisons of Causal Models
476(1)
Nested Models
476(1)
Longitudinal Data in Causal Models
476(1)
Summary
477(2)
Alternative Regression Models: Logistic, Poisson Regression, and the Generalized Linear Model
479(57)
Ordinary Least Squares Regression Revisited
479(3)
Three Characteristics of Ordinary Least Squares Regression
480(1)
The Generalized Linear Model
480(1)
Relationship of Dichotomous and Count Dependent Variables Y to a Predictor
481(1)
Dichotomous Outcomes and Logistic Regression
482(37)
Extending Linear Regression: The Linear Probability Model and Discriminant Analysis
483(2)
The Nonlinear Transformation From Predictor to Predicted Scores: Probit and Logistic Transformation
485(1)
The Logistic Regression Equation
486(1)
Numerical Example: Three Forms of the Logistic Regression Equation
487(5)
Understanding the Coefficients for the Predictor in Logistic Regression
492(1)
Multiple Logistic Regression
493(1)
Numerical Example
494(3)
Confidence Intervals on Regression Coefficients and Odds Ratios
497(1)
Estimation of the Regression Model: Maximum Likelihood
498(1)
Deviances: Indices of Overall Fit of the Logistic Regression Model
499(3)
Multiple R2 Analogs in Logistic Regression
502(2)
Testing Significance of Overall Model Fit: The Likelihood Ratio Test and the Test of Model Deviance
504(3)
Χ2 Test for the Significance of a Single Predictor in a Multiple Logistic Regression Equation
507(1)
Hierarchical Logistic Regression: Likelihood Ratio Χ2 Test for the Significance of a Set of Predictors Above and Beyond Another Set
508(1)
Akaike's Information Criterion and the Bayesian Information Criterion for Model Comparison
509(1)
Some Treachery in Variable Scaling and Interpretation of the Odds Ratio
509(3)
Regression Diagnostics in Logistic Regression
512(4)
Sparseness of Data
516(1)
Classification of Cases
516(3)
Extensions of Logistic Regression to Multiple Response Categories: Polytomous Logistic Regression and Ordinal Logistic Regression
519(6)
Polytomous Logistic Regression
519(1)
Nested Dichotomies
520(2)
Ordinal Logistic Regression
522(3)
Models for Count Data: Poisson Regression and Alternatives
525(7)
Linear Regression Applied to Count Data
525(1)
Poisson Probability Distribution
526(2)
Poisson Regression Analysis
528(2)
Overdispersion and Alternative Models
530(2)
Independence of Observations
532(1)
Sources on Poisson Regression
532(1)
Full Circle: Parallels Between Logistic and Poisson Regression, and the Generalized Linear Model
532(3)
Parallels Between Poisson and Logistic Regression
532(2)
The Generalized Linear Model Revisited
534(1)
Summary
535(1)
Random Coefficient Regression and Multilevel Models
536(32)
Clustering Within Data Sets
536(3)
Clustering, Alpha Inflation, and the Intraclass Correlation
537(1)
Estimating the Intraclass Correlation
538(1)
Analysis of Clustered Data With Ordinary Least Squares Approaches
539(4)
Numerical Example, Analysis of Clustered Data With Ordinary Least Squares Regression
541(2)
The Random Coefficient Regression Model
543(1)
Random Coefficient Regression Model and Multilevel Data Structure
544(6)
Ordinary Least Squares (Fixed Effects) Regression Revisited
544(1)
Fixed and Random Variables
544(1)
Clustering and Hierarchically Structured Data
545(1)
Structure of the Random Coefficient Regression Model
545(1)
Level 1 Equations
546(1)
Level 2 Equations
547(1)
Mixed Model Equation for Random Coefficient Regression
548(1)
Variance Components---New Parameters in the Multilevel Model
548(1)
Variance Components and Random Coefficient Versus Ordinary Least Squares (Fixed Effects) Regression
549(1)
Parameters of the Random Coefficient Regression Model: Fixed and Random Effects
550(1)
Numerical Example: Analysis of Clustered Data With Random Coefficient Regression
550(3)
Unconditional Cell Means Model and the Intraclass Correlation
551(1)
Testing the Fixed and Random Parts of the Random Coefficient Regression Model
552(1)
Clustering as a Meaningful Aspect of the Data
553(1)
Multilevel Modeling With a Predictor at Level 2
553(2)
Level 1 Equations
553(1)
Revised Level 2 Equations
554(1)
Mixed Model Equation With Level 1 Predictor and Level 2 Predictor of Intercept and Slope and the Cross-Level Interaction
554(1)
An Experimental Design as a Multilevel Data Structure: Combining Experimental Manipulation With Individual Differences
555(1)
Numerical Example: Multilevel Analysis
556(4)
Estimation of the Multilevel Model Parameters: Fixed Effects, Variance Components, and Level 1 Equations
560(3)
Fixed Effects and Variance Components
560(1)
An Equation for Each Group: Empirical Bayes Estimates of Level 1 Coefficients
560(3)
Statistical Tests in Multilevel Models
563(1)
Fixed Effects
563(1)
Variance Components
563(1)
Some Model Specification Issues
564(1)
The Same Variable at Two Levels
564(1)
Centering in Multilevel Models
564(1)
Statistical Power of Multilevel Models
565(1)
Choosing Between the Fixed Effects Model and the Random Coefficient Model
565(1)
Sources on Multilevel Modeling
566(1)
Multilevel Models Applied to Repeated Measures Data
566(1)
Summary
567(1)
Longitudinal Regression Methods
568(40)
Introduction
568(1)
Chapter Goals
568(1)
Purposes of Gathering Data on Multiple Occasions
569(1)
Analyses of Two-Time-Point Data
569(4)
Change or Regressed Change?
570(1)
Alternative Regression Models for Effects Over a Single Unit of Time
571(2)
Three- or Four-Time-Point Data
573(1)
Repeated Measure Analysis of Variance
573(5)
Multiple Error Terms in Repeated Measure Analysis of Variance
574(1)
Trend Analysis in Analysis of Variance
575(1)
Repeated Measure Analysis of Variance in Which Time Is Not the Issue
576(2)
Multilevel Regression of Individual Changes Over Time
578(10)
Patterns of Individual Change Over Time
578(4)
Adding Other Fixed Predictors to the Model
582(1)
Individual Differences in Variation Around Individual Slopes
583(1)
Alternative Developmental Models and Error Structures
584(2)
Alternative Link Functions for Predicting Y From Time
586(1)
Unbalanced Data: Variable Timing and Missing Data
587(1)
Latent Growth Models: Structural Equation Model Representation of Multilevel Data
588(7)
Estimation of Changes in True Scores
589(1)
Representation of Latent Growth Models in Structural Equation Model Diagrams
589(5)
Comparison of Multilevel Regression and Structural Equation Model Analysis of Change
594(1)
Time Varying Independent Variables
595(1)
Survival Analysis
596(4)
Regression Analysis of Time Until Outcome and the Problem of Censoring
596(3)
Extension to Time-Varying Independent Variables
599(1)
Extension to Multiple Episode Data
599(1)
Extension to a Categorical Outcome: Event-History Analysis
600(1)
Time Series Analysis
600(2)
Units of Observation in Time Series Analyses
601(1)
Time Series Analyses Applications
601(1)
Time Effects in Time Series
602(1)
Extension of Time Series Analyses to Multiple Units or Subjects
602(1)
Dynamic System Analysis
602(2)
Statistical Inference and Power Analysis in Longitudinal Analyses
604(1)
Summary
605(3)
Multiple Dependent Variables: Set Correlation
608(35)
Introduction to Ordinary Least Squares Treatment of Multiple Dependent Variables
608(2)
Set Correlation Analysis
608(1)
Canonical Analysis
609(1)
Elements of Set Correlation
610(1)
Measures of Multivariate Association
610(3)
R2Y, X, the Proportion of Generalized Variance
610(1)
T2Y, X and P2Y, X, Proportions of Additive Variance
611(2)
Partialing in Set Correlation
613(2)
Frequent Reasons for Partialing Variable Sets From the Basic Sets
613(1)
The Five Types of Association Between Basic Y and X Sets
614(1)
Tests of Statistical Significance and Statistical Power
615(2)
Testing the Null Hypothesis
615(1)
Estimators of the Population R2Y, X, T2Y, X, and P2Y, X
616(1)
Guarding Against Type I Error Inflation
617(1)
Statistical Power Analysis in Set Correlation
617(2)
Comparison of Set Correlation With Multiple Analysis of Variance
619(1)
New Analytic Possibilities With Set Correlation
620(1)
Illustrative Examples
621(6)
A Simple Whole Association
621(1)
A Multivariate Analysis of Partial Variance
622(1)
A Hierarchical Analysis of a Quantitative Set and Its Unique Components
623(2)
Bipartial Association Among Three Sets
625(2)
Summary
627(4)
APPENDICES
Appendix 1: The Mathematical Basis for Multiple Regression/Correlation and Identification of the Inverse Matrix Elements
631(5)
A1.1 Alternative Matrix Methods
634(1)
A1.2 Determinants
634(2)
Appendix 2: Determination of the Inverse Matrix and Applications Thereof
636(7)
A2.1 Hand Calculation of the Multiple Regression/Correlation Problem
636(4)
A2.2 Testing the Difference Between Partial βs and Bs From the Same Sample
640(2)
A2.3 Testing the Difference Between βs for Different Dependent Variables From a Single Sample
642(1)
Appendix Tables
643(12)
Table A t Values for α = .01, .05 (Two Tailed)
643(1)
Table B z' Transformation of r
644(1)
Table C Normal Distribution
645(1)
Table D F Values for α = .01, .05
646(4)
Table E L Values for α = .01, .05
650(2)
Table F Power of Significance Test of r at α = .01, .05 (Two Tailed)
652(2)
Table G n* to Detect r by t Test at α = .01, .05 (Two Tailed)
654(1)
References 655(16)
Glossary 671(12)
Statistical Symbols and Abbreviations 683(4)
Author Index 687(4)
Subject Index 691


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