Multivariable Modeling and Multivariate Analysis for the Behavioral Sciences

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ISBN: 9781439807699 | 1439807698
Cover: Nonspecific Binding
Copyright: 9/28/2009

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Statistical books aimed for those in the behavioral sciences rarely go beyond hypothesis testing. However, to carry out any valid research, professionals in the behavioral sciences need to know how to apply statistical methods in a variety of ways. This book focuses on the most crucial of these, the analysis of data. Assuming some knowledge of basic statistical terminology, but avoiding complex math, this text provides a full explanation of the most useful methods for comparing and examining data. Examples and exercises making use of the free software R help to bring home the book's relevance.

Preface	p. xiii
Acknowledgments	p. xvii
Data, Measurement, and Models	p. 1
Introduction	p. 1
Types of Study	p. 2
Surveys	p. 3
Experiments	p. 4
Observational Studies	p. 5
Quasi-Experiments	p. 6
Types of Measurement	p. 7
Nominal or Categorical Measurements	p. 7
Ordinal Scale Measurements	p. 8
Interval Scales	p. 8
Ratio Scales	p. 9
Response and Explanatory Variables	p. 9
Missing Values	p. 10
The Role of Models in the Analysis of Data	p. 11
Determining Sample Size	p. 14
Significance Tests, P-Values, and Confidence Intervals	p. 16
Summary	p. 19
Exercises	p. 19
Looking at Data	p. 21
Introduction	p. 21
Simple Graphics-Pie Charts, Bar Charts, Histograms, and Boxplots	p. 22
Categorical Data	p. 22
Interval/Quasi-Interval Data	p. 30
The Scatterplot and Beyond	p. 35
The Bubbleplot	p. 38
The Bivariate Boxplot	p. 40
Scatterplot Matrices	p. 44
Conditioning Plots and Trellis Graphics	p. 45
Graphical Deception	p. 52
Summary	p. 58
Exercises	p. 58
Simple Linear and Locally Weighted Regression	p. 61
Introduction	p. 61
Simple Linear Regression	p. 62
Fitting the Simple Linear Regression Model to the Pulse Rates and Heights Data	p. 64
An Example from Kinesiology	p. 65
Regression Diagnostics	p. 68
Locally Weighted Regression	p. 72
Scatterplot Smoothers	p. 73
Summary	p. 79
Exercises	p. 80
Multiple Linear Regression	p. 81
Introduction	p. 81
An Example of Multiple Linear Regression	p. 84
Choosing the Most Parsimonious Model When Applying Multiple Linear Regression	p. 89
Regression Diagnostics	p. 96
Summary	p. 100
Exercises	p. 100
The Equivalence of Analysis of Variance and Multiple Linear Regression, and an Introduction to the Generalized Linear Model	p. 103
Introduction	p. 103
The Equivalence of Multiple Regression and ANOVA	p. 103
The Generalized Linear Model	p. 110
Summary	p. 112
Exercises	p. 113
Logistic Regression	p. 115
Introduction	p. 115
Odds and Odds Ratios	p. 115
Logistic Regression	p. 117
Applying Logistic Regression to the GHQ Data	p. 120
Selecting the Most Parsimonious Logistic Regression Model	p. 124
Summary	p. 128
Exercises	p. 128
Survival Analysis	p. 131
Introduction	p. 131
The Survival Function	p. 132
The Hazard Function	p. 136
Cox's Proportional Hazards Model	p. 138
Summary	p. 143
Exercises	p. 144
Linear Mixed Models for Longitudinal Data	p. 145
Introduction	p. 145
Linear Mixed Effects Models for Longitudinal Data	p. 146
How Do Rats Grow?	p. 150
Fitting the Independence Model to the Rat Data	p. 151
Fitting Linear Mixed Models to the Rat Data	p. 153
Computerized Delivery of Cognitive Behavioral Therapy-Beat the Blues	p. 157
The Problem of Dropouts in Longitudinal Studies	p. 162
Summary	p. 165
Exercises	p. 166
Multivariate Data and Multivariate Analysis	p. 169
Introduction	p. 169
The Initial Analysis of Multivariate Data	p. 170
Summary Statistics for Multivariate Data	p. 170
Graphical Descriptions of the Body Measurement Data	p. 173
The Multivariate Normal Probability Density Function	p. 174
Summary	p. 180
Exercises	p. 181
Principal Components Analysis	p. 183
Introduction	p. 183
Principal Components Analysis (PCA)	p. 183
Finding the Sample Principal Components	p. 185
Should Principal Components Be Extracted from the Covariance or the Correlation Matrix?	p. 188
Principal Components of Bivariate Data with Correlation Coefficient r	p. 190
Rescaling the Principal Components	p. 192
How the Principal Components Predict the Observed Covariance Matrix	p. 193
Choosing the Number of Components	p. 193
Calculating Principal Component Scores	p. 195
Some Examples of the Application of PCA	p. 196
Head Size of Brothers	p. 196
Crime Rates in the United States	p. 200
Drug Usage by American College Students	p. 205
Using PCA to Select a Subset of the Variables	p. 208
Summary	p. 209
Exercises	p. 210
Factor Analysis	p. 211
Introduction	p. 211
The Factor Analysis Model	p. 212
Estimating the Parameters in the Factor Analysis Model	p. 215
Estimating the Numbers of Factors	p. 217
Fitting the Factor Analysis Model: An Example	p. 218
Rotation of Factors	p. 220
A Simple Example of Graphical Rotation	p. 222
Numerical Rotation Methods	p. 223
Rotating the Crime Rate Factors	p. 226
Estimating Factor Scores	p. 227
Exploratory Factor Analysis and Principal Component Analysis Compared	p. 228
Confirmatory Factor Analysis	p. 229
Ability and Aspiration	p. 230
A Confirmatory Factor Analysis Model for Drug Usage	p. 233
Summary	p. 235
Exercises	p. 236
Cluster Analysis	p. 239
Introduction	p. 239
Cluster Analysis	p. 241
Agglomerative Hierarchical Clustering	p. 241
Clustering Individuals Based on Body Measurements	p. 243
Clustering Countries on the Basis of Life Expectancy Data	p. 246
K-Means Clustering	p. 250
Model-Based Clustering	p. 253
Summary	p. 258
Exercises	p. 259
Grouped Multivariate Data	p. 261
Introduction	p. 261
Two-Group Multivariate Data	p. 262
Hotelling's T2 Test	p. 262
Fisher's Linear Discriminant Function	p. 265
More Than Two Groups	p. 270
Multivariate Analysis of Variance (MANOVA)	p. 270
Classification Functions	p. 273
Summary	p. 277
Exercises	p. 277
References	p. 279
Appendix: Solutions to Selected Exercises	p. 285
Index	p. 299
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Multivariable Modeling and Multivariate Analysis for the Behavioral Sciences

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