Muutke küpsiste eelistusi

E-raamat: Multivariate Statistical Methods: A First Course [Taylor & Francis e-raamat]

(University of Califonia, Riverside, USA),
  • Formaat: 334 pages
  • Ilmumisaeg: 01-Feb-1997
  • Kirjastus: Psychology Press
  • ISBN-13: 9781315805771
  • Taylor & Francis e-raamat
  • Hind: 101,56 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 145,08 €
  • Säästad 30%
  • Formaat: 334 pages
  • Ilmumisaeg: 01-Feb-1997
  • Kirjastus: Psychology Press
  • ISBN-13: 9781315805771
Multivariate statistics refer to an assortment of statistical methods that have been developed to handle situations in which multiple variables or measures are involved. Any analysis of more than two variables or measures can loosely be considered a multivariate statistical analysis.

An introductory text for students learning multivariate statistical methods for the first time, this book keeps mathematical details to a minimum while conveying the basic principles. One of the principal strategies used throughout the book--in addition to the presentation of actual data analyses--is pointing out the analogy between a common univariate statistical technique and the corresponding multivariate method. Many computer examples--drawing on SAS software --are used as demonstrations.

Throughout the book, the computer is used as an adjunct to the presentation of a multivariate statistical method in an empirically oriented approach. Basically, the model adopted in this book is to first present the theory of a multivariate statistical method along with the basic mathematical computations necessary for the analysis of data. Subsequently, a real world problem is discussed and an example data set is provided for analysis. Throughout the presentation and discussion of a method, many references are made to the computer, output are explained, and exercises and examples with real data are included.
Preface ix
Introduction
1(8)
The Impact of Computers
2(1)
A Summary of SAS
3(2)
The SAS Package and multivatite Analysis
5(1)
Exercises
6(3)
Basic Matrix Algebra
9(14)
Matrix Definitions
9(1)
Matrix Operations
10(1)
Matrix Addition and Subtraction
11(1)
Scalar Multiplication
12(1)
Matrix Multiplication
12(3)
Matrix Inversion
15(3)
Eigenvalues and Eigenvectors of a Matrix
18(3)
Exercises
21(2)
The Multivariate Normal Distribution and Tests of Significance
23(33)
The Univariate Standard Normal Distribution
24(2)
Univariate Sampling Distributions and Statistical Inference
26(1)
Other Sampling Distributions
27(1)
Inferences About Differences Between Group Means
28(2)
The F Statistic and Analysis of Variance
30(2)
The Multivariate Normal Distribution
32(3)
Multivariate Sampling Distributions and Statistical Inference
35(1)
Hotelling's Statistic
36(1)
Inferences About Differences Between Group Means
36(3)
Multivariate Analysis of Variance
39(3)
An Example of Multivariate Analysis of Variance Using SAS
42(6)
Evaluating Multivariate Normality
48(4)
Exercises
52(4)
Factorial Multivariate Analyusis of Variance
56(29)
The Univariate Two-Way Analysis of Variance
57(6)
Fixed, Random, and Mixed Factorial Designs
63(1)
Two-Way Multivariate Analysis of Variance
64(4)
An Example of Two-Way MANOVA Using SAS
68(11)
More Advanced Factorial MANOVAs
79(1)
Designs With Unequal Observations
80(1)
Exercises
80(5)
Discriminant Analysis
85(48)
Discriptive Discriminant Analysis
86(1)
Selecting the Discriminant Criterion
87(1)
Maximizing the Discriminant Criterion
88(1)
Discriminant Functions
89(1)
Interpretation of Discriminant Functions
89(8)
Discriminant Function Plots
97(1)
Tests of Statistical Silgnificance in Discriminant Analysis
97(3)
An Example of Descriptive Discriminant Analysis Using SAS
100(2)
Factorial Descriptive Discriminant Analysis Designs
102(2)
Predictive Discriminant Analysis
104(1)
Classification Based on Generalized Distance
105(1)
Posterior Probability of Group Membership
105(2)
An Overview of the Different Types of Classification Rules
107(1)
Linear/Equal Prior Probability Classification Rules
107(1)
Linear/Unequal Prior Probability Rules
108(1)
Quadratic/Equal Prior Probability Rules
109(1)
Quadratic/Unequal Prior Probability Rules
110(1)
Type of Data Used for Classification
110(1)
The Fisher Two-Group Classification Function
111(1)
Evaluating Classification Accuracy
112(2)
Numerical Classification Example
114(15)
Exercises
129(4)
Canonical Correlation
133(29)
Multiple Correlation/Regression
134(4)
An Example of Regression Analysis Using SAS
138(4)
Discriminant Analysis and Regression Analysis
142(2)
Canonical Correlation Analysis
144(3)
Obtaining the Canonical Correlations
147(2)
Interpretation of Canonical Variates
149(2)
Tests of Significance of Canonical Correlations
151(1)
The Practical Importance of Canonical Correlations
152(1)
Numerical Example Using SAS
152(6)
Exercises
158(4)
Principal Components and Factors Analysis
162(46)
PCA Versus FA
164(1)
Principal Component Analysis
164(1)
An Example of PCA
165(2)
The Principal Components
167(1)
Principal Component Loadings
168(4)
How Many Components?
172(1)
Loose Ends
173(1)
An Example of PCA Using SAS
174(2)
Factor Analysis
176(8)
Methods of Estimation
184(3)
How Many Factors Should Be Used in a Factor Analysis?
187(2)
Rotation of Factors
189(5)
Loose Ends
194(1)
An Example of Factors Analysis Using SAS
195(8)
Exercises
203(5)
Confirmatory Factor Analysis and Structural Equation Modeling
208(73)
A Short History of Confirmatory Factor Analysis
209(2)
Why the Term ``Structural Equation Model''?
211(2)
Using Diagrams to Represent Models
213(1)
Mathematical Representation of Structural Equation Models
214(4)
The Confirmatory Factor Analysis Model
218(2)
Model Estimation
220(3)
The Problem of Identification
223(3)
A Numerical CFA Example
226(17)
Goodness-of-Fit Indices
243(9)
Multisample Analysis
252(3)
Second-Order Factor Analysis
255(5)
An Extension to a Simple Structural Equation Model
260(3)
A SEM With Recursive and Nonrecursive Paths
263(6)
Exercises
269(12)
Appendix A 281(9)
Appendix B 290(18)
References 308(7)
Author Index 315(4)
Subject Index 319


Marcoulides, George A.; Hershberger, Scott L.