Applied Multivariate Data Analysis

A Second Course in Statistics The past decade has seen a tremendous increase in the use of statistical data analysis and in the availability of both computers and statistical software. Business and government professionals, as well as academic researchers, are now regularly employing techniques that go far beyond the standard two-semester, introductory course in statistics. Even though for this group of users shorl courses in various specialized topics are often available, there is a need to improve the statistics training of future users of statistics while they are still at colleges and universities. In addition, there is a need for a survey reference text for the many practitioners who cannot obtain specialized courses. With the exception of the statistics major, most university students do not have sufficient time in their programs to enroll in a variety of specialized one-semester courses, such as data analysis, linear models, experimental de­ sign, multivariate methods, contingency tables, logistic regression, and so on. There is a need for a second survey course that covers a wide variety of these techniques in an integrated fashion. It is also important that this sec­ ond course combine an overview of theory with an opportunity to practice, including the use of statistical software and the interpretation of results obtained from real däta.

Inhalt

6 Contingency Tables.- 6.1 Multivariate Data Analysis Data Matrices and Measurement Scales.- 6.1.1 Data Matrices.- 6.1.2 Measurement Scales.- Quantitative Scales.- Qualitative Scales.- Measurement Scales and Analysis.- 6.1.3 Data Collection and Statistical Inference.- Probability Samples and Random Samples.- Exploratory and Confirmatory Analysis.- 6.1.4 An Outline of the Techniques to be Studied.- Topics in Volume.- 6.2 Two-Dimensional Contingency Tables.- 6.2.1 Bivariate Distributions for Categorical Data.- Joint Density Table.- Indepencence.- Row and Column Proportions.- Row and Column Profiles.- Odds Ratios.- 6.2.2 Statistical Inference in Two-Dimensional Tables.- The Two-Dimensional Contingency Table.- Sampling Models for Contingency Tables.- Multinomial.- Hypergeometric.- Poisson.- Product Multinomial.- Test of Independence.- Sampling Model Assumptions.- Poisson Distribution.- Product Multinomial Distribution.- Standardized Residuals.- Correspondence Analysis.- 6.2.3 Measures of Association.- Goodman and Kruskal's Lambda.- Inference for Lambda.- 6.2.4 Models for Two-Dimensional Tables.- Equal Cell Probability Model.- Constant Row or Column Densities.- The Independence Model as a Composite of Three Simple Models.- The Saturated Model.- Loglinear Characterization for Cell Densities.- A Loglinear Model for Independence.- Parameters for the Loglinear Model.- The Loglinear Model with Interaction.- Matrix Notation for Loglinear Model.- 6.2.5 Statistical Inference for Loglinear Models.- The Loglinear Model Defined in Terms of Cell Frequencies.- Multiplicative Form of the Loglinear Model.- Estimation for the Loglinear Model.- Standardized Estimates of Loglinear Parameters.- A Loglinear Representation for Some Simpler Models.- Inference Procedures for the Three Simple Models.- 6.2.6 An Additive Characterization for Cell Densities.- 6.2.7 Two-Dimensional Contingency Tables in a Multivariate Setting.- Simpson's Paradox.- 6.2.8 Other Sources of Information.- 6.3 Multidimensional Contingency Tables.- 6.3.1 The Three-Dimensional Contingency Table.- Models for Three-Way Tables.- Inference for the Independence Model.- Other Models for Three-Way Tables.- Partial Independence.- Conditional Independence.- No Three-Way Interaction.- Saturated Model.- Loglinear Models for Three-Way Tables.- Definitions of Parameters in Terms of Cell Frequencies.- Independence Model.- Partial Independence Model.- Conditional Independence Model.- No Three-Way Interactions Model.- Saturated Model.- Multiplicative Form of the Loglinear Model.- Hierarchical Models.- Notation for Loglinear Models.- Model Selection.- Standardized Estimates and Standardized Residuals.- Summary of Loglinear Model Fitting Procedure.- Product Multinomial Sampling.- 6.3.2 Some Examples.- Three-way Interaction.- Goodness of Fit and Model Selection.- 6.3.3 Four-Dimensional Contingency Tables and Stepwise.- Fitting Procedures 70 Stepwise Model Selection.- Tests of Partial and Marginal Association.- Marginal Association.- 6.3.4 The Effects of Collapsing a Contingency Table and.- Structural Zeroes.- Collapsing Contingency Tables.- Random Zeroes.- Structural Zeroes and Incomplete Tables.- Quasi-loglinear Models for Incomplete Tables.- 6.3.5 Logit Models for Response Variables.- The Logit Function.- Fitting a Logit Model.- Relationship to Logistic Regression.- Polychotomous Response Variables.- 6.3.6 Other Sources of Information.- 6.4 The Weighted Least Squares Approach.- 6.4.1 The Weighted Least Squares Theory.- The Product Multinomial Distribution Assumption.- Sampling Properties of the Row Proportions.- Determining Linear Functions Among the Row Proportions.- The Linear Model to be Estimated.- Determining the Weighted Least Squares Estimator.- 6.4.2 Statistical Inference for the Weighted Least Squares.- Procedure.- 6.4.3 Some Alternative Analyses.- Marginal Analysis.- Continuation Differences.- Averaging or Summing Response Functions.- Weighted Sums for Ordinal Responses.- 6.4.4 Weighted Least Squares Estimation for Logit Models.- The Logit Model as a Special Case of a Weighted.- Least Squares Model.- Continuation Ratios.- 6.4.5 Two or More Response Variables.- Defining Response Functions.- Repeated Measurement Designs.- Adding Interaction Effects.- 6.4.6 Other Sources of Information.- Cited Literature and References.- Exercises for Chapter 6.- Questions for Chapter 6.- 7 Multivariate Distributions Inference Regression and Canonical Correlation.- 7.1 Multivariate Random Variables and Samples.- 7.1.1 Multivariate Distributions and Multivariate Random Variables.- Joint Distribution.- Partitioning the Random Variable.- Conditional Distributions and Independence.- Mean Vector and Covariance Matrix.- Correlation Matrix.- 7.1.2 Multivariate Samples.- Sample Mean Vector and Covariance Matrix.- Sample Correlation Matrix.- Sums of Squares and Cross Product Matrices.- Multivariate Central Limit Theorem.- 7.1.3 Geometric Interpretations for Data Matrices.- p-Dimensional Space.- n-Dimensional Space.- Mahalanobis Distance and Generalized Variance.- p-Dimensional Ellipsoid.- Generalized Variance.- Trace Measure of Overall Variance.- Generalized Variance for Correlation Matrices.- Eigenvalues and Eigenvectors for Sums of Squares and Cross Product Matrices.- 7.1.4 Other Sources of Information.- 7.2 The Multivariate Normal Distribution.- 7.2.1 The Multivariate Normal.- Multivariate Normal Density.- Constant Probability Density Contour.- Linear Transformations.- Distribution of Probability Density Contour.- 7.2.2 Partitioning the Normal.- Marginal Distributions.- Conditional Distributions.- Multivariate Regression Function.- Partial Correlation.- 7.3 Testing for Normality Outliers and Robust Estimation.- 7.3.1 Testing for Normality.- Mahalanobis Distances from the Sample Mean.- Mul-.- tivariate Skewness and Kurtosis.- Transforming to Normality.- 7.3.2 Multivariate Outliers.- Multivariate Outliers and Mahalanobis Distance.- Testing for Multivariate Outliers.- Multiple Outliers.- 7.3.3 Robust Estimation.- Obtaining Robust Estimators of Covariance and Cor-.- relation Matrices.- Multivariate Trimming.- 7.3.4 Other Sources of Information.- 7.4 Inference for the Multivariate Normal.- 7.4.1 Inference Procedures for the Mean Vector.- Sample Likelihood Function.- Hotelling's T2.- Inference.- Simultaneous Confidence Regions.- Inferences for Linear Functions.- 7.4.2 Repeated Measures Comparisons.- Repeated Measurements on a Single Variable.- Profile Characterization.- Repeated Measures in a Randomized Block Design.- Necessary and Sufficient Conditions for Validity of Univariate…