An important problem in personnel psychology, namely, the psychometric problem known as "validity generalization" is addressed in this volume. From a statistical point of view, the problem is how to make statements about a population correlation coefficient based on inferences from a collection of sample correlation coefficients. The first part of the book examines the largely ad hoc procedures which have been used to determine validity generalization. The second part develops a new model formulated from the perspective of finite mixture theory and, in addition, illustrates its use in several applications.…mehr
An important problem in personnel psychology, namely, the psychometric problem known as "validity generalization" is addressed in this volume. From a statistical point of view, the problem is how to make statements about a population correlation coefficient based on inferences from a collection of sample correlation coefficients. The first part of the book examines the largely ad hoc procedures which have been used to determine validity generalization. The second part develops a new model formulated from the perspective of finite mixture theory and, in addition, illustrates its use in several applications.
1. Introduction.- 1.1 Motivation and Background.- 1.2 Conceptual Problems of Validity Generalization.- 1.3 An Alternative Formulation.- 2. A Validity Generalization Model.- 2.1 Introduction.- 2.2 Classical Test Theory.- 2.3 A Validity Generalization Random Model.- 2.4 The Joint Space of P and E.- 2.5 P and E Are Dependent Variables.- 2.6 The Distribution of R, c(r).- 2.7 Are P and E Correlated?.- 2.8 Identifiability.- 3. Estimation.- 3.1 Introduction.- 3.2 Lehmann's Classification.- 3.3 Sample Data.- 3.4 The Basic Sample Estimates.- 3.5 The Estimator SP2 = SR2 ? S*2.- 3.6 Interpreting Estimators.- 3.7 The Expectation of SR2.- 3.8 The Expectation of S*2.- 3.9 The Expectation of SP2.- 3.10 Numerical Evaluation of ?(SP2).- 3.11 The Distribution of Sp and the Power Problem.- 3.12 The Consistency of SP2.- 3.13 The Limiting Behavior of SR2.- 3.14 Multifactor Estimation Procedures.- 3.15 A Representative Multifactor Estimator.- 3.16 A Comment on Z Transformations.- 4. Summary and Discussion of Validity Generalization.- 4.1 Summary of Model Properties.- 4.2 Validity Generalization and Classical Test Theory.- 4.3 Summary of Estimation Procedures.- 4.4 Consistency and Identifiability.- 4.5 The Bayesian Connection.- 4.6 Computer Simulation Studies.- 5. A Conditional Mixture Model for Correlation Coefficients.- 5.1 Introduction.- 5.2 Finite Mixture Distributions.- 5.3 A Modeling Distribution for R.- 5.4 A Mixture Model Distribution for R.- 5.5 A Parent Distribution for Histograms of R.- 5.6 Comment.- 6. Parameter Estimation.- 6.1 Introduction.- 6.2 Estimation Equations.- 7. Examples and Applications.- 7.1 Introduction.- 7.2 Artificial Data, Example 1.- 7.3 How Many Components in the Mixture?.- 7.4 Electrical Workers, Example 2.- 7.5 Army Jobs, Example 3.- 7.6 Army Jobs,Example 4.- 7.7 College Grades, Example 5.- 7.8 Law School Test Scores and Grades, Example 6.- 8. Artifact Corrections and Model Assumptions.- 8.1 Artifact Corrections.- 8.2 Identifiability of Mixtures.- 8.3 Failure of Model Assumptions.- 8.4 Properties of the Maximum Likelihood Estimates.- 8.5 Miscellaneous Comments.- Notes.- References.- Author Index.
1. Introduction.- 1.1 Motivation and Background.- 1.2 Conceptual Problems of Validity Generalization.- 1.3 An Alternative Formulation.- 2. A Validity Generalization Model.- 2.1 Introduction.- 2.2 Classical Test Theory.- 2.3 A Validity Generalization Random Model.- 2.4 The Joint Space of P and E.- 2.5 P and E Are Dependent Variables.- 2.6 The Distribution of R, c(r).- 2.7 Are P and E Correlated?.- 2.8 Identifiability.- 3. Estimation.- 3.1 Introduction.- 3.2 Lehmann's Classification.- 3.3 Sample Data.- 3.4 The Basic Sample Estimates.- 3.5 The Estimator SP2 = SR2 ? S*2.- 3.6 Interpreting Estimators.- 3.7 The Expectation of SR2.- 3.8 The Expectation of S*2.- 3.9 The Expectation of SP2.- 3.10 Numerical Evaluation of ?(SP2).- 3.11 The Distribution of Sp and the Power Problem.- 3.12 The Consistency of SP2.- 3.13 The Limiting Behavior of SR2.- 3.14 Multifactor Estimation Procedures.- 3.15 A Representative Multifactor Estimator.- 3.16 A Comment on Z Transformations.- 4. Summary and Discussion of Validity Generalization.- 4.1 Summary of Model Properties.- 4.2 Validity Generalization and Classical Test Theory.- 4.3 Summary of Estimation Procedures.- 4.4 Consistency and Identifiability.- 4.5 The Bayesian Connection.- 4.6 Computer Simulation Studies.- 5. A Conditional Mixture Model for Correlation Coefficients.- 5.1 Introduction.- 5.2 Finite Mixture Distributions.- 5.3 A Modeling Distribution for R.- 5.4 A Mixture Model Distribution for R.- 5.5 A Parent Distribution for Histograms of R.- 5.6 Comment.- 6. Parameter Estimation.- 6.1 Introduction.- 6.2 Estimation Equations.- 7. Examples and Applications.- 7.1 Introduction.- 7.2 Artificial Data, Example 1.- 7.3 How Many Components in the Mixture?.- 7.4 Electrical Workers, Example 2.- 7.5 Army Jobs, Example 3.- 7.6 Army Jobs,Example 4.- 7.7 College Grades, Example 5.- 7.8 Law School Test Scores and Grades, Example 6.- 8. Artifact Corrections and Model Assumptions.- 8.1 Artifact Corrections.- 8.2 Identifiability of Mixtures.- 8.3 Failure of Model Assumptions.- 8.4 Properties of the Maximum Likelihood Estimates.- 8.5 Miscellaneous Comments.- Notes.- References.- Author Index.
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