TESTING LATENT VARIABLE MODELS WITH SURVEY DATA
       

      

Robert A. Ping, Jr.
Associate Professor of Marketing
Department of Marketing
Wright State University
Dayton, OH 45435
937-775-3047 (FAX -3545)
rping@wright.edu

    
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The following is a work-in-progress monograph on the process of testing models containing 
unobserved or latent variables that, although it is not quite finished, should be of some use to 
substantive researchers in the Social Sciences (see the INTRODUCTION for more).
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TABLE OF CONTENTS
       

      
SECOND-ORDER CONSTRUCTS
INTERACTIONS AND QUADRATICS
DEFINING CONCEPTS
IDENTIFYING IMPORTANT ANTECEDENTS
SUGGESTIONS FOR STEP I-- DEFINING MODEL CONCEPTS

        

      
STATING AND JUSTIFYING HYPOTHESES

      
JUSTIFICATION
FORM
SUGGESTIONS FOR STEP II-- STATING AND JUSTIFYING RELATIONSHIPS 
AMONG CONCEPTS

      
SCENARIO ANALYSIS
STEP IV-- GATHERING DATA

      
SAMPLE REPRESENTATIVENESS
RESEARCH DESIGNS

      
CROSS-SECTIONAL RESEARCH DESIGNS
LONGITUDINAL RESEARCH
EXPERIMENTS
INTERORGANIZATIONAL RESEARCH
MULTIPLE DATA SETS FOR MODEL VALIDATION
SAMPLE SIZE
STEP V-- VALIDATING MEASURES

        
 

      
UNIDIMENSIONALITY
CONSISTENCY
PROCEDURES FOR ATTAINING UNIDIMENSIONALITY AND CONSISTENCY
COMMENTS ON UNIDIMENSIONALITY AND CONSISTENCY

      
SINGLE INDICATOR STRUCTURAL EQUATION ANALYSIS
RELIABILITY

      
COMMENTS ON RELIABILITY
VALIDITY

      
CONTENT OR FACE VALIDITY
CRITERION VALIDITY
CONSTRUCT VALIDITY
CONVERGENT AND DISCRIMINANT VALIDITY

      
Average Variance Extracted
COMMENTS ON STEP V-- MEASURE VALIDATION

      
SCENARIO ANALYSIS
PREVIOUSLY-USED MEASURES
RELIABILITY AND AVERAGE VARIANCE EXTRACTED
INTERACTIONS AND QUADRATICS
SECOND ORDER CONSTRUCTS
BOOTSTRAPPING
MEASURE PRETESTS AND SAMPLE SIZE
FINAL TEST PSYCHOMETRIC ASSESSMENT
SINGLE CONSTRUCT MEASUREMENT MODEL
FULL MEASUREMENT MODEL
SMALL DATA SETS
REGRESSION-BASED TECHNIQUES
DICOTOMOUS VARIABLES
NONNORMALITY
SUGGESTIONS FOR STEP V-- VALIDATING MEASURES
STEP VI-- VALIDATING THE MODEL

      
CAUSALITY
VIOLATIONS OF ASSUMPTIONS

      
REGRESSION
STRUCTURAL EQUATION ANALYSIS

      
Ordinal Data
Nonnormality
Sample Size
Missing Variables
GENERALIZABILITY
ERROR-ADJUSTED REGRESSION
NONSIGNIFICANT RELATIONSHIPS
INTERACTIONS AND QUADRATICS

      
SECOND ORDER INTERACTIONS
INTERPRETING INTERACTIONS AND QUADRATICS
INDIRECT AND TOTAL EFFECTS
EXPLAINED VARIANCE
MODEL-TO-DATA FIT
IMPROVING MODEL FIT

      
ALTERING THE MODEL
CORRELATED MEASUREMENT ERRORS
MEASUREMENT MODEL FIT
STRUCTURAL MODEL-TO-DATA FIT
MISSPECIFICATION
MEASUREMENT ERRORS
SECOND ORDER CONSTRUCTS
DICHOTOMOUS VARIABLES
SUMMARY AND SUGGESTIONS FOR STEP VI-- VALIDATING THE MODEL
REFERENCES
TABLES

      
Table 1- The Number of Cases per Unique Covariance Matrix Element, Based 
on the Number of Variables in the Covariance Matrix and the Number of 
Cases per Variable in a Data Set 
Table 2a- The Number of Cases Required for 4 Indicators per Latent Variable 
(LV), Based on the Number of Latent Variables (LV's), and the Number of 
Cases per Indicator Variable in a Data Set 
Table 2b- The Number of Cases Required for 5 Indicators per Latent Variable 
(LV), Based on the Number of Latent Variables (LV's), and the Number of 
Cases per Indicator Variable in a Data Set 
Table 2c- The Number of Cases Required for 6 Indicators per Latent Variable 
(LV), Based on the Number of Latent Variables (LV's), and the Number of 
Cases per Indicator Variable in a Data Set 
APPENDICES

      
Appendix A- Interaction Specification Using a Single Product-of-Sums Indicator 
and Structural Equation Analysis
Figure A- An Abbreviated Structural Model
Appendix B- OLS Regression and Structural Equation Analysis
Table B - Structural Equation Analysis and OLS Regression Coefficient 
Estimates
Appendix C- Interaction Interpretation
Table C1- Appendix A Structural Model Estimation Results
Table C2- Table C1 UxT Interaction Statistical Significance
Appendix D- Indirect and Total Effects
Table D1- Figure A Model Standardized Indirect Effects 
Table D2- Figure A Model Standardized Total Effects
Appendix E- Consistency Improvement using Summed First Derivatives
Table E1- First Derivatives for the Eight Item Measure 
Table E2- First Derivatives with x4 Deleted 
Table E3- First Derivatives with x3 and x4 Deleted 
Table E4- First Derivatives with x1, x3 and x4 Deleted
Appendix F- Ordered Similarity Coefficients and Consistency
Table F- Ordered Similarity Coefficients for the Appendix E Items
Appendix G- Error Adjusted Regression Estimates for the Figure A Model
Table G1-- Unadjusted Covariances for A, B, C, D, and E: with 
Reliabilities, Estimated Loadings, and Estimated Measurement 
Errors
Table G2-- Adjusted Covariances for A, B, C, D, and E, with 
Coefficient Estimates
Appendix H- Scenario Example
Exhibit H- A Scenario
Appendix I- Structural Equation Analysis with Summed Indicators
Table I- Coefficient Estimates
Appendix J- Second-Order Construct Example
Figure J- Second-Order Constructs
Appendix K- Scenario Analysis Results Comparison
Table K1- Comparison of Scenario and Survey Data from a 
Common Questionnaire Using Factor Analysis
Table K2- Comparison of Scenario and Field Survey Data from a 
Common Questionnaire Using Regression
Appendix L- Average Variance Extracted
Appendix M- Nonrecursive Analysis Example
Figure M- A Nonrecursive Model
Appendix N- Second-Order Interactions
Table N1- Results for T First-Order and UxT as Single Indicator with 
Ping (1995) Specification
Table N2- Results for T First-Order and UxT as Single Indicator with 
Single Indicator structural equation analysis Specification
Table N3- Results of T 2nd Order and UxT with all 60 Kenny and 
Judd Indicators
Table N4- Results of T 2nd Order and UxT with 4 Arbitrary Kenny and 
Judd Indicators
Table N5- Results of T 2nd Order and UxT with 4 Different but Arbitrary 
Kenny and Judd Indicators
Table N6- Results of T 2nd Order and UxT with 4 Consistent Kenny and 
Judd Indicators
Table N7- Results of T 1st Order and UxT with all 15 Kenny and Judd 
Indicators
Table N8- Results of T 1st Order and UxT with 4 Arbitrary Kenny and 
Judd Indicators
Table N9- Results of T 1st Order and UxT with 4 Different but Arbitrary 
Kenny and Judd Indicators
Table N10- Results of T 1st Order and UxT with 4 Consistent Kenny and 
Judd Indicators