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).

        
Click on the chapter titles shown below to view them (please be patient while the chapters 
are downloading, some of them are a little long). As a compromise between formatting and 
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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