INTERACTIONS AND QUADRATICS IN SURVEY DATA

INTERACTIONS AND QUADRATICS IN SURVEY DATA: A SOURCE BOOK FOR THEORETICAL MODEL TESTING (2nd Edition)
	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
Pls. note: If you have visited this page before you may want to click on the browser's Refresh or Reload button (above) to view the current version of this page. FOREWORD: The following is an on-line monograph about latent variable (LV) interactions and quadratics. It provides details about LV interactions and quadratics, their estimation, and needed work on these matters that should be of interest and use to Ph.D. students, educators and researchers in the Social Sciences who are interested in, or want to find out more about, LV interactions and quadratics (see the INTRODUCTION for more).

			TABLE OF CONTENTS

Click on the chapter titles 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 download time, the chapters below are in Microsoft Word. You may want to open several browser windows: one for chapters, one for tables, etc. To open another browser window, launch your browser again without closing this instance of your browser, and go to the URL shown in this instance's "Address" box at the top of the screen. FOREWORD-- Why this book was written, what it's about, printing and citing the monograph... FAST START FOR ESTIMATING INTERACTIONS/QUADRATICS IN LATENT VARIABLES-- Step by step... INTRODUCTION-- Some of the difficulties and confusion surrounding latent variable interactions and quadratics in survey data... I. INTERACTIONS AND QUADRATICS IN SURVEY DATA AS FACTORED COEFFICIENTS-- An instructive and useful view of an interaction or quadratic... II. THE IMPORTANCE OF INTERACTIONS AND QUADRATICS IN SURVEY RESEARCH-- Interactions/Quadratics can "cause" hypothesized associations to be nonsignificant III. UNDERSTANDING INTERACTIONS AND QUADRATICS
	VISUALIZING INTERACTIONS AND QUADRATICS-- interactions are warped...
	INTERPRETING INTERACTIONS AND QUADRATICS IN LATENT VARIABLES
		An Example Procedural Summary Discussion of the Approach
			- Producing Standardized Factored Coefficients. - When There Are No Loadings Equal to 1. - Invariance of Factored Coefficients with Mean Centering. - Verbally Explaining Interactions and Quadratics. - Standard Errors of Factored Coefficients. - Critical (Significance) Points of Factored Coefficients. - Interactions and Quadratics with Common First Order Terms.
IV. INVESTIGATING INTERACTIONS AND QUADRATICS IN STRUCTURAL EQUATION ANALYSIS-- They are routinely tested in model tests involving experiments and ANOVA; why not survey models?
V. CLASSICAL APPROACHES TO DETECTING OR ESTIMATING INTERACTIONS AND QUADRATICS

	CLASSICAL REGRESSION-BASED APPROACHES TO DETECTING OR ESTIMATING INTERACTIONS AND QUADRATICS:
		Product Term Regression. Errors-in-variables Regression. Subgroup Analysis. Variations-- ANOVA, Dummy Variable Regression, and the Chow Test.
	EFFICACY OF REGRESSION-BASED TECHNIQUES. CLASSICAL STRUCTURAL EQUATION ANALYSIS ESTIMATION APPROACHES:
		Kenny and Judd (1984) Hayduk (1987) Comments on the Classical Structural Equation Analysis Estimation Approaches
VI. RECENT APPROACHES TO ESTIMATING INTERACTIONS AND QUADRATICS
	RECENT STRUCTURAL EQUATION ANALYSIS ESTIMATION APPROACHES:
		Jaccard and Wan (1995) Bollen (1995) Jöreskog and Yang (1996) 2-step Estimation Single Indicator Approaches Single Indicator Specification Using Reliabilities Comments on the Recent Structural Equation Analysis Estimation Approaches
	RECENT REGRESSION-BASED ESTIMATION APPROACHES:
		Latent Variable Regression Comments on Latent Variable Regression Psuedo Latent Variable Regression Comments on Psuedo Latent Variable Regression
VII. THE BALANCE OF THE MONOGRAPH
VII. THE BALANCE OF THE MONOGRAPH
VIII. ESTIMATING LATENT VARIABLE INTERACTIONS AND QUADRATICS
	CONSIDERATIONS
		Mean Centering Intercorrelations Correlated Measurement Errors and Interactions Quadratics and Correlated Measurement Errors Comments on Correlated Measurement Errors Starting Values Unidimensionality First Derivatives Reliability Multicollinearity

	DATA CONDITIONS THAT INFLUENCE LATENT VARIABLE INTERACTION AND QUADRATIC DETECTION
		Reliability Systematic Error, Sample Size Research Design Intercorrelation Non Normality
	INCREASING THE LIKELIHOOD OF DETECTION INTERACTIONS AND QUADRATICS
	SUGGESTIONS/"STEP-BY-STEP"
	INTERACTION AND QUADRATIC ESTIMATION EXAMPLES
		A SINGLE INTERACTION
			SxA Unidimensionalization Structural Model Discussion Interpretation
		TWO INTERACTIONS Discussion
		ALL INTERACTIONS Discussion
		OTHER EXAMPLES
IX. POST HOC PROBING FOR LATENT VARIABLE INTERACTIONS AND QUADRATICS
	AN OVERALL F TEST A SIGNIFICANT F NONSIGNIFICANT HYPOTHESIZED ASSOCIATIONS A SUMMARY COMMENTS AN EXAMPLE OF PROBING FOR LATENT VARIABLE INTERACTIONS AND QUADRATICS
		F Test Probing
			TU, TT and UU TV, TT and VV TW, UV, UW and VW In Summary
		Interpretation Comments
			Overall F Test Stepwise-One-at-a-Time Scenario Analysis Reliability Loadings and Errors Averaging Shortcuts Specification Cautions Appendix AH Other Comments
X. OTHER HIGHER-ORDER LATENT VARIABLES LATENT VARIABLE CUBICS Specification Factored Coefficients and Their Standard Errors Interpretations Interactions Quadratics Cubics Combinations An Example Comments ESTIMATING INTERACTIONS INVOLVING A "SECOND-ORDER" LATENT VARIABLE First-order Latent Variables "Second-Orders" Unidimensionality Reliability Validity "Second-Order" Interaction Specification An Example Unidimensionality Respecification of T Reliability Mean Centering Interaction Specification Validity Interaction Estimation Discussion
XI. NEEDED RESEARCH ON LATENT VARIABLE INTERACTION AND QUADRATIC ESTIMATION
	Interpretation of Latent Variable Interactions and Quadratics Latent Variable Regression Psuedo Latent Variable Regression Interaction/quadratic Detection and Nonnormality Needed Examples Endogenous Interactions/quadratics Overall F Test The Stepwise-one-at-a-time Technique Quadratics Lubinski and Humphrey's Results Higher Order Interactions/quadratics Correlations and Standardized Variables Approximate Loadings and Errors Approximate Models Uncentered Data Interactions and Nonnormality Interactions as Constructs? Interaction/quadratic Consistency Automation Violations of Assumptions Indirect and Total Effects Reliability and Average Variance Extracted Formative Variables and Other Models
XII. FREQUENTLY ASKED QUESTIONS ABOUT LATENT VARIABLE INTERACTION AND QUADRATIC ESTIMATION
	A. What Are the Available Latent Variable Interaction and Quadratic Estimation Techniques? B. What Are the Differences among Them? C. Which One Should Be Used? D. How Does One Test an Hypothesized Interaction(s) and/or Quadratic(s)? E. What about the Assumptions Behind These Techniques, and Violation of These Assumptions in Real-world Data? F. What If One or More Measures Have a Natural Zero Point and Mean or Zero Centering Is Inappropriate? G. How Does One Test for Unhypothesized Interactions or Quadratics as Experimental Researchers Do in ANOVA? H. How Does One Interpret a Significant Interaction or Quadratic? I. Can These Interaction and Quadratic Estimation Techniques Be Used with All of the Popular SEM Software Packages? J. How Should Reviewer Comments Regarding Interactions And/or Quadratics Be Handled? K. How Does One Investigate the Possibility That a Significant but Unmodeled Interaction or Quadratic Might Be Responsible for a Nonsignificant Hypothesized Association? L. What about Latent Variable Cubics? M. How Is a "Second-order" Interaction Specified?
XII. SUGGESTIONS FOR USING THIS MONOGRAPH IN THE CLASSROOM
XIII. DATA AND PROGRAM LISTINGS
XV. EXCEL TEMPLATES FOR COMPUTING STARTING OR FIXED VALUES FOR LATENT VARIABLE INTERACTIONS AND QUADRATICS, OR FOR ADJUSTING A COVARIANCE MATRIX For a Single Indicator Specification and Direct (LISREL 8) or 2-step Estimation Using LISREL, EQS, AMOS, Etc. (i.e., Ping 1995, JMR) For Kenny and Judd (1984) Multiple Indicator Specification and LISREL, EQS, AMOS, Etc. (i.e., Ping 1996, Psych. Bull.) For Latent Variable Regression (I.e., Ping 1996, MVBR)
REFERENCES
FIGURES, TABLES AND APPENDICES AA through AG
	APPENDIX AH
BIBLIOGRAPHY RELATING TO INTERACTIONS AND QUADRATICS
BIBLIOGRAPHY RELATING TO INTERACTIONS AND QUADRATICS
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