The author proposes an alternative estimation technique for quadratic and interaction latent variables in structural equation models using LISREL, EQS, and CALIS. The technique specifies these variables with single indicants. The loading and error terms for the single indicants can be specified as constants in the structural model. The author's technique is shown to perform adequately using synthetic data sets.
Get full access to this article
View all access options for this article.
References
1.
AikenLeona S., and WestStephen G. (1991), Multiple Regression: Testing and Interpreting Interactions.Newbury Park, CA: Sage Publications, Inc.
2.
AjzenIcek, and FishbeinMartin (1980), Understanding Attitudes and Predicting Social Behavior.Englewood Cliffs, NJ: Prentice Hall.
3.
AndersonJames C., and GerbingDavid W. (1982), “Some Methods for Respecifying Measurement Models to Obtain Unidimensional Construct Measurement,”Journal of Marketing Research, 19(November), 453–60.
4.
AndersonJames C., and GerbingDavid W. (1988), “Structural Equation Modeling in Practice: A Review and Recommended Two-Step Approach,”Psychological Bulletin, 103(May), 411–23.
5.
AndersonTheodore W., and AmemiyaYasuo (1985), “The Asymptotic Normal Distribution of Estimators in Factor Analysis under General Conditions,” Technical Report 12, Econometric Workshop, Stanford University.
6.
AndersonTheodore W., and AmemiyaYasuo (1986), “Asymptotic Distribution in Factor Analysis and Linear Structural Relations,” Technical Report 18, Econometric Workshop, Stanford University.
7.
BatraRajeev, and RayMichael L. (1986), “Affective Responses Mediating Acceptance of Advertising,”Journal of Consumer Research”, 13(September), 249.
8.
BentlerPeter M. (1989), EQS Structural Equations Program Manual.Los Angeles, CA: BMDP Software.
9.
BentlerPeter M. (1990), “Comparative Fit Indexes in Structural Models,”Psychological Bulletin, 107(March), 238–46.
10.
BentlerPeter M., and DijkstraT. (1985), “Efficient Estimation via Linearization in Structural Models,” in Multivariate Analysis VI, KirshnaiahParuchuri R., ed. Amsterdam: North-Holland, 9–42.
11.
BollenKenneth A. (1989), Structural Equations with Latent Variables.New York: John Wiley & Sons, Inc.
12.
BollenKenneth A., and Scott LongJ. (1993), Testing Structural Equation Models.Newbury Park, CA: Sage Publications, Inc.
13.
BoomsmaAnne (1983), On the Robustness of LISREL (Maximum Likelihood Estimation) Against Small Sample Size and Nonnormality.Amsterdam: Sociometric Research Foundation.
14.
BrowneMichael W. (1982), “Covariance Structures,” in Topics in Applied Multivariate Analysis, HawkinsDouglas M., ed. Cambridge: Cambridge University Press, 72–141.
15.
BrowneMichael W. (1987), “Robustness of Statistical Inference in Factor Analysis and Related Models,”Biometrika, 74(June), 375–84.
16.
BurtRonald S. (1976), “Interpretational Confounding of Unobserved Variables in Structural Equation Models,”Sociological Methods and Research, 5(August), 3–52.
17.
BusemeyerJerome R., and JonesLawrence E. (1983), “Analysis of Multiplicative Combination Rules when the Causal Variables are Measured with Error,”Psychological Bulletin, 93(May), 549–62.
18.
CohenJacob, and CohenPatricia (1983), Applied Multiple Regression/Correlation Analyses for the Behavioral Sciences.Hillsdale, NJ: Lawrence Erlbaum Associates.
19.
DwyerF. Robert, SchurrPaul H., and OhSejo (1987), “Developing Buyer-Seller Relationships,”Journal of Marketing, 51(April), 11–27.
20.
EngelJames F., BlackwellRodger D., and KollatDavid T. (1978), Consumer Behavior, 3d. ed. Hinsdale, IL: Dryden.
21.
FeuchtThomas E. (1989), “Estimating Multiplicative Regression Terms in the Presence of Measurement Error,”Sociological Methods and Research, 17(February), 257–82.
22.
GerbingDavid W., and AndersonJames C. (1988), “An Updated Paradigm for Scale Development Incorporating Unidimensionality and Its Assessment,”Journal of Marketing Research, 25(May), 186–92.
23.
HarlowLawrence L. (1985), Behavior of Some Elliptical Theory Estimators with Nonnormal Data in a Covariance Structures Framework: A Monte Carlo Study, unpublished dissertation, University of California, Los Angeles.
24.
HaydukLeslie A. (1987), Structural Equation Modeling with LISREL: Essential and Advances.Baltimore, MD: Johns Hopkins Press.
25.
HeideJan B., and JohnGeorge (1992), “Do Norms Matter in Marketing Relationships?”Journal of Marketing, 56(April), 32–44.
26.
HowardJohn A. (1977), Consumer Behavior: Application of Theory.New York: McGraw Hill.
27.
HowardJohn A. (1989), Consumer Behavior in Marketing Strategy.Englewood Cliffs, NJ: Prentice Hall.
28.
HowardJohn A., and ShethJagdish N. (1969), The Theory of Buyer Behavior.New York: John Wiley & Sons, Inc.
29.
HuLi-tze, BentlerPeter M., and KanoYutaka (1992), “Can Test Statistics in Covariance Structure Analysis Be Trusted?”Psychological Bulletin, 112(September), 351–62.
30.
JaccardJames, and WanChoi K. (1995), “Measurement Error in the Analysis of Interaction Effects Between Continuous Predictors Using Multiple Regression: Multiple Indicator and Structural Equation Approaches,”Psychological Bulletin, 117(March), 348–57.
31.
JaccardJames, TurrisiRobert, and WanChoi K. (1990), Interaction Effects in Multiple Regression.Newbury Park, CA: Sage Publications, Inc.
32.
JöreskogKarl G. (1993), “Testing Structural Equation Models,” in Testing Structural Equation Models, BollenKenneth A., and Scott LongJ., eds. Newbury Park, CA: Sage Publications, Inc., 294–316.
33.
JöreskogKarl G., and SörbomDag (1989), LISREL 7: A Guide to the Program and Applications, 2d ed. Chicago: SPSS, Incorporated.
34.
KennyDavid, and JuddCharles M. (1984), “Estimating the Nonlinear and Interactive Effects of Latent Variables,”Psychological Bulletin, 96(July), 201–10.
35.
KohliAjay K. (1989), “Effects of Supervisory Behavior: The Role of Individual Differences Among Salespeople,”Journal of Marketing, 53(October), 40–50.
36.
LarocheMichel, and HowardJohn A. (1980), “Non-Linear Relations in a Complex Model of Buyer Behavior,”Journal of Consumer Research, 6(March), 377–88.
37.
NeterJohn, WassermanWilliam, and KunterMichael H. (1988), Applied Linear Statistical Models.Homewood, IL: Richard D. Irwin, Inc.
38.
PingRobert A. (1994), “Does Satisfaction Moderate the Association Between Alternative Attractiveness and Exit Intention in a Marketing Channel?”Journal of the Academy of Marketing Science, 22(Fall), 364–71.
39.
PingRobert A. (1995), “Latent Variable Interaction and Quadratic Effect Estimation: A Two-Step Technique Using Structural Equation Analysis,”Psychological Bulletin, forthcoming.
40.
SharmaSubhash, DurandRichard M., and Gur-ArieOded (1981), “Identification and Analysis of Moderator Variables,”Journal of Marketing Research, 28(August), 291–300.
41.
SharmaSubhash, DurvasulaSrinivas, and DillonWilliam R. (1989), “Some Results on the Behavior of Alternative Covariance Structure Estimation Procedures in the Presence of Nonnormal Data,”Journal of Marketing Research, 24(May), 214–21.
42.
SherifMuzafer, and HovlandCarl I. (1961), Social Judgement: Assimilation and Contrast Effects in Communication and Attitude Change.New Haven, CT: Yale University Press.
43.
SternLouis W., and ReveTorger (1980), “Distribution Channels as Political Economies: A Framework for Comparative Analysis,”Journal of Marketing, 44(Summer), 52–64.
44.
TanakaJeffrey S. (1984), Some Results on the Estimation of Co-variance Structure Models, unpublished dissertation, University of California, Los Angeles.
45.
TeasR. Kenneth (1981), “An Empirical Test of Models of Salespersons’ Job Expectancy and Instrumentality Perceptions,”Journal of Marketing Research, 18(May), 209–26.
46.
WalkerOrville C, ChurchillGilbert A., and FordNeil M. (1977), “Motivation and Performance in Industrial Selling: Present Knowledge and Needed Research,”Journal of Marketing Research, 14(May), 156–68.
47.
WeitzBarton A. (1981), “Effectiveness in Sales Interactions: A Contingency Framework,”Journal of Marketing, 45(Winter), 85–103
