The author develops a new ridge estimator for the treatment of multicollinearity in structural equation models with unobservable variables. The method is illustrated by a simple model of advertising in the multiproduct firm. For the nonlinear interaction model, ordinary partial least squares (PLS) estimation leads to highly unstable results and meaningless estimates of advertising effectiveness. In contrast, the ridge PLS estimates are remarkably stable under perturbation and lead to managerially useful results.
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References
1.
AakerDavid, and BagozziR. P. (1979), “Unobservable Variables in Structural Equation Models with an Application in Industrial Selling,”Journal of Marketing Research, 16(May), 147–58.
2.
AreskougB., and LyttkensE., and WoldH. (1975), “Six Models with Two Blocks of Observables as Indicators for One of Two Latent Variables,” Research Report 1973:3, Department of Statistics, University of Göteborg.
3.
BagozziR. P. (1977), “Structural Equation Models in Experimental Research,”Journal of Marketing Research, 14(May), 209–26.
4.
BagozziR. P. (1981a), “Attitudes, Intentions and Behavior: A Test of Some Key Hypotheses,“Journal of Personality and Social Psychology, 41(4), 607–27.
5.
BagozziR. P. (1981b), “An Examination of the Validity of Two Models of Attitude,”Multivariate Behavioral Research, 16, 323–59.
6.
BeardenWilliam O., and HeadenR. S., and KlompmakerJ. E., and TeelJ. E. (1981), “Attentive Audience Delivery of TV Advertising Schedules,”Journal of Marketing Research, 18(May), 187–91.
7.
BelsleyDavid A. (1981), “Collinearity and Forecasting,” Technical Report No. 27, Center for Computational Research in Economics and Management Science, Sloan School of Management, MIT (April).
8.
BelsleyDavid A., and KuhE., and WelschR. E. (1980), Regression Diagnostics: Identifying Influential Data and Sources of Collinearity.New York: John Wiley & Sons, Inc.
9.
ChristensenL. R., and JorgensonD. W., and LauL. J. (1973), “Transcendental Logarithmic Production Frontiers,”Review of Economics and Statistics, 55(February), 28–45.
10.
DupacovaJitka, and WoldH. (1975), “NIPALS vs. Maximum Likelihood Modelling,” Research Report 1975:5, Department of Statistics, University of Goteburg.
11.
FornellClaes, and LarckerD. F. (1981), “Evaluating Structural Equation Models with Unobservable Variables and Measurement Error,”Journal of Marketing Research, 18(February), 39–50.
12.
HoerlA. E., and KennardR. W. (1970a), “Ridge Regression: Biased Estimation for Nonorthogonal Problems,”Technometrics, 12(February), 55–64.
13.
HoerlA. E., and KennardR. W. (1970b), “Ridge Regression: Application to Nonorthogonal Problems,”Technometrics, 12(February), 69–82.
14.
JagpalH. S. (1981), “Measuring Joint Advertising Effects in Multiproduct Firms,”Journal of Advertising Research, 21(1), 65–9.
15.
JagpalH. S., and SuditE. F., and VinodH. D. (1982), “Measuring Dynamic Marketing Mix Interactions Using Translog Functions,”Journal of Business (July), forthcoming.
16.
JöreskogK. G. (1973), “A General Method for Estimating a Linear Structural Equation System,” in Structural Equation Models in the Social Sciences, GoldbergerA. S., and DuncanO. D., eds. New York: Seminar Press.
17.
JöreskogK. G., and GoldbergerA. S. (1975), “Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable,”Journal of the American Statistical Association, 70, 631–9.
18.
JöreskogK. G., and SörbomD. (1978), LISREL IV: Analysis of Linear Structural Relations by the Method of Maximum Likelihood.Chicago: National Education Resources.
19.
LavidgeR., and SteinerG. A. (1961), “A Model for Predictive Measurement of Advertising Effectiveness,”Journal of Marketing, 25(October), 59–62.
20.
LearnerEdward E. (1973), “Multicollinearity: A Bayesian Interpretation,”Review of Economics and Statistics, 55, 371–80.
21.
MarquardtDonald W. (1970), “Generalized Inverses, Ridge Regression, Biased Linear Estimation and Nonlinear Estimation,”Technometrics, 12(August), 591–612.
22.
RothenbergT. J. (1971), “Identification in Parametric Models,”Econometrica, 39, 577–91.
23.
SharmaS., and JamesW. L. (1981), “Latent Root Regression: An Alternate Procedure for Estimating Parameters in the Presence of Multicollinearity,”Journal of Marketing Research, 18(May), 154–61.
24.
TheilH., and GoldbergerA. S. (1961), “On Pure and Mixed Statistical Estimation in Economics,”International Economic Review, 2, 65–78.
25.
VinodH. D. (1976), “Application of New Ridge Methods to a Study of Bell System Scale Economies,”Journal of the American Statistical Association, 71(December), 835–41.
26.
VinodH. D. (1978), “A Survey of Ridge Regression and Related Techniques for Improvements Over Ordinary Least Squares,”Review of Economics and Statistics, 60(February), 121–31.
27.
WoldHerman A. (1979), “Estimation and Evaluation of Models Where Theoretical Knowledge is Scarce: An Example of Partial Least Squares,” in Evaluation of Econometric Models, RamseyJ., and KmentaJ., eds. New York: Academic Press.
