Skip to main content

Advertisement

SpringerLink
Log in

Constrained Stochastic Extended Redundancy Analysis

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

We devise a new statistical methodology called constrained stochastic extended redundancy analysis (CSERA) to examine the comparative impact of various conceptual factors, or drivers, as well as the specific predictor variables that contribute to each driver on designated dependent variable(s). The technical details of the proposed methodology, the maximum likelihood estimation algorithm, and model selection heuristics are discussed. A sports marketing consumer psychology application is provided in a Major League Baseball (MLB) context where the effects of six conceptual drivers of game attendance and their defining predictor variables are estimated. Results compare favorably to those obtained using traditional extended redundancy analysis (ERA).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1.
Figure 2.
Figure 3.

Similar content being viewed by others

Notes

  1. Under proper normalization conditions, the squared regression coefficients in CSERA are equivalent to the total variance accounted for by the specific items that make up each set.

  2. We also estimated a variety of different solutions varying the predictor variables utilized in the analysis as well as with and without the orthogonality constraints. In terms of model selection heuristics and/or interpretation, the presented solution dominated all others.

  3. One reviewer suggested a formal comparison with principal components regression (PCR). Note, PCR extracts a series of components from a single set of predictors without consideration of the dependent variable. Thus, there is no guarantee that the components extracted are the best ones for explaining the variance of the dependent variable. This is a major departure from CSERA, where a component is extracted from each of multiple sets of predictors such that it also explains the maximum amount of variance in the dependent variable. In addition, as stated above, another distinction is that PCR deals with a single set of predictor variables only, whereas CSERA deals with multiple sets of predictor variables. Thus, from a technical standpoint, it is difficult to directly compare PCR to CSERA. Moreover, from an empirical standpoint, it is not suitable to apply PCR to the analysis of our data, which involve multiple sets of predictors.

References

  • Allan, S. (2004). Satellite television and football attendance: the not so super effect. Applied Economics Letters, 11(2), 123–125.

    Article  Google Scholar 

  • Anderson, T.W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distributions. The Annals of Mathematical Statistics, 22(3), 327–351.

    Article  Google Scholar 

  • Baade, R.A., & Tiehen, L.J. (1990). An analysis of Major League Baseball attendance, 1969–1987. Journal of Sport & Social Issues, 14(1), 14–32.

    Article  Google Scholar 

  • Badenhausen, K., Ozanian, M., & Settimi, C. (2013, March 27). MLB team values: the business of baseball. Forbes. Retrieved from http://www.forbes.com/mlb-valuations/list/.

  • Baimbridge, M., Cameron, S., & Dawson, P. (1996). Satellite television and the demand for football: a whole new ball game? Scottish Journal of Political Economy, 43(3), 317–333.

    Article  Google Scholar 

  • Barilla, A.G., Gruben, K., & Levernier, W. (2008). The effect of promotions on attendance at Major League Baseball games. Journal of Applied Business Research, 24(3), 1–14.

    Google Scholar 

  • Baseball-Reference.com (2013). Pittsburgh Pirates team history & encyclopedia. Retrieved from http://www.baseball-reference.com/teams/PIT/.

  • Becker, M.A., & Suls, J. (1983). Take me out to the ballgame: the effects of objective, social, and temporal performance information on attendance at Major League Baseball games. Journal of Sport Psychology, 5(3), 302–313.

    Google Scholar 

  • Beckman, E.M., Cai, W., Esrock, R.M., & Lemke, R.J. (2012). Explaining game-to-game ticket sales for Major League Baseball games over time. Journal of Sports Economics, 13(5), 536–553.

    Article  Google Scholar 

  • Bird, P.J.W.N. (1982). The demand for league football. Applied Economics, 14(6), 637–649.

    Article  Google Scholar 

  • Boyd, T.C., & Krehbiel, T.C. (2003). Promotion timing in Major League Baseball and the stacking effects of factors that increase game attractiveness. Sport Marketing Quarterly, 12(3), 173–183.

    Google Scholar 

  • Broughton, D. (2012, November 12). Everybody loves bobbleheads: popular giveaway climbs past t-shirts, headwear to top spot on promotions list. Sports Business Journal. Retrieved from http://www.sportsbusinessdaily.com/Journal/Issues/2012/11/12/Research-and-Ratings/Bobbleheads.aspx.

  • Carroll, J.D. (1968). Generalizations of canonical correlation to three or more sets of variables. In Proceedings of the 76th annual meeting of the American Psychological Association (pp. 227–228).

    Google Scholar 

  • Davies, P.T., & Tso, M.K.S. (1982). Procedures for reduced-rank regression. Applied Statistics, 31(3), 244–255.

    Article  Google Scholar 

  • DeSarbo, W.S. (2009, December 21). Measuring fan avidity can help marketers narrow their focus. Sports Business Journal. Retrieved from http://www.sportsbusinessdaily.com/Journal/Issues/2009/12/20091221/From-The-Field-Of/Measuring-Fan-Avidity-Can-Help-Marketers-Narrow-Their-Focus.aspx.

  • DeSarbo, W.S., Stadler Blank, A., & McKeon, C. (2012, May 14). Proper mix of promotional offerings can produce for teams. Sports Business Journal. Retrieved from http://www.sportsbusinessdaily.com/Journal/Issues/2012/05/14/Opinion/From-the-Field-of-Research.aspx.

  • Dvorchak, R. (2008, March 30). Losing has lost its luster. Pittsburgh Post-Gazette. Retrieved from http://www.post-gazette.com/stories/sports/pirates/losing-has-lost-its-luster-387105/.

  • Efron, B. (1982). The jackknife, the bootstrap and other resampling plans (Vol. 38). Philadelphia: SIAM.

    Book  Google Scholar 

  • Efron, B., & Tibshirani, R.J. (1998). An introduction to the bootstrap (Vol. 57). Boca Raton: CRC Press.

    Google Scholar 

  • Fizel, J.L., & Bennett, R.W. (1989). The impact of college football telecasts on college football attendance. Social Science Quarterly, 70(4), 980–988.

    Google Scholar 

  • Gitter, S.R., & Rhoads, T.A. (2010). Determinants of Minor League Baseball attendance. Journal of Sports Economics, 11(6), 614–628.

    Article  Google Scholar 

  • Green, P.J. (1984). Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives. Journal of the Royal Statistical Society. Series B. Methodological, 46(2), 149–192.

    Google Scholar 

  • Greenstein, T.N., & Marcum, J.P. (1981). Factors affecting attendance of Major League Baseball: I. Team performance. Review of Sport & Leisure, 6(2), 21–34.

    Google Scholar 

  • Hansen, H., & Gauthier, R. (1989). Factors affecting attendance at professional sport events. Journal of Sport Management, 3(1), 15–32.

    Google Scholar 

  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: data mining, inference, and prediction (2nd ed.). New York: Springer.

    Book  Google Scholar 

  • Hill, J.R., Madura, J., & Zuber, R.A. (1982). The short run demand for Major League Baseball. Atlantic Economic Journal, 10(2), 31–35.

    Article  Google Scholar 

  • Hoerl, A.E., & Kennard, R.W. (1970). Ridge regression: applications to nonorthogonal problems. Technometrics, 12(1), 69–82.

    Article  Google Scholar 

  • Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3/4), 321–377.

    Article  Google Scholar 

  • Hwang, H. (2009). Regularized generalized structured component analysis. Psychometrika, 74(3), 517–530.

    Article  Google Scholar 

  • Hwang, H., & Takane, Y. (2004). Generalized structured component analysis. Psychometrika, 69(1), 81–99.

    Article  Google Scholar 

  • Hwang, H., Suk, H.W., Lee, J.H., Moskowitz, D.S., & Lim, J. (2012). Functional extended redundancy analysis. Psychometrika, 77(3), 524–542.

    Article  Google Scholar 

  • Hwang, H., Suk, H.W., Takane, Y., Lee, J.H., & Lim, J. (2013). Generalized functional extended redundancy analysis (Working paper). McGill University.

  • Izenman, A.J. (1975). Reduced-rank regression for the multivariate linear model. Journal of Multivariate Analysis, 5(2), 248–264.

    Article  Google Scholar 

  • Jöreskog, K.G. (1973). A general method for estimating a linear structural equation system. In A.S. Goldberger & O.D. Duncan (Eds.), Structural equation models in the social sciences (pp. 85–112). New York: Seminar Press.

    Google Scholar 

  • Kappe, E., Stadler Blank, A., & DeSarbo, W.S. (2014). A general multiple distributed lag framework for estimating the dynamic effects of promotions. Management Science, fothcoming.

  • Kettenring, J.R. (1971). Canonical analysis of several sets of variables. Biometrika, 58(3), 433–451.

    Article  Google Scholar 

  • Le Cessie, S., & Van Houwelingen, J.C. (1992). Ridge estimators in logistic regression. Applied Statistics, 41(1), 191–201.

    Article  Google Scholar 

  • Lee, A.H., & Silvapulle, M.J. (1988). Ridge estimation in logistic regression. Communications in Statistics. Simulation and Computation, 17(4), 1231–1257.

    Article  Google Scholar 

  • Lemke, R.J., Leonard, M., & Tlhokwane, K. (2010). Estimating attendance at Major League Baseball games for the 2007 season. Journal of Sports Economics, 11(3), 316–348.

    Article  Google Scholar 

  • Lohmöller, J.B. (1989). Latent variable path modeling with partial least squares. Heidelberg: Physica-Verlag.

    Book  Google Scholar 

  • Marcum, J.P., & Greenstein, T.N. (1985). Factors affecting attendance of Major League Baseball: II. A within-season analysis. Sociology of Sport Journal, 2(4), 314–322.

    Google Scholar 

  • McDonald, M., & Rascher, D. (2000). Does bat day make cents? The effect of promotions on the demand for Major League Baseball. Journal of Sport Management, 14, 8–27.

    Google Scholar 

  • Plunkett Research, Ltd. (2013). Sports industry overview. Retrieved from www.plunkettresearch.com/sports-recreation-leisure-market-research/industry-statistics.

  • Ramsay, J.O., & Silverman, B.W. (2005). Functional data analysis (2nd ed.). New York: Springer.

    Google Scholar 

  • Rao, C.R. (1964). The use and interpretation of principal component analysis in applied research. Sankhyā: The Indian Journal of Statistics, Series A, 26(4), 329–358.

    Google Scholar 

  • Reinsel, G.C., & Velu, R.P. (1998). Multivariate reduced-rank regression: theory and applications. New York: Springer.

    Book  Google Scholar 

  • Richards, F.S.G. (1961). A method of maximum-likelihood estimation. Journal of the Royal Statistical Society. Series B. Methodological, 23(2), 469–475.

    Google Scholar 

  • Siegfried, J.J., & Hinshaw, C.E. (1977). Professional football and the anti-blackout law. Journal of Communication, 27(3), 169–174.

    Article  Google Scholar 

  • Siegfried, J.J., & Hinshaw, C.E. (1979). The effect of lifting television blackouts on professional football no-shows. Journal of Economics and Business, 32(1), 1–13.

    Google Scholar 

  • Sports Business Journal (2013, May 13). MLB turnstile tracker. Sports Business Journal. Retrieved from http://www.sportsbusinessdaily.com/Journal/Issues/2013/05/13/Research-and-Ratings/MLB-Turnstile-Tracker.aspx.

  • Takane, Y., & Hwang, H. (2005). An extended redundancy analysis and its applications to two practical examples. Computational Statistics & Data Analysis, 49(3), 785–808.

    Article  Google Scholar 

  • Trail, G.T., Robinson, M.J., & Kim, Y.K. (2008). Sport consumer behavior: a test for group differences on structural constraints. Sport Marketing Quarterly, 17(4), 190–200.

    Google Scholar 

  • Van Den Wollenberg, A.L. (1977). Redundancy analysis an alternative for canonical correlation analysis. Psychometrika, 42(2), 207–219.

    Article  Google Scholar 

  • Velu, R.P. (1991). Reduced rank models with two sets of regressors. Applied Statistics, 40(1), 159–170.

    Article  Google Scholar 

  • Wedel, M., & DeSarbo, W.S. (1995). A mixture likelihood approach for generalized linear models. Journal of Classification, 12(1), 21–55.

    Article  Google Scholar 

  • Welki, A.M., & Zlatoper, T.J. (1999). U.S. professional football game-day attendance. Atlantic Economic Journal, 27(3), 285–298.

    Article  Google Scholar 

  • Wold, H. (1975). Path models with latent variables: the NIPALS approach. In H.M. Blalock, A. Aganbegian, F.M. Borodkin, R. Boudon, & V. Cappecchi (Eds.), Quantitative sociology: international perspectives on mathematical and statistical modeling (pp. 307–357). New York: Academic Press.

    Chapter  Google Scholar 

  • Wold, H. (1982). Soft modeling: the basic design and some extensions. In K.G. Jöreskog & H. Wold (Eds.), Systems under indirect observation: causality, structure, prediction (Part II) (pp. 1–54). Amsterdam: North-Holland.

    Google Scholar 

  • Yee, T.W., & Hastie, T.J. (2003). Reduced-rank vector generalized linear models. Statistical Modelling, 3(1), 15–41.

    Article  Google Scholar 

  • Zhang, J.J., & Smith, D.W. (1997). Impact of broadcasting on the attendance of professional basketball games. Sport Marketing Quarterly, 6(1), 23–29.

    Google Scholar 

Download references

Acknowledgements

The authors wish to thank three anonymous reviewers and the section editor for their constructive comments. The authors also wish to thank Frank Coonelly, President of the Pirates, Lou DePaoli, Executive Vice President and CMO of the Pirates, Jim Plake, Executive Vice President and CFO of the Pirates, and Jim Alexander, Senior Director of Business Analytics of the Pirates, for their cooperation in the execution of this research.

Author information

Authors and Affiliations

  1. Smeal College of Business, Pennsylvania State University, University Park, PA, 16802, USA

    Wayne S. DeSarbo, Ashley Stadler Blank & Eelco Kappe

  2. Department of Psychology, McGill University, Montreal, Quebec, H3A 1B1, Canada

    Heungsun Hwang

  3. Marketing Department, Smeal College of Business, Pennsylvania State University, University Park, PA, 16802, USA

    Wayne S. DeSarbo

Authors
  1. Wayne S. DeSarbo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heungsun Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ashley Stadler Blank
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Eelco Kappe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wayne S. DeSarbo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

DeSarbo, W.S., Hwang, H., Stadler Blank, A. et al. Constrained Stochastic Extended Redundancy Analysis. Psychometrika 80, 516–534 (2015). https://doi.org/10.1007/s11336-013-9385-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11336-013-9385-6

Key words

Search

Navigation