×

zbMATH — the first resource for mathematics

A Dirichlet random coefficient regression model for quality indicators. (English) Zbl 1077.62128
Summary: We present a random coefficient regression model in which a response is linearly related to some explanatory variables with random coefficients following a Dirichlet distribution. These coefficients can be interpreted as weights because they are nonnegative and add up to one. The proposed estimation procedure combines iteratively reweighted least squares and the maximization on an approximated likelihood function. We also present a diagnostic tool based on a residual Q-Q plot and two procedures for estimating individual weights. The model is used to construct an index for measuring the quality of the railroad system in Spain.

MSC:
62P30 Applications of statistics in engineering and industry; control charts
62F10 Point estimation
62J99 Linear inference, regression
PDF BibTeX Cite
Full Text: DOI
References:
[1] Allenby, G.M.; Rossi, P.E., Marketing models of consumer heterogeneity, J. econometrics, 89, 57-78, (1999) · Zbl 0959.62116
[2] Carroll, J.D.; Green, P.E., Psychometric methods in marketing researchpart I, conjoint analysis, J. marketing res., XXXII, 385-391, (1995)
[3] Cronin, J.; Taylor, S., Measuring service qualitya reexamination and extension, J. marketing, 56, July, 55-68, (1992)
[4] Cronin, J.; Taylor, S., SERVPERF versus servqualreconciling performance-based and perceptions-minus-expectations measurement of service quality, J. marketing, 58, January, 125-131, (1994)
[5] Gumpertz, M.L.; Pantula, S.G., Regression, random coefficient, (), 581-586
[6] Härdle, W., Applied nonparametric regression, () · Zbl 0714.62030
[7] Johnson, V., On Bayesian analysis of multirated ordinal dataan application to automated essay grading, J. amer. statist. assoc., 91, 42-51, (1996) · Zbl 0925.62104
[8] Lawson, C.L.; Hanson, R.J., Solving least squares problems, (1974), Prentice-Hall Englewood Cliffs, NJ · Zbl 0185.40701
[9] Lenk, P.J.; DeSarbo, W.S.; Green, P.E.; Young, M.R., Hierarchical Bayesian analysisrecovery of partworth heterogeneity from reduced experimental, Marketing sci., 28, May, 215-222, (1996)
[10] Luce, D.R.; Tukey, J.W., Simultaneous conjoint measurementa new type of fundamental measurement, J. math. psychol., 1, 1-27, (1964) · Zbl 0166.42201
[11] Lynch, J.G.; Bouzas, T.E.; y Berg, S.V., Regulatory measurement and evaluation of telephone service quality, Management sci., 40, 2, 168-194, (1994)
[12] Mallet, A., A maximum likelihood estimation method for random coefficient regression models, Biometrika, 73, 645-646, (1986) · Zbl 0615.62083
[13] McLachlan, G.J.; Krishnan, T., The EM algorithm and extensions, (1997), Wiley New York · Zbl 0882.62012
[14] Moreno, A., Rios-Insúa, D., 1998. Issues in Service Quality Modelling. In: Bernardo, J.M., et al. (Eds.), Bayesian Statistics, vol. 6. pp. 441-457. · Zbl 0974.62113
[15] Ostrom, A.; Iacobucci, D., Consumer trade-offs and the evaluation of services, J. marketing, 59, 17-28, (1995)
[16] Parasuraman, A.; Zeithaml, V.A.; Berry, L.L., SERVQUALA multiple item scale for measuring consumer perceptions of service quality, J. retailing, 64, 12-40, (1988)
[17] Parasuraman, A.; Zeithaml, V.A.; Berry, L.L., Refinement and reassessment of the SERVQUAL scale, J. retailing, 67, 4, 420-450, (1991)
[18] Parasuraman, A.; Zeithaml, V.A.; Berry, L.L., Reassessment of expectations as a comparison standard in measuring service qualityimplications for further research, J. marketing, 58, 111-124, (1994)
[19] Peña, D., Measuring service quality by linear indicators, (), 35-51
[20] Rossi, P.E.; Gilula, Z.; Allenby, G.M., Overcoming scale usage heterogeneitya Bayesian hierarchical approach, J. amer. statist. assoc., 96, 20-31, (2001)
[21] Teas, R.K., Expectations, performance evaluation, and consumers’ perceptions of quality, J. marketing, 57, 18-34, (1993)
[22] Teas, R.K., Expectations as a comparison standard in measuring service qualityan assessment of a reassessment, J. marketing, 58, January, 132-139, (1994)
[23] Wedel, M.; DeSarbo, W., A review of recent developments in latent class regression models, (), 353-388
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.