Abstract
This paper develops diagnostic measures to identify those observations in Thurstonian models for ranking data which unduly influence parameter estimates that are obtained by the partition maximum likelihood approach of Chan and Bentler (1998). Diagnostic measures are constructed by employing the local influence approach that uses geometric techniques to assess the effect of small perturbations on a postulated statistical model. Very little additional effort is required to compute the proposed diagnostic measures, because all of the necessary building blocks are readily available after a usual fit of the model.
Similar content being viewed by others
References
Andersen, E.B. (1992). Diagnostics in categorical data analysis.Journal of the Royal Statistical Society, Series B,54, 781–791.
Böckenholt, U. (1992). Thurstonian representation for partial ranking data.British Journal of Mathematical and Statistical Psychology, 45, 31–49.
Chan, W. & Bentler, P.M. (1998). Covariance structure analysis of ordinal ipsative data.Psychometrika, 63, 369–399.
Cook, R.D. (1977). Detection of influential observations in linear regression.Technometrics, 19, 15–18.
Cook, R.D. (1986). Assessment of local influence (with discussion).Journal of the Royal Statistical Society, Series B,48, 133–169.
Cox, D.R., & Hinkley, D.V. (1974).Theoretical statistics. London, U.K.: Chapman and Hall.
Lawrance, A.J. (1991). Local and deletion influence. In W. Stahel & S. Weisberg (Eds.),Directions in robust statistics and diagnostics (Part 1, pp. 141–157). Berlin, Germany: Springer.
Lee, S.Y., Poon, W.Y., & Bentler, P.M. (1990). A three-stage estimation procedure for structural equation models with polytomous variables.Psychometrika, 55, 45–52.
McKeon, J.J. (1961).Measurement procedures based on comparative judgment. Unpublished doctoral dissertation, University of North Carolina, Chapel Hill, North Carolina.
Parke, W.R. (1986). Pseudo maximum likelihood estimation: The asymptotic distribution.The Annals of Statistics, 14, 355–357.
Poon, W.Y., & Poon, Y.S. (1999). Conformal normal curvature and assessment of local influence.Journal of the Royal Statistical Society, Series B,61, 51–61.
Poon, W.Y., & Poon, Y.S. (2002). Influential observations in the estimation of mean vector and covariance matrix.British Journal of Mathematical and Statistical Psychology, 55, 177–192.
Poon, W.Y., Lew, S.F., & Poon, Y.S. (2000). A local influence approach to identifying multiple multivariate outliers.British Journal of Mathematical and Statistical Psychology, 53, 255–273.
Poon, W.Y., Wang, S.J., & Lee, S.Y. (1999). Influence analysis of structural equation models with polytomous variables.Psychometrika, 64, 461–473.
Tanaka, Y., Watadani, S., & Moon, S.H. (1991). Influence in covariance structure analysis: With an application to confirmatory factor analysis.Communications in Statistics, Series A,20, 3805–3821.
Thomas, W., & Cook, R.D. (1990). Assessing influence on predictions in generalized linear models.Technometrics, 32, 59–65.
Thurstone, L.L. (1927). A law of comparative judgment.Psychological Review, 34, 273–286.
Yuan, K.H., and Bentler, P.M. (2001). Effect of outliers on estimators and tests in covariance structure analysis.British Journal of Mathematical and Statistical Psychology, 54, 161–175.
Yuan, K.H., Chan, W., & Bentler, P.M. (2000). Robust transformation with applications to structural equation modelling.British Journal of Mathematical and Statistical Psychology, 53, 31–50.
Author information
Authors and Affiliations
Corresponding author
Additional information
The work described in this paper was partially supported by the grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (RGC Ref. No. CUHK4186/98P and RGC Direct Grant ID2060178). The authors are grateful to the Editor and four anonymous referees for their helpful comments.
Rights and permissions
About this article
Cite this article
Poon, WY., Chan, W. Influence analysis of ranking data. Psychometrika 67, 421–436 (2002). https://doi.org/10.1007/BF02294994
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294994