Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T23:22:47.249Z Has data issue: false hasContentIssue false
  • English
  • Français

A Latent Variable Model for Discrete Multivariate Psychometric Waiting Times

Published online by Cambridge University Press:  01 January 2025

Jeffrey A. Douglas ,
Michael R. Kosorok  and
Betty A. Chewning
Jeffrey A. Douglas*
Affiliation:
Department of Biostatistics, University of Wisconsin-Madison
Michael R. Kosorok
Affiliation:
Departments of Statistics and Biostatistics, University of Wisconsin-Madison
Betty A. Chewning
Affiliation:
School of Pharmacy, University of Wisconsin-Madison
*
Requests for reprints should be sent to Jeffrey A. Douglas, Department of Biostatistics, K6-446 Clinical Science Center, University of Wisconsin, 600 Highland Avenue, Madison, WI 53792. E-mail: douglas@biostat.wisc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A version of the discrete proportional hazards model is developed for psychometrical applications. In such applications, a primary covariate that influences failure times is a latent variable representing a psychological construct. The Metropolis-Hastings algorithm is studied as a method for performing marginal likelihood inference on the item parameters. The model is illustrated with a real data example that relates the age at which teenagers first experience various substances to the latent ability to avoid the onset of such behaviors.

Keywords

latent variablefrailtyMetropolis-Hastings algorithmsurvival analysis

Information

Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 1 , March 1999 , pp. 69 - 82
Copyright
Copyright © 1999 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

We thank Michael Newton and Daode Huang for their helpful comments and suggestions.

References

Albert, J.H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17, 251–269.CrossRefGoogle Scholar
Andersen, P.K., Borgan, O., Gill, R.D., & Keiding, N. (1992). Statistical models based on counting processes, New York: Springer-Verlag.Google Scholar
Besag, J., & Green, P.J. (1993). Spatial statistics and Bayesian computation. Journal of the Royal Statistical Society, Series B, 55, 25–37.CrossRefGoogle Scholar
Besag, J., Green, P., Higdon, D., & Mengersen, K. (1995). Bayesian computation and stochastic systems. Statistical Science, 10, 3–66.Google Scholar
Bloxom, B. (1985). Considerations in psychometric modeling of response time. Psychometrika, 50, 383–397.CrossRefGoogle Scholar
Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, 327–335.CrossRefGoogle Scholar
Clayton, D. (1991). A Monte Carlo Method for Bayesian inference in frailty models. Biometrics, 47, 467–485.CrossRefGoogle Scholar
Clayton, D., & Cuzick, J. (1985). Multivariate generalizations of the proportional hazards model. Journal of the Royal Statistical Society, Series A, 148, 82–117.CrossRefGoogle Scholar
Cox, D.R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B, 34, 187–220.CrossRefGoogle Scholar
Gelman, A., Carlin, J.B., Stern, H.S., & Rubin, D.B. (1995). Bayesian analysis, London: Chapman & Hall.CrossRefGoogle Scholar
Guo, G., & Rodriguez, G. (1992). Estimating a multivariate proportional hazards model for clustered data using the EM algorithm, with an application to child survival in Guatemala. Journal of the American Statistical Association, 87, 969–976.CrossRefGoogle Scholar
Hambleton, R.K., & Swaminathan, H. (1985). Item response theory; Principles and applications, Boston: Kluwer Nyhoff.CrossRefGoogle Scholar
Hastings, W.K. (1970). Monte Carlo sampling methods using Markov Chains and their applications. Biometrika, 57, 57–109.CrossRefGoogle Scholar
Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika, 73, 671–678.Google Scholar
Johnson, R.A. (1967). An asymptotic expansion for posterior distributions. Annals of Mathematical Statistics, 38, 1899–1906.CrossRefGoogle Scholar
Johnson, R.A. (1970). Asymptotic expansions associated with posterior distributions. Annals of Mathematical Statistics, 41, 851–864.CrossRefGoogle Scholar
Kalbfleisch, J.D., & Prentice, R.L. (1980). The statistical analysis of failure time data, New York: Wiley.Google Scholar
Lehmann, E.L. (1983). Theory of point estimation, New York: Wiley.CrossRefGoogle Scholar
Luce, R.D. (1986). Response times: Their role in inferring elementary mental organization, New York: Oxford University Press.Google Scholar
Maris, E. (1993). Additive and multiplicative models for gamma distributed random variables, and their application as psychometric models for response times. Psychometrika, 58, 445–469.CrossRefGoogle Scholar
McGill, W.J., & Gibbon, J. (1965). The general gamma distribution and reaction times. Journal of Mathematical Psychology, 2, 1–18.CrossRefGoogle Scholar
Meng, X., & Schilling, S. (1996). Fitting full-information item factor models and an empirical investigation of bridge sampling. Journal of the American Statistical Association, 91, 1254–1267.CrossRefGoogle Scholar
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., & Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.CrossRefGoogle Scholar
Millsap, R.E., & Meredith, W. (1987). Structure in semantic memory: A probabilistic approach using continuous response task. Psychometrika, 52, 19–41.CrossRefGoogle Scholar
Oakes, D. (1986). Semiparametric inference in a model of association in bivariate survival data. Biometrika, 73, 353–361.Google Scholar
Oakes, D. (1989). Bivariate survival models induced by frailties. Journal of the American Statistical Association, 84, 487–493.CrossRefGoogle Scholar
Smith, A.F.M., & Roberts, G.O. (1993). Bayesian computation via the Gibbs sampler and related Markov Chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B, 55, 3–24.CrossRefGoogle Scholar
Thissen, D. (1983). Timed testing: An approach using item response theory. In Weiss, D.J. (Eds.), New horizons in testing: Latent trait test theory and computerized adaptive testing (pp. 179–203). New York: Academic Press.Google Scholar
Tierney, L. (1994). Markov chains for exploring posterior distributions. (with discussion). Annals of Statistics, 22, 1701–1762.Google Scholar
Vaupel, J.W., Manton, K.G., & Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–454.CrossRefGoogle ScholarPubMed
Zeger, Scott L., Liang, Kung-Yee, & Albert, Paul S. (1988). Models for longitudinal data: A generalized estimating equation approach. Biometrics, 44, 1049–1060.CrossRefGoogle Scholar