• General Issues
  • Andrich, D. (1996). A hyperbolic cosine latent trait model for unfolding polytomous responses: Reconciling Thurstone and Likert methodologies. British Journal of Mathematical and Statistical Psychology, 49, 347-365.

  • Andrich, D. & Styles, I. M. (1998). The structural relationship between attitude and behaviour statements from the unfolding perspective. Psychological Methods, 3(4), 454-469.

  • Coombs, C. H. (1964). A theory of data. New York: Wiley.

  • Davison M. L. (1977). On a metric, unidimensional unfolding model for attitudinal and developmental data. Psychometrika, 42, 523-548.

  • Maraun, M. D., & Rossi, N. T. (2001). The extra-factor phenomenon revisited: Unidimensional unfolding as a quadratic factor analysis. Applied Psychological Measurement, 25(1), 77-87.

  • Noel, Y. (1999). Recovering unimodal latent patterns of change by unfolding analysis: Applications to smoking cessation. Psychological Methods, 4(2), 173-191.

  • Roberts, J. S. (1995). Item Response Theory Approaches to Attitude Measurement. (Doctoral dissertation, University of South Carolina, Columbia, 1995). Dissertation Abstracts International, 56, 7089B.

  • Roberts, J. S., Wedell, D. H., Laughlin, J. E. (1998). Heightened Sensitivity of Likert Attitude Scales to Restriction of Sample Range. Paper presented at the 1998 American Educational Research Association Annual Meeting, April 17, San Diego, California.

  • Roberts, J. S., Laughlin, J. E., & Wedell, D. H. (1999). Validity issues in the Likert and Thurstone Approaches to Attitude Measurement. Educational and Psychological Measurement, 59(2), 211-233.

  • van Schuur, W. H., & Kiers, H. A. L. (1994). Why factor analysis often is the incorrect model for analyzing bipolar concepts, and what model to use instead. Applied Psychological Measurement, 18(2), 97-110.

   

• Binary IRT Unfolding Models
  • Parametric Approaches
    • Andrich, D. (1988). The application of an unfolding model of the PIRT type to the measurement of attitude. Applied Psychological Measurement, 12, 33-51.

    • Andrich, D., & Luo, G. (1993). A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses. Applied Psychological Measurement, 17, 253-276.

    • Andrich, D. (1995). Hyperbolic cosine latent trait models for unfolding direct responses and pairwise preferences. Applied Psychological Measurement, 19, 269-290.

    • DeSarbo, W. S., & Hoffman, D. L. (1986). Simple and weighted unfolding threshold models for the spatial representation of binary choice data. Applied Psychological Measurement, 10, 247-264.

    • DeSarbo, W. S., & Hoffman, D. L. (1987). Constructing MDS joint spaces from binary choice data: A multidimensional unfolding threshold model for marketing research. Journal of Marketing Research, 24, 40-54.

    • Hoijtink, H. (1990). A latent trait model for dichotomous choice data. Psychometrika, 55, 641-656.

    • Hoijtink, H. (1991). The measurement of latent traits by proximity items. Applied Psychological Measurement, 15, 153-169.

    • Hoijtink, H. (1991). PARELLA: Measurement of latent traits by proximity items. Leiden: DSWO Press.

    • Johnson, M. (2001). Parametric and non-parametric extensions to unfolding respnse models. Doctoral dissertation, Carnegie Mellon University, Pittsburg.

    • Johnson, M., & Junker, B. W. (2003). Using data augmentation and Markov chain Monte Carlo for the estimation of unfolding response models. Journal of Educational and Behavioral Statistics, 28, 195-230.

    • Luo, G. (1998). A general formulation for unidimensional unfolding and pairwise preference models: Making explicit the latitude of acceptance. Journal of Mathematical Psychology, 42, 400-417.

    • Luo, G., Andrich, D., & Styles, I. (1998). The JML estimation of the generalised unfolding model incorporating the latitude of acceptance parameter. Australian Journal of Psychology, 50(3), 187-198.

    • Luo, G. (2000). Joint maximum likelihood estimation for the hyperbolic cosine model for single stimulus responses. Applied Psychological Measurement, 24, 33-49.

    • Verhelst N. D., & Verstralen H. H. F. M. (1993). A stochastic unfolding model derived from the partial credit model. Kwantitative Methoden, 42, 73-92.

  • Non-parametric Approaches
    • Johnson, M. (2001). Parametric and non-parametric extensions to unfolding respnse models. Doctoral dissertation, Carnegie Mellon University, Pittsburg.

    • Post, W. J. (1992). Nonparametric unfolding models: A latent structure approach. Leiden: DSWO Press.

    • Post, W. J., & Snijders T. A. B. (1993). Nonparametric unfolding models for dichotomous data. Sonderdruck Methodika, VII, 130-156.

    • van Schuur, W. H. (1984). Structure in political beliefs: A new model for stochastic unfolding with application to European party activists. Amsterdam: CT Press.

   

• Polytomous IRT Unfolding Models
  • Parametric Approaches
    • Andrich, D. (1996). A hyperbolic cosine latent trait model for unfolding polytomous responses: Reconciling Thurstone and Likert methodologies. British Journal of Mathematical and Statistical Psychology, 49, 347-365.

    • Finch, H., Habing, B., Roberts, J., Nandakumar, R. (April, 2002). A Q3 statistic for unfolding item response theory models. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, Louisiana.

    • Luo, G. (2001). A class of probabilistic unfolding models for polytomous responses. Journal of Mathematical Psychology, 45, 224-248.

    • Nandakumar, R., & Hotchkiss, L., & Roberts, J. S. (April, 2002). Attitudinal data: Dimensionality and approximate item scale values. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, Louisiana.

    • Roberts, J. S. (1995). Item Response Theory Approaches to Attitude Measurement. (Doctoral dissertation, University of South Carolina, Columbia, 1995). Dissertation Abstracts International, 56, 7089B.

    • Roberts, J. S. (2001). Equating parameter estimates from the generalized graded unfolding model. Paper presented at the annual meeting of the American Educational Research Association, April 14, Seattle, Washington.

    • Roberts, J. S. (2001). GGUM2000: Estimation of parameters in the generalized graded unfolding model. Applied Psychological Measurement, 25(1), 38.

    • Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (1996). A generalized item response model for unfolding responses from a graded scale. Paper presented at the 61st annual meeting of the Psychometric Society, June 28, Banff, Alberta, Canada.

    • Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (1998). The generalized graded unfolding model: A general parametric item response model for unfolding graded responses (RR-98-32). Princeton, NJ: Educational Testing Service.

    • Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (1999). Estimability of parameters in the generalized graded unfolding model. Presented at the annual meeting of the American Educational Research Association, April 22, Montreal, Canada.

    • Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (1999). Estimating parameters in the generalized graded unfolding model: Sensitivity to the prior distribution assumption and the number of quadrature points used. Paper Presented at the Annual Meeting of the National Council on Measurement in Education, April 22, Montreal, PQ, Canada.

    • Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (2000). A general item response theory model for unfolding unidimensional polytomous responses. Applied Psychological Measurement, 24, 3-32.

    • Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (2002). Characteristics of MML/EAP parameter estimates in the generalized graded unfolding model. Applied Psychological Measurement, 26, 192-207.

    • Roberts, J. S., & Huang, C. (2003). GGUMLINK: A computer program to link parameter estimates of the generalized graded unfolding model from item response theory. Behavior Research Methods, Instrumentation and Computers, 35, 525-549.

    • Roberts, J. S., & Laughlin, J. E. (1996). A unidimensional item response model for unfolding responses from a graded disagree-agree response scale. Applied Psychological Measurement, 20, 231-255.

    • Roberts, J. S., & Laughlin, J. E. (1996). The graded unfolding model: A unidimensional item response model for unfolding graded responses (RR-96-16). Princeton, NJ: Educational Testing Service.

    • Roberts, J. S., Lin, Y., & Laughlin, J. E. (2001). Computerized adaptive testing with the generalized graded unfolding model. Applied Psychological Measurement, 25, 177-196.

    • Roberts, J. S., Rost, J., & Macready, G. B. (2000). An unfolding mixture model to explore the latitude of acceptance concept in attitude measurement. Invited paper presented at the Fifth International Conference on Social Science Methodology, Cologne, Germany.

    • Rost J. & Luo G. (1997). An application of a Rasch-based unfolding model to a questionnaire on adolescent centrism. In J. Rost & Rolf L. (Eds.), Applications of latent trait and latent class models in the social sciences. New York: Waxmann Munster.

  • Non-parametric Approaches
    • Cliff, N., Collins, L. M., Zatkin, J., Gallipeau, D., & McCormick, D. J. (1988). An ordinal scaling method for questionnaire and other ordinal data. Applied Psychological Measurement, 12, 83-97.

    • van Schuur, W. H. (1993). Nonparametric unidimensional unfolding for multicategory data. Political Analysis, 4, 41-74.

If you know of other publications related to IRT unfolding models in addition to those listed above, please email James S. Roberts. We would like to add them on this page. Thanks.