Hostname: page-component-5f745c7db-f9j5r Total loading time: 0 Render date: 2025-01-06T07:19:27.034Z Has data issue: true hasContentIssue false
  • English
  • Français

Analysis of Multiple Partially Ordered Responses to Belief Items with Don’t Know Option

Published online by Cambridge University Press:  01 January 2025

Edward H. Ip ,
Shyh-Huei Chen  and
Sara A. Quandt
Edward H. Ip*
Affiliation:
Wake Forest School of Medicine
Shyh-Huei Chen
Affiliation:
Wake Forest School of Medicine
Sara A. Quandt
Affiliation:
Wake Forest School of Medicine
*
Correspondence should be made to Edward H. Ip, Department of Biostatistical Sciences, Wake Forest School of Medicine, Medical Center Blvd., Winston-Salem, NC 27157, USA. Email: eip@wakehealth.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Understanding beliefs, values, and preferences of patients is a tenet of contemporary health sciences. This application was motivated by the analysis of multiple partially ordered set (poset) responses from an inventory on layman beliefs about diabetes. The partially ordered set arises because of two features in the data—first, the response options contain a Don’t Know (DK) option, and second, there were two consecutive occasions of measurement. As predicted by the common sense model of illness, beliefs about diabetes were not necessarily stable across the two measurement occasions. Instead of analyzing the two occasions separately, we studied the joint responses across the occasions as a poset response. Few analytic methods exist for data structures other than ordered or nominal categories. Poset responses are routinely collapsed and then analyzed as either rank ordered or nominal data, leading to the loss of nuanced information that might be present within poset categories. In this paper we developed a general class of item response models for analyzing the poset data collected from the Common Sense Model of Diabetes Inventory. The inferential object of interest is the latent trait that indicates congruence of belief with the biomedical model. To apply an item response model to the poset diabetes inventory, we proved that a simple coding algorithm circumvents the requirement of writing new codes such that standard IRT software could be directly used for the purpose of item estimation and individual scoring. Simulation experiments were used to examine parameter recovery for the proposed poset model.

Keywords

posetitem response theoryposet partitioned conditional IRTweakly ordered setcommon sense modeldiabeteslay beliefs about disease
Type
Article
Information
Psychometrika , Volume 81 , Issue 2 , June 2016 , pp. 483 - 505
Copyright
Copyright © 2014 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.)

References

American Diabetes Association, ADA. (2012). Standards of medical care in diabetes. Diabetes Care, 35(Suppl. 1), S11–S63.Google Scholar
Arcury, T.A., Grzywacz, J.G., Ip, E.H., Saldana, S., Nguyen, H.T., Bell, R.A., Kirk, J.K., Quandt, S.A. (2012). Social integration and diabetes management among rural older adults. Journal of Aging and Health, 24, 899–922CrossRefGoogle ScholarPubMed
Baer, R.D., Weller, S.C., de Alba, Garcia, Garcia, J., Salcedo Rocha, A.L. (2004). A comparison of community and physician explanatory models of AIDS in Mexico and the United States. Medical Anthropology Quarterly, 18, 3–22CrossRefGoogle ScholarPubMed
Baer, R.D., Weller, S.C., de Alba, Garcia, Garcia, J., Salcedo Rocha, A.L. (2008). Cross-cultural perspectives on physician and lay models of the common cold. Medical Anthropology Quarterly, 22, 148–66CrossRefGoogle ScholarPubMed
Birkhoff, G. (1940). Lattice theory, Providence, RI: American Mathematical Society, Colloquium PublicationGoogle Scholar
Bock, R. (1972). Estimating item parameters and latent ability when responses are scored in two or more latent categories. Psychometrika, 57, 29–51CrossRefGoogle Scholar
Bock, R., Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443–459CrossRefGoogle Scholar
Bock, R.D. The nominal categories model. (1996). In van der Linder, W.J., Hambleton, R.K. (Eds.), Handbook of item response theory (pp. 33–50) New York: SpringerGoogle Scholar
Böckenholt, U. (2012). Modeling multiple response processes in judgment and choice. Psychological Methods, 17, 665–678CrossRefGoogle ScholarPubMed
Bond, T.G., Fox, J.C. (2012). Applying the Rasch model: Fundamental measurement in the human sciences, (2nd ed.). New York: RoutledgeGoogle Scholar
Braeken, J., Tuerlinckx, F. (2009). Investigating latent constructs with item response models: A MATLAB IRTm toolbox. Behavior Research Methods, 41, 1127–1137CrossRefGoogle ScholarPubMed
Brock, B. (1984). Factors influencing intentions and behaviors toward swine flu vaccine. Doctoral dissertation, University of Michigan, Ann Arbor, MI.Google Scholar
Brüggemann, R., Patil, G.P. (2009). Ranking and prioritization for multi-indicator systems, New York: SpringerGoogle Scholar
Brüggermann, R., Voigt, K. (2009). Analysis of partial orders in environmental systems applying the new software PyHasse. In Jochen, W., Michael, F. (Eds.), Simulation in Umwel- ad Geowissenchaften, workshop Potsdam 2009 (pp. 43–55), Aachen: Shaker VerlagGoogle Scholar
Cai, L., Thissen, D., du Toit, S.H.C. (2011). IRTPRO for windows [computer software], Lincolnwood, IL: Scientific Software InternationalGoogle Scholar
Chavez, L.R., Hubbell, F.A., McMullin, J.M., Martinez, R.G., Mishra, S.I. (1995). Structure and meaning in models of breast and cervical cancer risk factors: A comparison of perceptions among Latinas, Anglo women, and physicians. Medical Anthropology Quarterly, 9, 40–74CrossRefGoogle ScholarPubMed
De Boeck, P., Wilson, M. (2004). Explanatory item response models: A generalized linear and nonlinear approach, New York: SpringerCrossRefGoogle Scholar
De Boeck, P., Partchev, I. (2012). IRTrees: Tree-based item response models of the GLMM family. Journal of Statistical Software, 48, 1–28CrossRefGoogle Scholar
Dushnik, B., Miller, E.W. (1941). Partially ordered sets. American Journal of Mathematics, 63, 600–610CrossRefGoogle Scholar
Embretson, S., Reise, S. (2000). Item response theory for psychologists, Mahwah, NJ: ErlbaumGoogle Scholar
Epstein, R.M., Street, R.L. (2011). The values and value of patient-centered care. Annals of Family Medicine, 9, 100–103CrossRefGoogle ScholarPubMed
Grzywacz, J., Arcury, T.A., Ip, E.H., Chapman, C., Kirk, J.C., Bell, R.A., Quandt, S. (2011). Older adults’ common-sense models of diabetes: A multi-method approach illustrating the importance of viewing health beliefs holistically. American Journal of Health Behavior, 35, 318–333CrossRefGoogle Scholar
Ip, E.H., Wang, Y., de Boeck, P., Meulders, M. (2004). Locally dependent latent trait model for polytomous responses with application to inventory of hostility. Psychometrika, 62, 191–216CrossRefGoogle Scholar
Ip, E., Zhang, Q., Rejeski, J., Harris, T., Kritchevsky, S. (2013). Partially ordered mixed hidden Markov model for the disablement process of older adults. Journal of the American Statistical Association, 108, 370–384CrossRefGoogle ScholarPubMed
Ip, E.H., Molenberghs, G., Chen, S., Goegebeur, Y., De Boeck, P. (2013). Functional unidimensional item response models for multivariate binary data. Multivariate Behavioral Research, 48, 534–562CrossRefGoogle ScholarPubMed
Ip, E. H., Saldana, S., Chen, S.-H., Kirk, J. K., Bell, R. A., Nguyen, H., Grzywacz, J. G., Arcury, T. A., & Quandt, S. A. (2013c). Unreliable item or inconsistent person? A study of variation in health beliefs and belief—anchors to biomedical models. Journal of Health Psychology. doi:10.1177/1359105313506761.CrossRefGoogle Scholar
Kleinman, A. (1980). Patients and healers in the context of culture, Berkeley, CA: University of California PressCrossRefGoogle Scholar
Kleinman, A. (1988). Illness narratives: Suffering, healing and the human condition, New York: Basic PressGoogle Scholar
Kleinman, A., Eisenberg, L., Good, B. (1978). Culture, illness, and care: Clinical lessons from anthropological and cross-cultural research. Annals of Internal Medicine, 88, 251–288CrossRefGoogle ScholarPubMed
Konisky, D.M., Milyo, J., Richardson, LE Jr (2008). Environmental policy attitudes: Issues, geographical scale, and political trust. Social Science Quarterly, 89, 1066–1085CrossRefGoogle Scholar
Leventhal, H., Brissette, I., Leventhal, E.A. (2003). The common-ense model of self-regulation of health and illness. In Cameron, L.D., Levethal, H. (Eds.), The self-regulation of health and illness behavior, (pp. 42–65). London: RoutledgeGoogle Scholar
Lord, F. (1980). Applications of item response theory to practical testing problems, Mahwah, NJ: ErlbaumGoogle Scholar
Masters, G. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174CrossRefGoogle Scholar
Meulders, M., Ip, E., De Boeck, P. (2005). Latent variable models for partially ordered responses and trajectory analysis of anger-related feelings. British Journal of Mathematical and Statistical Psychology, 58, 117–143CrossRefGoogle ScholarPubMed
Muraki, E., Bock, R.D. (2003). PARSCALE 4 for Windows: IRT based test scoring and item analysis for graded items and rating scales [Computer software], Skokie, IL: Scientific Software International IncGoogle Scholar
Muthén, L.K., Muthén, B.O. (2012). Mplus user’s guide, (7th ed.). Los Angeles, CA: Muthén & MuthéGoogle Scholar
Ostini, R., Nering, M.L. (2010). New perspective and applications. In Nering, M.L., Osini, R. (Eds.), Handbook of polytomous item response theory models (pp. 3–20), New York: Taylor & FrancisGoogle Scholar
Quandt, S.A., Ip, E.H., Saldana, S., Arcury, T.A. (2012). Comparing two questionnaires for eliciting CAM use in a multi-ethnic US population of older adults. European Journal of Integrative Medicine, 4, e205–e211CrossRefGoogle Scholar
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests, Copenhagen: Denmarks Paedagogiske InstitutGoogle Scholar
Reise, S.P., Waller, N.G. (2001). Dichotomous IRT models. In Drasgow, F., Schmitt, N. (Eds.), Advances in measurement and data analysis (pp. 88–122), Williamsburg, VA: Jossey-BassGoogle Scholar
Rejeski, J., Ip, E.H., Katula, J., White, L. (2006). Older adults’ desire for physical competence. Medicine and Science in Sports and Exercise, 38, 100–105CrossRefGoogle ScholarPubMed
Rijmen, F., Tuerlinckx, F., De Boeck, P., Kuppens, P. (2003). A nonlinear mixed modelframework for item response theory. Psychological Methods, 8, 185–205CrossRefGoogle Scholar
Rizopoulos, D. (2006). ltm: An R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17, 125CrossRefGoogle Scholar
Rosenstock, I. (1974). The health belief model and preventive health behavior. Health Education Monograph, 2, 354–386CrossRefGoogle Scholar
Rosenstock, I., Kirscht, J.P. (1979). Why people seek health care. In Stone, G., Cohen, F., Adler, N. (Eds.), Health Psychology, (pp. 161–188). San Francisco: Jossey-BassGoogle Scholar
Samejima, F. (1969). Estimation of ability using a response pattern of graded scores. Psychometrika Monograph, 34 Suppl100–114Google Scholar
Samejima, F. (1972). A general model for free-response data. Psychometrika Monograph 18.Google Scholar
Samejima, F. Graded response model. In van der Linder, W.J., Hambleton, R.K. (Eds.), Handbook of item response theory, 1996 New York: Springer 85–100Google Scholar
Sampson, A., Singh, H. (2002). Min and max scorings for two-sample partially ordered categorical data. Journal of Statistical Planning and Inference, 107, 219–236CrossRefGoogle Scholar
Smirnov, N.V. (1944). Approximate distribution laws for random variables, constructed from empirical data. Uspekhi Matematicheskikh Nauk (In Russian), 10, 179–206Google Scholar
Stanley, R.D. (2012). Enumerative combinatorics, (2nd ed.). Cambridge, UK: Cambridge University PressGoogle Scholar
Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society Series C, 51, 337–350CrossRefGoogle Scholar
Tatsuoka, C., Varadi, F., Jaeger, J. (2013). Latent partially ordered classification models and normal mixtures. Journal of Educational & Behavioral Statistics, 38, 267–294CrossRefGoogle Scholar
Thissen, D., Steinberg, L. (1984). A response model for multiple choice items. Psychometrika, 49, 501–519CrossRefGoogle Scholar
Thissen, D., Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567–577CrossRefGoogle Scholar
Thissen, D., Chen, W.-H., Bock, R.D. (2003). MULTILOG 7 for Windows: Multiple-category item analysis and test scoring using item response theory [Computer software], Skokie, IL: Scientific Software International IncGoogle Scholar
van der Linden, W. J., & Hambleton, R. K. (Eds.). (1997). Handbook of modern item response theory. New York: Springer. doi: 10.1007/978-1-4757-2691-6.CrossRefGoogle Scholar
Wilson, M. (1992). The ordered partition model: An extension of the partial credit model. Applied Psychological Measurement, 16, 309–325CrossRefGoogle Scholar
Wu, M.L., Adams, R.J., Wilson, M.R. (1997). ConQuest: Multi-aspect test software, [computer program], Camberwell: Australian Council for Educational ResearchGoogle Scholar
Zimowski, M.F., Muraki, E., Mislevy, R.J., Bock, R.D. (2003). BILOG-MG 3 for Windows: Multiple-group IRT analysis and test maintenance for binary items [Computer software], Skokie, IL: Scientific Software International IncGoogle Scholar
Zhang, Q., Ip, E. (2012). Generalized linear model for partially ordered data. Statistics in Medicine, 31, 56–68CrossRefGoogle ScholarPubMed