Skip to main content
Erschienen in: Prevention Science 7/2015

01.10.2015

Methods for Multilevel Ordinal Data in Prevention Research

verfasst von: Donald Hedeker

Erschienen in: Prevention Science | Ausgabe 7/2015

Einloggen, um Zugang zu erhalten

Abstract

This paper discusses statistical models for multilevel ordinal data that may be more appropriate for prevention outcomes than models that assume continuous measurement and normality. Prevention outcomes often have distributions that make them inappropriate for many popular statistical models that assume normality and are more appropriately considered ordinal outcomes. Despite this, the modeling of ordinal outcomes is often not well understood. This article discusses ways to analyze multilevel ordinal outcomes that are clustered or longitudinal, including the proportional odds regression model for ordinal outcomes, which assumes that the covariate effects are the same across the levels of the ordinal outcome. The article will cover how to test this assumption and what to do if it is violated. It will also discuss application of these models using computer software programs.
Literatur
Zurück zum Zitat Agresti, A. (2002). Categorical data analysis (2nd ed.). Hoboken: Wiley.CrossRef Agresti, A. (2002). Categorical data analysis (2nd ed.). Hoboken: Wiley.CrossRef
Zurück zum Zitat Agresti, A., & Natarajan, R. (2001). Modeling clustered ordered categorical data: A survey. International Statistical Review, 69, 345–371.CrossRef Agresti, A., & Natarajan, R. (2001). Modeling clustered ordered categorical data: A survey. International Statistical Review, 69, 345–371.CrossRef
Zurück zum Zitat Armstrong, B. G., & Sloan, M. (1989). Ordinal regression models for epidemiologic data. American Journal of Epidemiology, 129, 191–204.PubMed Armstrong, B. G., & Sloan, M. (1989). Ordinal regression models for epidemiologic data. American Journal of Epidemiology, 129, 191–204.PubMed
Zurück zum Zitat Bauer, D. J., & Sterba, S. K. (2011). Fitting multilevel models with ordinal outcomes: Performance of alternative specifications and methods of estimation. Psychological Methods, 16, 337–390.CrossRef Bauer, D. J., & Sterba, S. K. (2011). Fitting multilevel models with ordinal outcomes: Performance of alternative specifications and methods of estimation. Psychological Methods, 16, 337–390.CrossRef
Zurück zum Zitat Bock, R. D., & Shilling, S. (1997). High-dimensional full-information item factor analysis. In M. Berkane (Ed.), Latent variable modeling and applications to causality (pp. 163–176). New York: Springer.CrossRef Bock, R. D., & Shilling, S. (1997). High-dimensional full-information item factor analysis. In M. Berkane (Ed.), Latent variable modeling and applications to causality (pp. 163–176). New York: Springer.CrossRef
Zurück zum Zitat Breslow, N. E., & Lin, X. (1995). Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82, 81–91.CrossRef Breslow, N. E., & Lin, X. (1995). Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82, 81–91.CrossRef
Zurück zum Zitat Flay BR, Brannon BR, Johnson CA, Hansen WB, Ulene AL, Whitney-Saltiel DAP., et al. (1988). The television school and family smoking prevention and cessation project. 1. Theoretical basis and program development. Preventive Medicine, 17, 585–607. Flay BR, Brannon BR, Johnson CA, Hansen WB, Ulene AL, Whitney-Saltiel DAP., et al. (1988). The television school and family smoking prevention and cessation project. 1. Theoretical basis and program development. Preventive Medicine, 17, 585–607.
Zurück zum Zitat Goldstein, H. (2011). Multilevel statistical models (4th ed.). New York: Wiley. Goldstein, H. (2011). Multilevel statistical models (4th ed.). New York: Wiley.
Zurück zum Zitat Goldstein, H., & Rasbash, J. (1996). Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical Society, Series B, 159, 505–513.CrossRef Goldstein, H., & Rasbash, J. (1996). Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical Society, Series B, 159, 505–513.CrossRef
Zurück zum Zitat Hamilton, M. (1960). A rating scale for depression. Journal of Neurology and Neurosurgical Psychiatry, 23, 56–62.CrossRef Hamilton, M. (1960). A rating scale for depression. Journal of Neurology and Neurosurgical Psychiatry, 23, 56–62.CrossRef
Zurück zum Zitat Hedeker, D. (2004). An introduction to growth modeling. In D. Kaplan (Ed.), The SAGE handbook of quantitative methodology for the social sciences (pp. 215–234). Thousand Oaks: Sage Publications Inc. Hedeker, D. (2004). An introduction to growth modeling. In D. Kaplan (Ed.), The SAGE handbook of quantitative methodology for the social sciences (pp. 215–234). Thousand Oaks: Sage Publications Inc.
Zurück zum Zitat Hedeker, D., & Gibbons, R. D. (1994). A random effects ordinal regression model for multilevel analysis. Biometrics, 50, 933–944.CrossRefPubMed Hedeker, D., & Gibbons, R. D. (1994). A random effects ordinal regression model for multilevel analysis. Biometrics, 50, 933–944.CrossRefPubMed
Zurück zum Zitat Hedeker, D., & Gibbons, R. D. (1996). MIXOR: A computer program for mixed-effects ordinal probit and logistic regression analysis. Computer Methods and Programs in Biomedicine, 49, 157–176.CrossRefPubMed Hedeker, D., & Gibbons, R. D. (1996). MIXOR: A computer program for mixed-effects ordinal probit and logistic regression analysis. Computer Methods and Programs in Biomedicine, 49, 157–176.CrossRefPubMed
Zurück zum Zitat Hedeker, D., & Gibbons, R. D. (2006). Longitudinal data analysis. New York: Wiley. Hedeker, D., & Gibbons, R. D. (2006). Longitudinal data analysis. New York: Wiley.
Zurück zum Zitat Hedeker, D., & Mermelstein, R. J. (1998). A multilevel thresholds of change model for analysis of stages of change data. Multivariate Behavioral Research, 33, 427–455.CrossRef Hedeker, D., & Mermelstein, R. J. (1998). A multilevel thresholds of change model for analysis of stages of change data. Multivariate Behavioral Research, 33, 427–455.CrossRef
Zurück zum Zitat Hedeker, D., & Mermelstein, R. J. (2000). Analysis of longitudinal substance use outcomes using ordinal random-effects regression models. Addiction, 95, S381–S394.CrossRefPubMed Hedeker, D., & Mermelstein, R. J. (2000). Analysis of longitudinal substance use outcomes using ordinal random-effects regression models. Addiction, 95, S381–S394.CrossRefPubMed
Zurück zum Zitat Hedeker, D., & Mermelstein, R. J. (2011). Multilevel analysis of ordinal outcomes related to survival data. In J. J. Hox & J. K. Roberts (Eds.), Handbook of multilevel analysis (pp. 115–136). New York: Routledge. Hedeker, D., & Mermelstein, R. J. (2011). Multilevel analysis of ordinal outcomes related to survival data. In J. J. Hox & J. K. Roberts (Eds.), Handbook of multilevel analysis (pp. 115–136). New York: Routledge.
Zurück zum Zitat Hedeker, D., Mermelstein, R. J., & Weeks, K. A. (1999). The thresholds of change model: An approach for analyzing stages of change data. Annals of Behavioral Medicine, 21, 61–70.CrossRefPubMed Hedeker, D., Mermelstein, R. J., & Weeks, K. A. (1999). The thresholds of change model: An approach for analyzing stages of change data. Annals of Behavioral Medicine, 21, 61–70.CrossRefPubMed
Zurück zum Zitat Hedeker, D., Siddiqui, O., & Hu, F. B. (2000). Random-effects regression analysis of correlated grouped-time survival data. Statistical Methods in Medical Research, 9, 161–179.CrossRefPubMed Hedeker, D., Siddiqui, O., & Hu, F. B. (2000). Random-effects regression analysis of correlated grouped-time survival data. Statistical Methods in Medical Research, 9, 161–179.CrossRefPubMed
Zurück zum Zitat Hedeker, D., Gibbons, R. D., du Toit, M., & Cheng, Y. (2008). SuperMix: Mixed effects models. Lincolnwood: Scientific Software International, Inc. Hedeker, D., Gibbons, R. D., du Toit, M., & Cheng, Y. (2008). SuperMix: Mixed effects models. Lincolnwood: Scientific Software International, Inc.
Zurück zum Zitat Liu, Q., & Pierce, D. A. (1994). A note on Gauss-Hermite quadrature. Biometrika, 81, 624–629. Liu, Q., & Pierce, D. A. (1994). A note on Gauss-Hermite quadrature. Biometrika, 81, 624–629.
Zurück zum Zitat McCullagh, P. (1980). Regression models for ordinal data (with discussion). Journal of the Royal Statistical Society, Series B, 42, 109–142. McCullagh, P. (1980). Regression models for ordinal data (with discussion). Journal of the Royal Statistical Society, Series B, 42, 109–142.
Zurück zum Zitat McKelvey, R. D., & Zavoina, W. (1975). A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology, 4, 103–120.CrossRef McKelvey, R. D., & Zavoina, W. (1975). A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology, 4, 103–120.CrossRef
Zurück zum Zitat Pinheiro, J. C., & Bates, D. M. (1995). Approximations to the log-likelihood function in the non-linear mixed-effects model. Journal of Computational and Graphical Statistics, 4, 12–35. Pinheiro, J. C., & Bates, D. M. (1995). Approximations to the log-likelihood function in the non-linear mixed-effects model. Journal of Computational and Graphical Statistics, 4, 12–35.
Zurück zum Zitat Prochaska, J. O., & DiClemente, C. (1983). Stages and processes of self-change in smoking: Toward an integrative model of change. Journal of Consulting and Clinical Psychology, 51, 390–395.CrossRefPubMed Prochaska, J. O., & DiClemente, C. (1983). Stages and processes of self-change in smoking: Toward an integrative model of change. Journal of Consulting and Clinical Psychology, 51, 390–395.CrossRefPubMed
Zurück zum Zitat Prochaska, J. O., DiClemente, C., & Norcross, J. (1992). In search of how people change: Applications to addictive behaviors. American Psychologist, 47, 1102–1114.CrossRefPubMed Prochaska, J. O., DiClemente, C., & Norcross, J. (1992). In search of how people change: Applications to addictive behaviors. American Psychologist, 47, 1102–1114.CrossRefPubMed
Zurück zum Zitat Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2002). Reliable estimation of generalized linear mixed models using adaptive quadrature. The Stata Journal, 2, 1–21. Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2002). Reliable estimation of generalized linear mixed models using adaptive quadrature. The Stata Journal, 2, 1–21.
Zurück zum Zitat Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Gllamm manual. Berkeley, CA: U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 160. Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Gllamm manual. Berkeley, CA: U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 160.
Zurück zum Zitat Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2005). Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. Journal of Econometrics, 128, 301–323.CrossRef Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2005). Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. Journal of Econometrics, 128, 301–323.CrossRef
Zurück zum Zitat Raman, R., & Hedeker, D. (2005). A mixed-effects regression model for three-level ordinal response data. Statistics in Medicine, 24, 3331–3345.CrossRefPubMed Raman, R., & Hedeker, D. (2005). A mixed-effects regression model for three-level ordinal response data. Statistics in Medicine, 24, 3331–3345.CrossRefPubMed
Zurück zum Zitat Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models (2nd ed.). Thousand Oaks: Sage. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models (2nd ed.). Thousand Oaks: Sage.
Zurück zum Zitat Raudenbush, S. W., Yang, M.-L., & Yosef, M. (2000). Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics, 9, 141–157. Raudenbush, S. W., Yang, M.-L., & Yosef, M. (2000). Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics, 9, 141–157.
Zurück zum Zitat Reisby, N., Gram, L. F., Bech, P., Nagy, A., Petersen, G. O., Ortmann, J., Ibsen, I., Dencker, S. J., Jacobsen, O., Krautwald, O., Sondergaard, I., & Christiansen, J. (1977). Imipramine: Clinical effects and pharmacokinetic variability. Psychopharmacology, 54, 263–272.CrossRefPubMed Reisby, N., Gram, L. F., Bech, P., Nagy, A., Petersen, G. O., Ortmann, J., Ibsen, I., Dencker, S. J., Jacobsen, O., Krautwald, O., Sondergaard, I., & Christiansen, J. (1977). Imipramine: Clinical effects and pharmacokinetic variability. Psychopharmacology, 54, 263–272.CrossRefPubMed
Zurück zum Zitat Rodríguez, G., & Goldman, N. (1995). An assessment of estimation procedures for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 158, 73–89.CrossRef Rodríguez, G., & Goldman, N. (1995). An assessment of estimation procedures for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 158, 73–89.CrossRef
Zurück zum Zitat Rodríquez, G. (2008). Multilevel generalized linear models. In J. de Leeuw & E. Meijer (Eds.), Handbook of multilevel analysis (pp. 335–376). New York: Springer.CrossRef Rodríquez, G. (2008). Multilevel generalized linear models. In J. de Leeuw & E. Meijer (Eds.), Handbook of multilevel analysis (pp. 335–376). New York: Springer.CrossRef
Zurück zum Zitat Sankeya, S. S., & Weissfeld, L. A. (1998). A study of the effect of dichotomizing ordinal data upon modeling. Communications in Statistics - Simulation and Computation, 27, 871–887.CrossRef Sankeya, S. S., & Weissfeld, L. A. (1998). A study of the effect of dichotomizing ordinal data upon modeling. Communications in Statistics - Simulation and Computation, 27, 871–887.CrossRef
Zurück zum Zitat SAS/Stat. (2011). Sas/stat user’s guide, version 9.3. Cary: SAS Institute, Inc. SAS/Stat. (2011). Sas/stat user’s guide, version 9.3. Cary: SAS Institute, Inc.
Zurück zum Zitat Seiden, L. S., & Dykstra, L. A. (1977). Psychopharmacology: A biochemical and behavioral approach. New York: Van Nostrand Reinhold. Seiden, L. S., & Dykstra, L. A. (1977). Psychopharmacology: A biochemical and behavioral approach. New York: Van Nostrand Reinhold.
Zurück zum Zitat Siddiqui, O., Hedeker, D., Flay, B. R., & Hu, F. B. (1996). Intraclass correlation estimates in a school-based smoking prevention study: Outcome and mediating variables, by gender and ethnicity. American Journal of Epidemiology, 144, 425–433.CrossRefPubMed Siddiqui, O., Hedeker, D., Flay, B. R., & Hu, F. B. (1996). Intraclass correlation estimates in a school-based smoking prevention study: Outcome and mediating variables, by gender and ethnicity. American Journal of Epidemiology, 144, 425–433.CrossRefPubMed
Zurück zum Zitat StataCorp. (2013). Stata statistical software: Release 13. College Station: Stata Corporation. StataCorp. (2013). Stata statistical software: Release 13. College Station: Stata Corporation.
Zurück zum Zitat Strömberg, U. (1996). Collapsing ordered outcome categories: A note of concern. American Journal of Epidemiology, 144, 421–424.CrossRefPubMed Strömberg, U. (1996). Collapsing ordered outcome categories: A note of concern. American Journal of Epidemiology, 144, 421–424.CrossRefPubMed
Zurück zum Zitat Tutz, G., & Hennevogl, W. (1996). Random effects in ordinal regression models. Computational Statistics and Data Analysis, 22, 537–557.CrossRef Tutz, G., & Hennevogl, W. (1996). Random effects in ordinal regression models. Computational Statistics and Data Analysis, 22, 537–557.CrossRef
Zurück zum Zitat Winship, C., & Mare, R. D. (1984). Regression models with ordinal variables. American Sociological Review, 49, 512–525.CrossRef Winship, C., & Mare, R. D. (1984). Regression models with ordinal variables. American Sociological Review, 49, 512–525.CrossRef
Metadaten
Titel
Methods for Multilevel Ordinal Data in Prevention Research
verfasst von
Donald Hedeker
Publikationsdatum
01.10.2015
Verlag
Springer US
Erschienen in
Prevention Science / Ausgabe 7/2015
Print ISSN: 1389-4986
Elektronische ISSN: 1573-6695
DOI
https://doi.org/10.1007/s11121-014-0495-x

Weitere Artikel der Ausgabe 7/2015

Prevention Science 7/2015 Zur Ausgabe