Methods for Multilevel Ordinal Data in Prevention Research
Tóm tắt
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.
Tài liệu tham khảo
citation_title=Categorical data analysis; citation_publication_date=2002; citation_id=CR1; citation_author=A Agresti; citation_publisher=Wiley
citation_journal_title=International Statistical Review; citation_title=Modeling clustered ordered categorical data: A survey; citation_author=A Agresti, R Natarajan; citation_volume=69; citation_publication_date=2001; citation_pages=345-371; citation_doi=10.1111/j.1751-5823.2001.tb00463.x; citation_id=CR2
citation_journal_title=American Journal of Epidemiology; citation_title=Ordinal regression models for epidemiologic data; citation_author=BG Armstrong, M Sloan; citation_volume=129; citation_publication_date=1989; citation_pages=191-204; citation_id=CR3
citation_journal_title=Psychological Methods; citation_title=Fitting multilevel models with ordinal outcomes: Performance of alternative specifications and methods of estimation; citation_author=DJ Bauer, SK Sterba; citation_volume=16; citation_publication_date=2011; citation_pages=337-390; citation_doi=10.1037/a0025813; citation_id=CR4
citation_title=High-dimensional full-information item factor analysis; citation_inbook_title=Latent variable modeling and applications to causality; citation_publication_date=1997; citation_pages=163-176; citation_id=CR5; citation_author=RD Bock; citation_author=S Shilling; citation_publisher=Springer
citation_journal_title=Biometrika; citation_title=Bias correction in generalised linear mixed models with a single component of dispersion; citation_author=NE Breslow, X Lin; citation_volume=82; citation_publication_date=1995; citation_pages=81-91; citation_doi=10.1093/biomet/82.1.81; citation_id=CR6
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.
citation_title=Multilevel statistical models; citation_publication_date=2011; citation_id=CR8; citation_author=H Goldstein; citation_publisher=Wiley
citation_journal_title=Journal of the Royal Statistical Society, Series B; citation_title=Improved approximations for multilevel models with binary responses; citation_author=H Goldstein, J Rasbash; citation_volume=159; citation_publication_date=1996; citation_pages=505-513; citation_doi=10.2307/2983328; citation_id=CR9
citation_journal_title=Journal of Neurology and Neurosurgical Psychiatry; citation_title=A rating scale for depression; citation_author=M Hamilton; citation_volume=23; citation_publication_date=1960; citation_pages=56-62; citation_doi=10.1136/jnnp.23.1.56; citation_id=CR10
citation_title=An introduction to growth modeling; citation_inbook_title=The SAGE handbook of quantitative methodology for the social sciences; citation_publication_date=2004; citation_pages=215-234; citation_id=CR11; citation_author=D Hedeker; citation_publisher=Sage Publications Inc.
citation_journal_title=Biometrics; citation_title=A random effects ordinal regression model for multilevel analysis; citation_author=D Hedeker, RD Gibbons; citation_volume=50; citation_publication_date=1994; citation_pages=933-944; citation_doi=10.2307/2533433; citation_id=CR12
citation_journal_title=Computer Methods and Programs in Biomedicine; citation_title=MIXOR: A computer program for mixed-effects ordinal probit and logistic regression analysis; citation_author=D Hedeker, RD Gibbons; citation_volume=49; citation_publication_date=1996; citation_pages=157-176; citation_doi=10.1016/0169-2607(96)01720-8; citation_id=CR13
citation_title=Longitudinal data analysis; citation_publication_date=2006; citation_id=CR14; citation_author=D Hedeker; citation_author=RD Gibbons; citation_publisher=Wiley
citation_journal_title=Multivariate Behavioral Research; citation_title=A multilevel thresholds of change model for analysis of stages of change data; citation_author=D Hedeker, RJ Mermelstein; citation_volume=33; citation_publication_date=1998; citation_pages=427-455; citation_doi=10.1207/s15327906mbr3304_1; citation_id=CR15
citation_journal_title=Addiction; citation_title=Analysis of longitudinal substance use outcomes using ordinal random-effects regression models; citation_author=D Hedeker, RJ Mermelstein; citation_volume=95; citation_publication_date=2000; citation_pages=S381-S394; citation_doi=10.1046/j.1360-0443.95.11s3.7.x; citation_id=CR16
citation_title=Multilevel analysis of ordinal outcomes related to survival data; citation_inbook_title=Handbook of multilevel analysis; citation_publication_date=2011; citation_pages=115-136; citation_id=CR17; citation_author=D Hedeker; citation_author=RJ Mermelstein; citation_publisher=Routledge
citation_journal_title=Annals of Behavioral Medicine; citation_title=The thresholds of change model: An approach for analyzing stages of change data; citation_author=D Hedeker, RJ Mermelstein, KA Weeks; citation_volume=21; citation_publication_date=1999; citation_pages=61-70; citation_doi=10.1007/BF02895035; citation_id=CR18
citation_journal_title=Statistical Methods in Medical Research; citation_title=Random-effects regression analysis of correlated grouped-time survival data; citation_author=D Hedeker, O Siddiqui, FB Hu; citation_volume=9; citation_publication_date=2000; citation_pages=161-179; citation_doi=10.1191/096228000667253473; citation_id=CR19
citation_title=SuperMix: Mixed effects models; citation_publication_date=2008; citation_id=CR20; citation_author=D Hedeker; citation_author=RD Gibbons; citation_author=M Toit; citation_author=Y Cheng; citation_publisher=Scientific Software International, Inc.
citation_journal_title=Biometrika; citation_title=A note on Gauss-Hermite quadrature; citation_author=Q Liu, DA Pierce; citation_volume=81; citation_publication_date=1994; citation_pages=624-629; citation_id=CR21
citation_journal_title=Journal of the Royal Statistical Society, Series B; citation_title=Regression models for ordinal data (with discussion); citation_author=P McCullagh; citation_volume=42; citation_publication_date=1980; citation_pages=109-142; citation_id=CR22
citation_journal_title=Journal of Mathematical Sociology; citation_title=A statistical model for the analysis of ordinal level dependent variables; citation_author=RD McKelvey, W Zavoina; citation_volume=4; citation_publication_date=1975; citation_pages=103-120; citation_doi=10.1080/0022250X.1975.9989847; citation_id=CR23
citation_journal_title=Journal of Computational and Graphical Statistics; citation_title=Approximations to the log-likelihood function in the non-linear mixed-effects model; citation_author=JC Pinheiro, DM Bates; citation_volume=4; citation_publication_date=1995; citation_pages=12-35; citation_id=CR24
citation_journal_title=Journal of Consulting and Clinical Psychology; citation_title=Stages and processes of self-change in smoking: Toward an integrative model of change; citation_author=JO Prochaska, C DiClemente; citation_volume=51; citation_publication_date=1983; citation_pages=390-395; citation_doi=10.1037/0022-006X.51.3.390; citation_id=CR25
citation_journal_title=American Psychologist; citation_title=In search of how people change: Applications to addictive behaviors; citation_author=JO Prochaska, C DiClemente, J Norcross; citation_volume=47; citation_publication_date=1992; citation_pages=1102-1114; citation_doi=10.1037/0003-066X.47.9.1102; citation_id=CR26
citation_journal_title=The Stata Journal; citation_title=Reliable estimation of generalized linear mixed models using adaptive quadrature; citation_author=S Rabe-Hesketh, A Skrondal, A Pickles; citation_volume=2; citation_publication_date=2002; citation_pages=1-21; citation_id=CR27
Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Gllamm manual. Berkeley, CA: U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 160.
citation_journal_title=Journal of Econometrics; citation_title=Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects; citation_author=S Rabe-Hesketh, A Skrondal, A Pickles; citation_volume=128; citation_publication_date=2005; citation_pages=301-323; citation_doi=10.1016/j.jeconom.2004.08.017; citation_id=CR29
citation_journal_title=Statistics in Medicine; citation_title=A mixed-effects regression model for three-level ordinal response data; citation_author=R Raman, D Hedeker; citation_volume=24; citation_publication_date=2005; citation_pages=3331-3345; citation_doi=10.1002/sim.2186; citation_id=CR30
citation_title=Hierarchical linear models; citation_publication_date=2002; citation_id=CR31; citation_author=SW Raudenbush; citation_author=AS Bryk; citation_publisher=Sage
citation_journal_title=Journal of Computational and Graphical Statistics; citation_title=Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation; citation_author=SW Raudenbush, M-L Yang, M Yosef; citation_volume=9; citation_publication_date=2000; citation_pages=141-157; citation_id=CR32
citation_journal_title=Psychopharmacology; citation_title=Imipramine: Clinical effects and pharmacokinetic variability; citation_author=N Reisby, LF Gram, P Bech, A Nagy, GO Petersen, J Ortmann, I Ibsen, SJ Dencker, O Jacobsen, O Krautwald, I Sondergaard, J Christiansen; citation_volume=54; citation_publication_date=1977; citation_pages=263-272; citation_doi=10.1007/BF00426574; citation_id=CR33
citation_journal_title=Journal of the Royal Statistical Society, Series A; citation_title=An assessment of estimation procedures for multilevel models with binary responses; citation_author=G Rodríguez, N Goldman; citation_volume=158; citation_publication_date=1995; citation_pages=73-89; citation_doi=10.2307/2983404; citation_id=CR34
citation_title=Multilevel generalized linear models; citation_inbook_title=Handbook of multilevel analysis; citation_publication_date=2008; citation_pages=335-376; citation_id=CR35; citation_author=G Rodríquez; citation_publisher=Springer
citation_journal_title=Communications in Statistics - Simulation and Computation; citation_title=A study of the effect of dichotomizing ordinal data upon modeling; citation_author=SS Sankeya, LA Weissfeld; citation_volume=27; citation_publication_date=1998; citation_pages=871-887; citation_doi=10.1080/03610919808813515; citation_id=CR36
citation_title=Sas/stat user’s guide, version 9.3; citation_publication_date=2011; citation_id=CR37; citation_publisher=SAS Institute, Inc
citation_title=Psychopharmacology: A biochemical and behavioral approach; citation_publication_date=1977; citation_id=CR38; citation_author=LS Seiden; citation_author=LA Dykstra; citation_publisher=Van Nostrand Reinhold
citation_journal_title=American Journal of Epidemiology; citation_title=Intraclass correlation estimates in a school-based smoking prevention study: Outcome and mediating variables, by gender and ethnicity; citation_author=O Siddiqui, D Hedeker, BR Flay, FB Hu; citation_volume=144; citation_publication_date=1996; citation_pages=425-433; citation_doi=10.1093/oxfordjournals.aje.a008945; citation_id=CR39
citation_title=Stata statistical software: Release 13; citation_publication_date=2013; citation_id=CR40; citation_publisher=Stata Corporation
citation_journal_title=American Journal of Epidemiology; citation_title=Collapsing ordered outcome categories: A note of concern; citation_author=U Strömberg; citation_volume=144; citation_publication_date=1996; citation_pages=421-424; citation_doi=10.1093/oxfordjournals.aje.a008944; citation_id=CR41
citation_journal_title=Computational Statistics and Data Analysis; citation_title=Random effects in ordinal regression models; citation_author=G Tutz, W Hennevogl; citation_volume=22; citation_publication_date=1996; citation_pages=537-557; citation_doi=10.1016/0167-9473(96)00004-7; citation_id=CR42
citation_journal_title=American Sociological Review; citation_title=Regression models with ordinal variables; citation_author=C Winship, RD Mare; citation_volume=49; citation_publication_date=1984; citation_pages=512-525; citation_doi=10.2307/2095465; citation_id=CR43