DOCSLIB.ORG

Multinomial and Ordinal Logistic Regression Analyses with Multi- Categorical Variables Using R

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Multinomial and Ordinal Logistic Regression Analyses with Multi- Categorical Variables Using R 982 Editorial Page 1 of 8 Multinomial and ordinal Logistic regression analyses with multi- categorical variables using R Jiaqi Liang, Guoshu Bi, Cheng Zhan Department of Thoracic Surgery, Zhongshan Hospital, Fudan University, Shanghai, China Correspondence to: Department of Thoracic Surgery, Zhongshan Hospital, Fudan University, 180 Fenglin Road, Shanghai, China. Email: [email protected]. Provenance and Peer Review: This article was commissioned by the editorial office, Annals of Translational Medicine. The article did not undergo external peer review. Comment on: Zhou ZR, Wang WW, Li Y, et al. In-depth mining of clinical data: the construction of clinical prediction model with R. Ann Transl Med 2019;7:796. Submitted Mar 17, 2020. Accepted for publication Apr 28, 2020. doi: 10.21037/atm-2020-57 View this article at: http://dx.doi.org/10.21037/atm-2020-57 It is essential in a standard linear regression analysis that calculating the points of each variable together with survival dependent variables are continuous. However, using the probabilities. standard linear regression for the analysis of a double-level The general objective of logistic regression models is to or multi-level outcome can lead to unsatisfactory results predict outcomes using variables based on certain existing because the validity of this regression model relies on the data, which have been applied in medical research for various variability of the outcome being the same for all values of diseases (8). In the study by Zhou and his colleagues (3), predictors, which is contrary to the nature of double-level the authors converted multi-categorical outcomes into or multi-level outcomes (1). Therefore, when the dependent dichotomous ones and introduced a dichotomous logistic variable consists of several categories, a maximum likelihood regression using R codes. However, multi-categorical estimator, such as multinomial logit or probit, should be outcomes can be directly applied in multinomial or ordinal used instead of the ordinary least square estimator (2). logistic regression analyses in the R software, although Logistic regression can be used to describe the relationship the results might be difficult to be interpreted with more between an independent variable(s) (either continuous or complicated steps. This study aimed to display the methods not) and a dichotomous or multi-categorical dependent and processes used to apply multi-categorical variables in variable as a supplementary variable to the standard linear logistic regression models in the R software environment. regression. The sample data was made up of patients registered Zhou et al. (3) elaborated a series of reliable methodologies in the SEER database in 2015 with diagnoses of lung using the R software to construct clinical prediction models adenocarcinomas. Patients with unclear race, primary with detailed steps and operable code examples, according site(s) of their tumors, differentiation grade of their to different types of clinical data and categories of variables. tumors, tumor stage (AJCC, 6th edition), or cause of They summarized the process of the construction of their death were excluded. Finally, 6,483 patients met practical clinical prediction models (nomograms), including the inclusion and exclusion criteria, of which 3,000 were data screening, primary model training, and internal and randomly selected for the following analysis. Age, sex, race, external validations, which was an extraordinary work and primary site of the tumor, cell differentiation grade, AJCC a practical reference in the field of statistics (4-6). Based stage of the tumor, and history of chemotherapy, were on this study, a simpler and more accurate prediction chosen as independent variables. The ages of included model was introduced as an extension by Bi et al. (7), which patients, ranging from 20 to 100 years, were divided was designed for extracting polynomial equations and into eight groups, labeled as “AgeGroup”. Also, several © Annals of Translational Medicine. All rights reserved. Ann Transl Med 2020;8(16):982 | http://dx.doi.org/10.21037/atm-2020-57 Page 2 of 8 Liang et al. Logistic regression with multi-categorical variables in R subgroup variables were defined for each of the other six seer_multi$Grade <- factor(seer_multi$Grade, ordered = T, variables: “Sex” (male and female), “Race” (white, black, levels = c("GradeI", "GradeII", and others), “PrimarySite” (main, upper lobe, middle "GradeIII", "GradeIV")) lobe, lower lobe, and overlapped), “Grade” (I–IV), “Stage” seer_multi$Stage <- factor(seer_multi$Stage, ordered = T, (I–IV), and “Chemotherapy” (yes and no or unknown). levels = c("I", "II", "III", "IV")) Survival status labeled as “Causespecificdeathclassifica ## Specify the baseline level of the outcomes tion” was defined as the dependent variable consisting of three categories: alive, dead due to lung cancer, and seer_multi$Causespecificdeathclassification <- relevel( dead due to other causes. Survival months were extracted seer_multi$Causespecificdeathclassification, ref = "Alive") for constructing an ordinal outcome. Using the dplyr package in R, the survival months were converted into Step 2: model running “SurvivalStatus” based on the tertiles of survival months. Patient outcomes were defined as “0 = no response” for Second, the model was run using the multinorm function those whose survival months are in the first third tertile; in the nnet package in R as follows. In the outputs of the “1 = partial response” and “2 = complete response” were summary of the model (Figure 1A), a block of coefficients defined as outcomes for patients whose survival months displayed as logged odds was shown followed by their are in the middle and last third tertiles, respectively. standard errors. Multinomial logistic regressions can be applied for multi- Each of these blocks had one row of values corresponding categorical outcomes, whereas ordinal variables should be to a model equation. In the first row, for instance, preferentially analyzed using an ordinal logistic regression coefficients (logged odds) of each independent variable model. Besides, if the ordinal model does not meet the comparing “Dead (attributable to this cancer dx)” with parallel regression assumption, the multinomial one will “Alive” were shown. The coefficients were pulled out still be an alternative (9). A multinomial regression analysis from the model and converted into interpretable odds was started as follows with four main steps. ratios additionally by exponential analyses using the exp() command. Multinomial regression analysis ## Install and library the R package nnet Step 1: data preparation install.packages("nnet") First, the sample data set was imported into R, and the library(nnet) ordinal categorical variables (“Grade” and “Stage”) in ## Run the multinomial model with the multinom function and the data were rewritten as ordered factors using the summarize it factor function. The level of the outcome to be used as multimodel <- multinom(Causespecificdeathclassification ~ the baseline was selected and specified using the relevel AgeGroup + Sex + Race + PrimarySite + function. Here, “Alive” was defined as a baseline to be Grade + Stage + Chemotherapy, compared with “Dead (attributable to this cancer dx)” and data = seer_multi) “Dead of other cause” in the regression. The codes in R are summary(multimodel) shown below. The data we used in the analyses can be found ## Turn coefficients into interpretable odds ratios in http://cdn.amegroups.cn/static/application/949e8411be9 oddsratio <- exp(coef(multimodel)) 1d730d1670c07b0d01072/10.21037atm-2020-57-1.pdf. ## Import the data Step 3: tests of the coefficients seer_multi <- read.csv("D://Table S1.csv") After constructing the regression model, the next thing ## Display part of the data was to calculate P values of the regression coefficients head(seer_multi) using Wald tests (z tests used in this study). R codes and tail(seer_multi) part of the outputs are shown below. The coefficients were ## Rewrite the ordinal categorical variables considered to be of significance with a two-tailed value © Annals of Translational Medicine. All rights reserved. Ann Transl Med 2020;8(16):982 | http://dx.doi.org/10.21037/atm-2020-57 Annals of Translational Medicine, Vol 8, No 16 August 2020 Page 3 of 8 A B Figure 1 Outputs of the multinomial logistic regression model. (A) Summary of the model. (B) Results of ANOVA. Grade. L: Grade II; Grade. Q: Grade III; Grade. C: Grade IV; Stage. L: Stage II; Stage. Q: Stage III; Stage. C: Stage IV. of P<0.05, and no significance was attributed otherwise. zvalues <- summary(multimodel)$coefficients / Focusing on the block of P values below, variables with summary(multimodel)$standard.errors significant P values of their coefficients were determined as pvalues <- pnorm(abs(zvalues), lower.tail = FALSE) * 2 significant prognostic factors that contributed significantly pvalues differently to cancer-specific death or death of other causes rather than to survival in patients with lung ## (Intercept) AgeGroup30-39 adenocarcinoma. ##Dead (attributable to this cancer dx) 0.000000e+00 0 ##Dead of other cause 1.206239e-197 0 ## Wald tests/z tests of the coefficients … © Annals of Translational Medicine. All rights reserved. Ann Transl Med 2020;8(16):982 | http://dx.doi.org/10.21037/atm-2020-57 Page 4 of 8 Liang et al. Logistic regression with multi-categorical variables in R ## PrimarySiteUpper Grade.L multimodelfit5 <- multinom (data = seer_multi, ##Dead (attributable to this
Load more

Recommended publications
  • Regression Models for Ordinal Responses: a Review of Methods and Applications
    International Journal of Epidemiology Vol. 26, No. 6 © International Epidemiological Association 1997 Printed in Great Britain Regression Models for Ordinal Responses: A Review of Methods and Applications CANDE V ANANTH* AND DAVID G KLEINBAUM† Ananth C V (The Center for Perinatal Health Initiatives, Department of Obstetrics, Gynecology and Reproductive Sciences, University of Medicine and Dentistry of New Jersey, Robert Wood Johnson Medical School, 125 Paterson St, New Brunswick, NJ 08901–1977, USA) and Kleinbaum D G. Regression models for ordinal responses: A review of methods and applications. International Journal of Epidemiology 1997; 26: 1323–1333. Background. Epidemiologists are often interested in estimating the risk of several related diseases as well as adverse outcomes, which have a natural ordering of severity or certainty. While most investigators choose to model several dichotomous outcomes (such as very low birthweight versus normal and moderately low birthweight versus normal), this approach does not fully utilize the available information. Several statistical models for ordinal responses have been proposed, but have been underutilized. In this paper, we describe statistical methods for modelling ordinal response data, and illustrate the fit of these models to a large database from a perinatal health programme. Methods. Models considered here include (1) the cumulative logit model, (2) continuation-ratio model, (3) constrained and unconstrained partial proportional odds models, (4) adjacent-category logit model, (5) polytomous logistic model, and (6) stereotype logistic model. We illustrate and compare the fit of these models on a perinatal database, to study the impact of midline episiotomy procedure on perineal lacerations during labour and delivery. Finally, we provide a discus- sion on graphical methods for the assessment of model assumptions and model constraints, and conclude with a dis- cussion on the choice of an ordinal model.
    [Show full text]
  • Ordinal Probit Functional Outcome Regression with Application to Computer-Use Behavior in Rhesus Monkeys
    Ordinal Probit Functional Outcome Regression with Application to Computer-Use Behavior in Rhesus Monkeys Mark J. Meyer∗ Department of Mathematics and Statistics, Georgetown University and Jeffrey S. Morris Department of Biostatistics, Epidemiology, and Informatics, Perelman School of Medicine, University of Pennsylvania and Regina Paxton Gazes Department of Psychology and Program in Animal Behavior, Bucknell University and Brent A. Coull Department of Biostatistics, Harvard T. H. Chan School of Public Health March 19, 2021 Abstract arXiv:1901.07976v2 [stat.ME] 18 Mar 2021 Research in functional regression has made great strides in expanding to non- Gaussian functional outcomes, but exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (Macaca mulatta), we introduce the Ordinal Probit Functional Outcome Regression model (OPFOR). OPFOR models can be fit using one of several basis functions including penalized B-splines, wavelets, and O'Sullivan splines|the last of which typically performs best. Simulation using a variety of underlying covariance patterns shows ∗This work was supported by grants from the National Institutes of Health (ES-007142, ES-000002, CA- 134294, CA-178744, R01MH081862), the National Science Foundation (#IOS-1146316), and ORIP/OD (P51OD011132). 1 that the model performs reasonably well in estimation under multiple basis functions with near nominal coverage for joint credible intervals. Finally, in application, we use Bayesian model selection criteria adapted to functional outcome regression to best characterize the relation between several demographic factors of interest and the monkeys' computer use over the course of a year. In comparison with a standard ordinal longitudinal analysis, OPFOR outperforms a cumulative-link mixed-effects model in simulation and provides additional and more nuanced information on the nature of the monkeys' computer-use behavior.
    [Show full text]
  • Regression Models for Ordinal Dependent Variables
    Newsom 1 USP 656 Multilevel Regression Winter 2013 Regression Models for Ordinal Dependent Variables The Concept of Propensity and Threshold Binary responses can be conceptualized as a type of propensity for Y to equal 1. For example, we may ask respondents whether or not they use public transportation with a "yes" or "no" response. But individuals may differ on the likelihood that they will use public transportation with some occasionally using it and others using it very regularly. Even those who do not use public transportation at all might have a high favorability toward public transportation and under the right conditions might use it. This tendency or propensity that might underlie a "yes" or "no" response or many other dichotomous variables is sometimes referred to as a "latent" variable. The latent variable, often referred to as Y* in this context, is thought of as an unobserved continuous variable. When the value of this variable reaches a certain point, a "threshold," the observed response is "yes." In the following equation, is the threshold value, often considered to be 0 for convenience. 0*when Y observed Y 1*when Y If we imagine a z-distribution of scores, 0 is in the middle. For a binary variable, when the latent variable, Y*, exceeds 0, then we observed a response of 1. When it is less than or equal to the threshold value, then we observe a response of 0. The same conceptualization is used for a special type of correlation called polychoric correlations used to estimate the correlation between two latent continuous distributions when then observed variables are discrete (Olsson, 1979).1 It is not mathematically necessary to assume an underlying latent variable, it is merely a conceptual convenience to do so.
    [Show full text]
  • Logistic, Multinomial, and Ordinal Regression
    Logistic, multinomial, and ordinal regression I. Zeˇzulaˇ 1 1Faculty of Science P. J. Safˇ arik´ University, Kosiceˇ Robust 2010 31.1. – 5.2.2010, Kral´ıky´ Logistic regression Multinomial regression Ordinal regression Obsah 1 Logistic regression Introduction Basic model More general predictors General model Tests of association 2 Multinomial regression Introduction General model Goodness-of-fit and overdispersion Tests 3 Ordinal regression Introduction Proportional odds model Other models I. Zeˇzulaˇ Robust 2010 Introduction Logistic regression Basic model Multinomial regression More general predictors Ordinal regression General model Tests of association 1) Logistic regression Introduction Testing a risk factor: we want to check whether a certain factor adds to the probability of outbreak of a disease. This corresponds to the following contingency table: disease status risk factor sum ill not ill exposed n11 n12 n10 unexposed n21 n22 n20 sum n01 n02 n I. Zeˇzulaˇ Robust 2010 Introduction Logistic regression Basic model Multinomial regression More general predictors Ordinal regression General model Tests of association 1) Logistic regression Introduction Testing a risk factor: we want to check whether a certain factor adds to the probability of outbreak of a disease. This corresponds to the following contingency table: disease status risk factor sum ill not ill exposed n11 n12 n10 unexposed n21 n22 n20 sum n01 n02 n Odds of the outbreak for both groups are: n n 11 pˆ pˆ o 11 n10 1 o 2 1 = = n11 = , 2 = n10 − n11 1 − 1 − pˆ1 1 − pˆ2 n10 I. Zeˇzulaˇ Robust 2010 Introduction Logistic regression Basic model Multinomial regression More general predictors Ordinal regression General model Tests of association 1) Logistic regression As a measure of the risk, we can form odds ratio: o pˆ 1 − pˆ OR = 1 = 1 · 2 o2 1 − pˆ1 pˆ2 o1 = OR · o2 I.
    [Show full text]
  • Gaussian Processes for Ordinal Regression
    JournalofMachineLearningResearch6(2005)1019–1041 Submitted 11/04; Revised 3/05; Published 7/05 Gaussian Processes for Ordinal Regression Wei Chu [email protected] Zoubin Ghahramani [email protected] Gatsby Computational Neuroscience Unit University College London London, WC1N 3AR, UK Editor: Christopher K. I. Williams Abstract We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation prop- agation algorithm respectively, are derived for hyperparameter learning and model selection. We compare these two Gaussian process approaches with a previous ordinal regression method based on support vector machines on some benchmark and real-world data sets, including applications of ordinal regression to collaborative filtering and gene expression analysis. Experimental results on these data sets verify the usefulness of our approach. Keywords: Gaussian processes, ordinal regression, approximate Bayesian inference, collaborative filtering, gene expression analysis, feature selection 1. Introduction Practical applications of supervised learning frequently involve situations exhibiting an order among the different categories, e.g. a teacher always rates his/her students by giving grades on their overall performance. In contrast to metric regression problems, the grades are usually discrete and finite. These grades are also different from the class labels in classification problems due to the existence of ranking information. For example, grade labels have the ordering F < D < C < B < A. This is a learning task of predicting variables of ordinal scale, a setting bridging between metric regression and classification referred to as ranking learning or ordinal regression.
    [Show full text]
  • Support Vector Ordinal Regression
    Support Vector Ordinal Regression Wei Chu [email protected] Center for Computational Learning Systems, Columbia University, New York, NY 10115 USA S. Sathiya Keerthi [email protected] Yahoo! Research, Media Studios North, Burbank, CA 91504 USA Abstract In this paper, we propose two new support vector approaches for ordinal regression, which optimize multiple thresholds to define parallel discriminant hyperplanes for the ordinal scales. Both approaches guarantee that the thresholds are properly ordered at the optimal solution. The size of these optimization problems is linear in the number of training samples. The SMO algorithm is adapted for the resulting optimization problems; it is extremely easy to implement and scales efficiently as a quadratic function of the number of examples. The results of numerical experiments on some benchmark and real-world data sets, including applications of ordinal regression to information retrieval and collaborative filtering, verify the usefulness of these approaches. 1 Introduction We consider the supervised learning problem of predicting variables of ordinal scale, a setting that bridges metric regression and classification, and referred to as ranking learning or ordinal regression. Ordinal regression arises frequently in social science and information retrieval where human preferences play a major role. The training samples are labelled by ranks, which exhibits an ordering among the different categories. In contrast to metric regression problems, these ranks 1 are of finite types and the metric distances between the ranks are not defined. These ranks are also different from the labels of multiple classes in classification problems due to the existence of the ordering information. There are several approaches to tackle ordinal regression problems in the domain of machine learning.
    [Show full text]
  • Ordinal Regression Models in Psychology: a Tutorial
    1 Ordinal Regression Models in Psychology: A Tutorial 1 2 2 Paul-Christian Bürkner & Matti Vuorre 1 3 Department of Psychology, University of Münster, Germany 2 4 Department of Psychology, Columbia University, USA 5 Abstract Ordinal variables, while extremely common in Psychology, are almost exclu- sively analysed with statistical models that falsely assume them to be metric. This practice can lead to distorted effect size estimates, inflated error rates, and other problems. We argue for the application of ordinal models that make appropriate assumptions about the variables under study. In this tutorial article, we first explain the three major ordinal model classes; the cumulative, sequential and adjacent category models. We then show how to fit ordinal 6 models in a fully Bayesian framework with the R package brms, using data sets on stem cell opinions and marriage time courses. Appendices provide detailed mathematical derivations of the models and a discussion of censored ordinal models. Ordinal models provide better theoretical interpretation and numerical inference from ordinal data, and we recommend their widespread adoption in Psychology. Keywords: ordinal models, Likert items, brms, R 7 1 Introduction 8 Whenever a variable’s categories have a natural order, researchers speak of an ordinal 9 variable (Stevens, 1946). For example, peoples’ opinions are often probed with items 10 where respondents choose one of the following response options: “Completely disagree”, 11 “Moderately disagree”, “Moderately agree”, or “Completely agree”. Such ordinal data are 12 ubiquitous in Psychology. Although it is widely recognized that such ordinal data are not 13 metric, it is commonplace to analyze them with methods that assume metric responses.
    [Show full text]
  • Reduction from Cost-Sensitive Ordinal Ranking to Weighted Binary Classification
    LETTER Communicated by Krzysztof Dembczynski´ Reduction from Cost-Sensitive Ordinal Ranking to Weighted Binary Classification Hsuan-Tien Lin [email protected] Department of Computer Science, National Taiwan University, Taipei 106, Taiwan Ling Li [email protected] Department of Computer Science, California Institute of Technology, Pasadena, CA 91125, U.S.A. We present a reduction framework from ordinal ranking to binary clas- sification. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and con- structing a ranker from the binary classifier. Based on the framework, we show that a weighted 0/1 loss of the binary classifier upper-bounds the mislabeling cost of the ranker, both error-wise and regret-wise. Our framework allows not only the design of good ordinal ranking algo- rithms based on well-tuned binary classification approaches, but also the derivation of new generalization bounds for ordinal ranking from known bounds for binary classification. In addition, our framework uni- fies many existing ordinal ranking algorithms, such as perceptron rank- ing and support vector ordinal regression. When compared empirically on benchmark data sets, some of our newly designed algorithms enjoy ad- vantages in terms of both training speed and generalization performance over existing algorithms. In addition, the newly designed algorithms lead to better cost-sensitive ordinal ranking performance, as well as improved listwise ranking performance. 1 Introduction We work on a supervised learning problem, ordinal ranking, which is also referred to as ordinal regression (Chu & Keerthi, 2007) or ordinal clas- sification (Frank & Hall, 2001).
    [Show full text]
  • Ordinal Logistic Regression Model: an Application to Pregnancy Outcomes
    Journal of Mathematics and Statistics 6 (3): 279-285, 2010 ISSN 1549-3644 © 2010 Science Publications Ordinal Logistic Regression Model: An Application to Pregnancy Outcomes 1K.A. Adeleke and 2A.A. Adepoju 1Department of Statistics, University of Ibadan, Ibadan 2 Department of Mathematics, University of Mines and Technology, Tarkwa, Ghana Abstract: Problem statement: This research aimed at modeling a categorical response i.e., pregnancy outcome in terms of some predictors, determines the goodness of fit as well as validity of the assumptions and selecting an appropriate and more parsimonious model thereby proffered useful suggestions and recommendations. Approach: An ordinal logistic regression model was used as a tool to model the three major factors viz., environmental (previous cesareans, service availability), behavioral (antenatal care, diseases) and demographic (maternal age, marital status and weight) that affected the outcomes of pregnancies (livebirth, stillbirth and abortion). Results: The fit, of the model was illustrated with data obtained from records of 100 patients at Ijebu-Ode, State Hospital in Nigeria. The tested model showed good fit and performed differently depending on categorization of outcome, adequacy in relation to assumptions, goodness of fit and parsimony. We however see that weight and diseases increase the likelihood of favoring a higher category i.e., (livebirth), while medical service availability, marital status age, antenatal and previous cesareans reduce the likelihood/chance of having stillbirth. Conclusion/Recommendations: The odds of being in either of these categories i.e., livebirth or stillbirth showed that women with baby’s weight less than 2.5 kg are 18.4 times more likely to have had a livebirth than are women with history of babies ≥2.5 kg.
    [Show full text]
  • Ordinal Logistic and Probit Examples: SPSS and R
    Newsom Psy 522/622 Multiple Regression and Multivariate Quantitative Methods, Winter 2021 1 Ordinal Logistic and Probit Examples Below is an example borrowed from Karen Seccombe's project focusing on healthcare among welfare recipients in Oregon. The outcome for this model is a response to a question about how often the respondent cut meal sizes because of affordability, an indicator of food insecurity. Responses to two questions were coded into a single ordinal variable with three values, 0 = never or rarely, 1 = some months but not every month, and 2 = almost every month. Ordinal Logistic Model in SPSS Regresson ordinal options (choose link: Logit) plum cutmeal with mosmed depress1 educat marital /link = logit /print= parameter. Odds ratios are not printed, but are easily computed by hand. For example, the odds ratio for depress1 would .210 be e = 1.22. Ordered Logistic Model in R Note: The polr function requires the outcome be a factor, and does not like categorical predictors. So, I converted predictors that were nonnumeric to numeric [I use lessR command below, but base R can be used too, e.g., d$mosmed <- as.numeric(d$mosmed)]. Missing data are also problematic with polr, so I used the following listwise deletion routine to remove cases with missing data on any of the variables in the model (using lessR code). #make variables numeric for listwise deletion (different var types—double and char – won't work) > library(lessR) > d <-Transform(cutmeal = (as.numeric(cutmeal))) > d <-Transform(mosmed = (as.numeric(mosmed))) > d <-Transform(depress1
    [Show full text]
  • Ordinal Regression Earlier (“Analysis of Ordinal Contingency Tables”)
    Newsom Psy 525/625 Categorical Data Analysis, Spring 2021 1 Ordinal Regression Earlier (“Analysis of Ordinal Contingency Tables”), we considered ordinal variables in contingency tables. Such models do not generally assume designation of an explanatory (independent) and response (dependent) variable, but they also are limited in inclusion of covariates and more complex models that involve interactions between continuous and categorical predictors and so on. In discussing regression models thus far, the focus has been on binary response variables. But both logistic and probit regression models, however, can be applied to ordinal response variables with more than two ordered categories, such as response options of "never," "sometimes," and "a lot," which do not necessarily have equal distance between the values.1 The application of these models is typically to response variables with 3 or 4 rank-ordered categories, and when there are 5 or more categories, moderate sample size, and fairly symmetrically distributed variables, there will be minimal loss of power if ordinary least squares is used instead of ordinal regression (Kromrey & Rendina-Gobioff, 2002; Taylor, West, & Aiken, 2006). 2 For outcomes that can be considered ordinal, it is generally better to use all of the ordinal values rather than collapsing into fewer categories or dichotomizing variables, even with a sparse number of responses in some categories. Collapsing categories has been shown to reduce statistical power (Ananth & Kleinbaum 1997; Manor, Mathews, & Power, 2000) and increase Type I error rates (Murad, Fleischman, Sadetzki, Geyer, & Freedman, 2003). Ordered Logit Ordered logit models are logistic regressions that model the change among the several ordered values as a function of each unit increase in the predictor.
    [Show full text]
  • Using Generalized Ordinal Logistic Regression Models to Estimate Educational Data Xing Liu Eastern Connecticut State University, [email protected]
    Journal of Modern Applied Statistical Methods Volume 11 | Issue 1 Article 21 5-1-2012 Ordinal Regression Analysis: Using Generalized Ordinal Logistic Regression Models to Estimate Educational Data Xing Liu Eastern Connecticut State University, [email protected] Hari Koirala Eastern Connecticut State University Follow this and additional works at: http://digitalcommons.wayne.edu/jmasm Part of the Applied Statistics Commons, Social and Behavioral Sciences Commons, and the Statistical Theory Commons Recommended Citation Liu, Xing and Koirala, Hari (2012) "Ordinal Regression Analysis: Using Generalized Ordinal Logistic Regression Models to Estimate Educational Data," Journal of Modern Applied Statistical Methods: Vol. 11 : Iss. 1 , Article 21. DOI: 10.22237/jmasm/1335846000 Available at: http://digitalcommons.wayne.edu/jmasm/vol11/iss1/21 This Regular Article is brought to you for free and open access by the Open Access Journals at DigitalCommons@WayneState. It has been accepted for inclusion in Journal of Modern Applied Statistical Methods by an authorized editor of DigitalCommons@WayneState. Journal of Modern Applied Statistical Methods Copyright © 2012 JMASM, Inc. May 2012, Vol. 11, No. 1, 242-254 1538 – 9472/12/$95.00 Ordinal Regression Analysis: Using Generalized Ordinal Logistic Regression Models to Estimate Educational Data Xing Liu Hari Koirala Eastern Connecticut State University, Willimantic, CT The proportional odds (PO) assumption for ordinal regression analysis is often violated because it is strongly affected by sample size and the number of covariate patterns. To address this issue, the partial proportional odds (PPO) model and the generalized ordinal logit model were developed. However, these models are not typically used in research. One likely reason for this is the restriction of current statistical software packages: SPSS cannot perform the generalized ordinal logit model analysis and SAS requires data restructuring.
    [Show full text]