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The trend odds model for ordinal data.

ABSTRACT: Ordinal data appear in a wide variety of scientific fields. These data are often analyzed using ordinal logistic regression models that assume proportional odds. When this assumption is not met, it may be possible to capture the lack of proportionality using a constrained structural relationship between the odds and the cut-points of the ordinal values. We consider a trend odds version of this constrained model, wherein the odds parameter increases or decreases in a monotonic manner across the cut-points. We demonstrate algebraically and graphically how this model is related to latent logistic, normal, and exponential distributions. In particular, we find that scale changes in these potential latent distributions are consistent with the trend odds assumption, with the logistic and exponential distributions having odds that increase in a linear or nearly linear fashion. We show how to fit this model using SAS Proc NLMIXED and perform simulations under proportional odds and trend odds processes. We find that the added complexity of the trend odds model gives improved power over the proportional odds model when there are moderate to severe departures from proportionality. A hypothetical data set is used to illustrate the interpretation of the trend odds model, and we apply this model to a swine influenza example wherein the proportional odds assumption appears to be violated.

SUBMITTER: Capuano AW

PROVIDER: S-EPMC3650098 | biostudies-literature | 2013 Jun

REPOSITORIES: biostudies-literature

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The trend odds model for ordinal data.

Capuano Ana W AW Dawson Jeffrey D JD

Statistics in medicine 20121206 13

Ordinal data appear in a wide variety of scientific fields. These data are often analyzed using ordinal logistic regression models that assume proportional odds. When this assumption is not met, it may be possible to capture the lack of proportionality using a constrained structural relationship between the odds and the cut-points of the ordinal values. We consider a trend odds version of this constrained model, wherein the odds parameter increases or decreases in a monotonic manner across the c ...[more]

PMID: 23225520

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Project description:BackgroundMeasures in nursing research frequently use Likert scales that yield ordinal data. Confirmatory factor analysis using Pearson correlations commonly applies to such data, although this violates ordinal scale assumptions.ObjectivesThe aim of this study was to illustrate the application of polychoric correlations and polychoric confirmatory factor analysis as a valid alternative statistical approach using data on family members' perceived support from nurses as an exemplar.MethodsA primary analysis of cross-sectional data from a sample of 800 participants using data collected with the Iceland-Family Perceived Support Questionnaire was conducted using polychoric versus Pearson correlations, analysis of variance, and confirmatory factor analysis.ResultsA two-factor measurement model was compatible with data from family members in the Ugandan care settings. Two contextual factors (cognitive and emotional support) constituted the family support measurement model. A factor correlation indicated that the two factors reflected distinct but closely related aspects of family support. Polychoric correlation revealed 13.8% (range: 5.5%-25.2%) higher correlations compared to Pearson correlations. Moreover, the polychoric agreed with the data, whereas the Pearson confirmatory factor analysis did not fit based on multiple statistical criteria. Analyses indicated a difference in emotional and cognitive support perception across two family characteristics: education and relationship to the patient.DiscussionA polychoric correlation suggests stronger associations, and consequently, the approach can be more credible with an ordinal Likert scale than Pearson correlations. Hence, polychoric confirmatory factor analysis can address a larger proportion of variance. In nursing research, polychoric confirmatory factor analysis can confidently be utilized when conducting confirmatory factor analysis of ordinal variables in Likert scales. Furthermore, when a Pearson confirmatory factor analysis is used for ordinal Likert scales, the researcher should carefully evaluate the difference between the two approaches and justify their methodological choice. Even though we do not suggest dispensing with Pearson correlations entirely, we recommend using polychoric correlation for ordinal Likert scales.

Dataset Information

The trend odds model for ordinal data.

Publications

The trend odds model for ordinal data.

Similar Datasets

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