Survey Methodology
An alternative way of estimating a cumulative logistic model with complex survey data

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by Phillip S. Kott and Peter FrechtelNote 1

  • Release date: June 27, 2019
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Abstract

When fitting an ordered categorical variable with L > 2 levels to a set of covariates onto complex survey data, it is common to assume that the elements of the population fit a simple cumulative logistic regression model (proportional-odds logistic-regression model). This means the probability that the categorical variable is at or below some level is a binary logistic function of the model covariates. Moreover, except for the intercept, the values of the logistic-regression parameters are the same at each level. The conventional “design-based” method used for fitting the proportional-odds model is based on pseudo-maximum likelihood. We compare estimates computed using pseudo-maximum likelihood with those computed by assuming an alternative design-sensitive robust model-based framework. We show with a simple numerical example how estimates using the two approaches can differ. The alternative approach is easily extended to fit a general cumulative logistic model, in which the parallel-lines assumption can fail. A test of that assumption easily follows.

Key Words:      Parallel-lines assumption; Design-sensitive estimation; Standard model; Extended model.

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How to cite

Kott, P.S., and Frechtel, P. (2019). An alternative way of estimating a cumulative logistic model with complex survey data. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 45, No. 2. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2019002/article/00007-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2019

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

Ottawa

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Table of contents

Abstract - Article main page
Section 1. Introduction: Fitting a regression model with complex survey data
Section 2. A simple example
Section 3. Discussion
Appendix
References

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