Survey Methodology
Collinearity diagnostics in generalized linear models fitted with survey data

by Dan Liao and Richard ValliantNote 1

  • Release date: December 23, 2025
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Abstract

The class of generalized linear models (GLM) is a flexible generalization of ordinary least squares regression that allows the linear model to be related to the response variable via a link function and assumes the magnitude of the variance of each measurement to be a function of its predicted value. Multicollinearity in GLMs can inflate variances of the estimated coefficients and cause poor prediction in certain regions of the regression space. It may also cause a nonsignificant Wald statistic even when the predictors are highly predictive in a model of the family of GLMs. Little previous research has closely investigated the diagnostics of multicollinearity in GLMs, especially when complex survey data are used. In this paper, we develop variance inflation factors (VIFs) that measure the amount that the variance of a parameter estimator is increased due to multicollinearity in GLMs. We also extend VIFs and condition indexes to apply to complex survey data, accounting for design features, e.g. weights, clusters, and strata. Illustrations of these methods are given using data from a household survey of health and nutrition.

Key Words:    Condition indexes; Diagnostics for survey data; Multicollinearity; Regression with complex survey data; Variance inflation factors.

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How to cite

Liao, D. and Valliant, R. (2025). Collinearity diagnostics in generalized linear models fitted with survey data. Survey Methodology, 51(2), 561-588. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2025002/article/00004-eng.pdf.

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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.

© His Majesty the King in Right of Canada, as represented by the Minister of Industry, 2025

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Catalogue No. 12-001-X

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