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Generalized linear models with ordinally-observed covariates.

Timothy R Johnson1

  • 1Department of Statistics, University of Idaho, Moscow 83844-1104, USA. trjohns@uidaho.edu

The British Journal of Mathematical and Statistical Psychology
|October 28, 2006
PubMed
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Using ordinal surrogates for covariates in generalized linear models can cause measurement errors. This study proposes a new framework to address these errors and ensure accurate statistical inferences for observed covariates.

Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Ordinal surrogates partially observe variables, leading to ordinally-observed variables.
  • Statistical models for ordinally-observed responses are established, but ordinally-observed regressors are less studied.
  • Measurement error in covariates can arise when using ordinal surrogates.

Purpose of the Study:

  • To investigate the impact of measurement error from ordinally-observed covariates on generalized linear models.
  • To propose a general modeling framework for generalized linear models with ordinally-observed covariates.
  • To address issues of model specification, identification, and estimation in the presence of such measurement error.

Main Methods:

  • Development of a general modeling framework for generalized linear models (GLMs) with ordinally-observed covariates.

Related Experiment Videos

  • Analysis of measurement error introduced by using ordinal surrogates as regressors.
  • Examination of consistency of point estimators and standard errors for fully-observed regressors.

    • Main Results:

    • Measurement error from ordinally-observed covariates can compromise the consistency of estimators and standard errors for fully-observed regressors.
    • The proposed framework provides a method to properly account for this measurement error.
    • The study discusses critical aspects of model specification, identification, and estimation.

    Conclusions:

    • Ordinally-observed covariates require specific modeling approaches to avoid biased inferences.
    • The proposed framework offers a robust solution for handling measurement error in GLMs with ordinal covariates.
    • Accurate statistical inference is achievable with appropriate modeling of ordinally-observed regressors.