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Performance of tests of association in misspecified generalized linear models

Publication ,  Journal Article
O'Brien, SM; Kupper, LL; Dunson, DB
Published in: Journal of Statistical Planning and Inference
September 1, 2006

We examine the effects of modelling errors, such as underfitting and overfitting, on the asymptotic power of tests of association between an explanatory variable x and an outcome in the setting of generalized linear models. The regression function for x is approximated by a polynomial or another simple function, and a chi-square statistic is used to test whether the coefficients of the approximation are simultaneously equal to zero. Adding terms to the approximation increases asymptotic power if and only if the fit of the model increases by a certain quantifiable amount. Although a high degree of freedom approximation offers robustness to the shape of the unknown regression function, a low degree of freedom approximation can yield much higher asymptotic power even when the approximation is very poor. In practice, it is useful to compute the power of competing test statistics across the range of alternatives that are plausible a priori. This approach is illustrated through an application in epidemiology. © 2006 Elsevier B.V. All rights reserved.

Duke Scholars

Published In

Journal of Statistical Planning and Inference

DOI

ISSN

0378-3758

Publication Date

September 1, 2006

Volume

136

Issue

9

Start / End Page

3090 / 3100

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

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ICMJE
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O’Brien, S. M., Kupper, L. L., & Dunson, D. B. (2006). Performance of tests of association in misspecified generalized linear models. Journal of Statistical Planning and Inference, 136(9), 3090–3100. https://doi.org/10.1016/j.jspi.2004.12.004
O’Brien, S. M., L. L. Kupper, and D. B. Dunson. “Performance of tests of association in misspecified generalized linear models.” Journal of Statistical Planning and Inference 136, no. 9 (September 1, 2006): 3090–3100. https://doi.org/10.1016/j.jspi.2004.12.004.
O’Brien SM, Kupper LL, Dunson DB. Performance of tests of association in misspecified generalized linear models. Journal of Statistical Planning and Inference. 2006 Sep 1;136(9):3090–100.
O’Brien, S. M., et al. “Performance of tests of association in misspecified generalized linear models.” Journal of Statistical Planning and Inference, vol. 136, no. 9, Sept. 2006, pp. 3090–100. Scopus, doi:10.1016/j.jspi.2004.12.004.
O’Brien SM, Kupper LL, Dunson DB. Performance of tests of association in misspecified generalized linear models. Journal of Statistical Planning and Inference. 2006 Sep 1;136(9):3090–3100.
Journal cover image

Published In

Journal of Statistical Planning and Inference

DOI

ISSN

0378-3758

Publication Date

September 1, 2006

Volume

136

Issue

9

Start / End Page

3090 / 3100

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics