Ill-conditioned Information Matrices and the Generalized Linear Model: an Asymptotically Biased Estimation Approach

Marx, Brian D.

doi:10.1007/978-1-4612-3680-1_24

Cited by 3 publications

(1 citation statement)

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“…Marx (1988) has also suggested a ridge trace approach (ridge coefficient estimates versus k) and other approaches for the generalized linear model. Only the ridge trace are presented in the trout examples.…”

Section: Ridge Logistic Regression Estimatorsmentioning

confidence: 99%

Weighted Multicollinearity in Logistic Regression: Diagnostics and Biased Estimation Techniques with an Example from Lake Acidification

Marx¹,

Smith²

1990

Can. J. Fish. Aquat. Sci.

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1990. Weighted multicollinearity in logistic regression: diagnostics and biased estimation techniques with an example from lake acidification. Can. I. Fish. Aquat. Sci. 47: 1 128-1 135.An historical data set from the Adirondack region of New York is revisited to study the relationship between water chemistry variables associated with acid precipitation and the presencelabsence of brook trout (SaEvelinus dontinalis) and lake trout (Sabvelinus namaycush). For the trout species data sets, water chemistry variables associated with acid precipitation, for example pH and alkalinity, are highly correlated. Regression models to assess their effects on the probabi t ity of the presence of fish species are therefore affected by multicollinearity. Because the appropriate regressions are logistic, correction techniques based on least squares do not work. Maximum likelihood parameter estimation is highly unstable for the trout presencelabsence data. Developments in weighted multicollinearity diagnostics are used to evaluate maximum likelihood logistic regression parameter estimates. Further, an application of biased parameter estimation is presented as an option to the traditional maximum likelihood logistic regression. Biased estimation methods, like ridge, principal component, or Stein estimation can substantially reduce the variance of the parameter estimates and prediction variance for certain future observations. In many cases, only a slight modification to the converged maximum likelihood estimator is necessary.

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Section: Ridge Logistic Regression Estimatorsmentioning

confidence: 99%