Covariate Measurement Error in Logistic Regression.

Stefanski, Lukas; Carroll, R. J.

doi:10.21236/ada160277

Cited by 85 publications

(121 citation statements)

References 9 publications

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“…The second effect related with n 0 was model overfitting. Models of logistic regression in presence of measurement errors may be biased (Stefanski and Carroll 1985;Carroll et al 1995). When the data by chance appear to be separated better than they should be according to their distribution, the fitted maximum likelihood model has a threshold point, such that below the threshold it predicts risk close to 0, and above the threshold close to 1.…”

Section: Chemistry Data Variabilitymentioning

confidence: 99%

Models of lake invasibility by Bythotrephes longimanus, a non-indigenous zooplankton

et al. 2011

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We built a family of hierarchical risk models for the spread of invasions by the spiny waterflea (Bythotrephes longimanus) in lakes in Ontario, Canada. Knowledge of covariates determining lake invasibility and ability to predict risk of future invasions may help to develop management policy and slow the invasions in the future. The models are based on two component submodels. The first component was a stochastic gravity submodel for the propagule pressure between lakes via recreational boaters. The second component was a submodel for establishment risk, given that the invader has already been introduced to a lake. This component was a logistic regression model, incorporating up to 17 measured covariates that describe the physical and chemical condition of the lake. Variants of the risk model, each incorporating different subsets of the covariates, were calibrated using presence/absence data from a 300-lake survey conducted in 2005-2006 by the Canadian Aquatic Invasive Species Network (CAISN). The predictive capacity of the best model was high, giving AUC values close to 0.94. Of the model covariates considered, the most important predictors of existing invasions were propagule pressure and lake pH, and, to lesser extents, phosphorus (P) and lake elevation. Our fitting of the propagule pressure submodel demonstrated a significant Allee effect for Bythotrephes. Our development of the establishment risk predictor showed that it is essential to account for temporal variability in lake physico-chemistry. We demonstrated that invasions of lake networks by the spiny waterflea follow highly predictable patterns which can be understood with a properly calibrated, hierarchical risk model.

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Section: Chemistry Data Variabilitymentioning

confidence: 99%

Models of lake invasibility by Bythotrephes longimanus, a non-indigenous zooplankton

et al. 2011

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“…It is shown in the Appendix that for a 2-PL model with adaptive designs following the D-optimal design scheme of Kalish and Rosenberger (1978), the assumptions of Theorems 1 and 2 of Chang (2006) are satisfied, so that we can apply his results to the current online calibration problem. This reparametrization scheme was also used in Jones and Jin (1994); and under such a reparametrized model and assumption of independence of designs, they applied the results of Stefanski and Carroll (1985) to the online calibration problem. Although their numerical results did not show serious flaws, they still mentioned in their paper that under their online calibration setup, the independence assumption of the latent trait levels of examinees is inadequate, since sequential designs in online calibration lack this property.…”

Section: Reparametrizationmentioning

confidence: 99%

“…Thus, the assumption of independent observations is no longer valid in this situation. Jones and Jin (1994) applied the measurement error model method to online calibration problems based on Stefanski and Carroll (1985), which relies on the assumption of independence in designs that cannot be fulfilled if an adaptive design scheme is adopted in the calibration procedure. Actually, this flaw was also pointed out in Jones and Jin (1994) (p. 66).…”

Section: Introductionmentioning

confidence: 99%

Online Calibration Via Variable Length Computerized Adaptive Testing

Chang

2009

Psychometrika

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“…In such cases, statistical estimation and inference become very challenging. Several researchers, such as Stefanski and Carroll (1985), Aitkin (1996), and Rabe-Hesketh et al (2003), have studied the maximum likelihood estimation of the GLM with measurement error. However, most of the proposed approaches rely on the normality assumption for the unobserved covariates and measurement error, though some other parametric distributions have T. Abarin · L. Wang (B) Department of Statistics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada e-mail: liqun_wang@umanitoba.ca been considered (Schafer 2001, Aitkin and Rocci 2002, Kukush and Schneeweiss 2005, Roy and Banerjee 2006.…”

Section: Introductionmentioning

confidence: 99%

Instrumental variable approach to covariate measurement error in generalized linear models

Abarin

Wang

2010

Ann Inst Stat Math

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The paper presents the method of moments estimation for generalized linear measurement error models using the instrumental variable approach. The measurement error has a parametric distribution that is not necessarily normal, while the distributions of the unobserved covariates are nonparametric. We also propose simulation-based estimators for the situation where the closed forms of the moments are not available. The proposed estimators are strongly consistent and asymptotically normally distributed under some regularity conditions. Finite sample performances of the estimators are investigated through simulation studies.

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Covariate Measurement Error in Logistic Regression.

Cited by 85 publications

References 9 publications

Models of lake invasibility by Bythotrephes longimanus, a non-indigenous zooplankton

Models of lake invasibility by Bythotrephes longimanus, a non-indigenous zooplankton

Online Calibration Via Variable Length Computerized Adaptive Testing

Instrumental variable approach to covariate measurement error in generalized linear models

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