The General Linear Test in the Ridge Regression

Bae, Whasoo; Kim, Minji; Kim, Choongrak

doi:10.5351/csam.2014.21.4.297

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…This is only an approximation since the distribution of the ridge estimator is unknown 26 . Warnings against the use of confidence intervals in penalized regression are common due to the fact that the estimation of the linear coefficients is biased 24 (and thus of the aps-ridge coefficients).…”

Section: Adaptive Predictor-set Ridge Regressionmentioning

confidence: 99%

“…Methods 4): where and where v λ,Ω denotes the effective degrees of freedom 25 , computed as with Tr being the trace operator. Similar to aps-lm, we approximate confidence intervals for the mean response by and prediction intervals by This is only an approximation since the distribution of the ridge estimator is unknown 26 . Warnings against the use of confidence intervals in penalized regression are common due to the fact that the estimation of the linear coefficients is biased 24 (and thus of the aps-ridge coefficients).…”

Section: The Adaptive Predictor-set Linear Model (Aps-lm)mentioning

confidence: 99%

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Adaptive predictor-set linear model: an imputation-free method for linear regression prediction on datasets with missing values

Jiménez,

Kayser,

Vidaki

et al. 2024

Preprint

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SummaryLinear regression (LR) is vastly used in data analysis for continuous outcomes in biomedicine and epidemiology. Despite its popularity, LR is incompatible with missing data, which frequently occur in health sciences. For parameter estimation, this short-coming is usually resolved by complete-case analysis or imputation. Both workarounds, however, are inadequate for prediction, since they either fail to predict on incomplete records or ignore missingness-induced reduction in prediction accuracy and rely on (unrealistic) assumptions about the missing mechanism. Here, we derive adaptive predictor-set linear model (aps-lm), capable of making predictions for incomplete data without the need for imputation. It is derived by using a predictor-selection operation, the Moore-Penrose pseudoinverse and the reduced QR-decomposition. aps-lm is an LR generalization that inherently handles missing values. It is applied on a reference dataset, where complete predictors and outcome are available, and yields a set of privacy-preserving parameters. In a second stage, these are shared for making predictions of the outcome on external datasets with missing entries for predictors without imputation. Moreover, aps-lm computes prediction errors that account for the pattern of missing values even under extreme missingness. We benchmark aps-lm in a simulation study. aps-lm showed greater prediction accuracy and reduced bias compared to popular imputation strategies under a wide range of scenarios including variation of sample size, goodness-of-fit, missing value type and covariance structure. Finally, as a proof-of-principle, we apply aps-lm in the context of epigenetic aging clocks, linear models that predict a person’s biological age from epigenetic data with promising clinical applications.

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Section: Adaptive Predictor-set Ridge Regressionmentioning

confidence: 99%

Section: The Adaptive Predictor-set Linear Model (Aps-lm)mentioning

confidence: 99%

Adaptive predictor-set linear model: an imputation-free method for linear regression prediction on datasets with missing values

Jiménez,

Kayser,

Vidaki

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

Adaptive predictor‐set linear model: An imputation‐free method for linear regression prediction on data sets with missing values

Planterose Jiménez,

Kayser,

Vidaki

et al. 2024

Biometrical J

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Linear regression (LR) is vastly used in data analysis for continuous outcomes in biomedicine and epidemiology. Despite its popularity, LR is incompatible with missing data, which frequently occur in health sciences. For parameter estimation, this shortcoming is usually resolved by complete‐case analysis or imputation. Both work‐arounds, however, are inadequate for prediction, since they either fail to predict on incomplete records or ignore missingness‐induced reduction in prediction accuracy and rely on (unrealistic) assumptions about the missing mechanism. Here, we derive adaptive predictor‐set linear model (aps‐lm), capable of making predictions for incomplete data without the need for imputation. It is derived by using a predictor‐selection operation, the Moore–Penrose pseudoinverse, and the reduced QR decomposition. aps‐lm is an LR generalization that inherently handles missing values. It is applied on a reference data set, where complete predictors and outcome are available, and yields a set of privacy‐preserving parameters. In a second stage, these are shared for making predictions of the outcome on external data sets with missing entries for predictors without imputation. Moreover, aps‐lm computes prediction errors that account for the pattern of missing values even under extreme missingness. We benchmark aps‐lm in a simulation study. aps‐lm showed greater prediction accuracy and reduced bias compared to popular imputation strategies under a wide range of scenarios including variation of sample size, goodness of fit, missing value type, and covariance structure. Finally, as a proof‐of‐principle, we apply aps‐lm in the context of epigenetic aging clocks, linear models that predict a person's biological age from epigenetic data with promising clinical applications.

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Investigation on the Factors Affecting the Number of International Visitors Using Online Reviews

Park¹,

Hyeon²,

Kim³

2021

JKIIE

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The General Linear Test in the Ridge Regression

Cited by 3 publications

References 13 publications

Adaptive predictor-set linear model: an imputation-free method for linear regression prediction on datasets with missing values

Adaptive predictor-set linear model: an imputation-free method for linear regression prediction on datasets with missing values

Adaptive predictor‐set linear model: An imputation‐free method for linear regression prediction on data sets with missing values

Investigation on the Factors Affecting the Number of International Visitors Using Online Reviews

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