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Leverage and influential observations on the Liu type estimator in the linear regression model with the severe collinearity.

ABSTRACT: In the process of building a linear regression model, the essential part is to identify influential observations. Various influence measures involving Cook's distance and DFFITS are designed to detect the linear regression's influential observations using the Least Squares (LS). The existence of influential observations in the data is complicated by the presence of severe collinearity and affects the efficiency of the detection measures. This paper proposes new diagnostic methods based on the Liu type estimator (LTE) defined by Liu [1]. The Cook's distance and DFFITS for the LTE are introduced. Moreover, approximate formulas for Cook's distance and DFFITS are also proposed for LTE. Two real data sets with a high level of multicollinearity among the explanatory variables as well as the simulation study are used to illustrate and evaluate performance of the methodologies presented in this paper.

SUBMITTER: Eledum H

PROVIDER: S-EPMC8379455 | biostudies-literature | 2021 Aug

REPOSITORIES: biostudies-literature

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Leverage and influential observations on the Liu type estimator in the linear regression model with the severe collinearity.

Eledum Hussein H

Heliyon 20210817 8

In the process of building a linear regression model, the essential part is to identify influential observations. Various influence measures involving Cook's distance and DFFITS are designed to detect the linear regression's influential observations using the Least Squares (LS). The existence of influential observations in the data is complicated by the presence of severe collinearity and affects the efficiency of the detection measures. This paper proposes new diagnostic methods based on the Li ...[more]

PMID: 34458624

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Project description:BackgroundWhen estimating the causal effect on survival outcomes in observational studies, it is necessary to adjust confounding factors due to unbalanced covariates between treatment and control groups. There is no study on multiple robust method for estimating the difference in survival functions. In this study, we propose a multiply robust (MR) estimator, allowing multiple propensity score models and outcome regression models, to provide multiple protection.MethodBased on the previous MR estimator (Han 2014) and pseudo-observation approach, we proposed a new MR estimator for estimating the difference in survival functions. The proposed MR estimator based on the pseudo-observation approach has several advantages. First, the proposed estimator has a small bias when any PS and OR models were correctly specified. Second, the proposed estimator considers the advantage pf the pseudo-observation approach, which avoids proportional hazards assumption. A Monte Carlo simulation study was performed to evaluate the performance of the proposed estimator. And the proposed estimator was used to estimate the effect of chemotherapy on triple-negative breast cancer (TNBC) in real data.ResultsThe simulation studies showed that the bias of the proposed estimator was small, and the coverage rate was close to 95% when any model for propensity score or outcome regression is correctly specified regardless of whether the proportional hazard assumption holds, finite sample size and censoring rate. And the simulation results also showed that even though the propensity score models are misspecified, the bias of the proposed estimator was still small when there is a correct model in candidate outcome regression models. And we applied the proposed estimator in real data, finding that chemotherapy could improve the prognosis of TNBC.ConclusionsThe proposed estimator, allowing multiple propensity score and outcome regression models, provides multiple protection for estimating the difference in survival functions. The proposed estimator provided a new choice when researchers have a "difficult time" choosing only one model for their studies.

Dataset Information

Leverage and influential observations on the Liu type estimator in the linear regression model with the severe collinearity.

Publications

Leverage and influential observations on the Liu type estimator in the linear regression model with the severe collinearity.

Similar Datasets

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