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Estimation of Relative Importance of Predictors and Its Application in Linear Model

Author: DaiLuYan
Tutor: ShenQiJun
School: Ningbo University
Course: Epidemiology and Health Statistics
Keywords: relative importance linear model dominance analysis relative weight Bootstrap
CLC: R195
Type: Master's thesis
Year: 2012
Downloads: 35
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Abstract


Objective The thesis is aim at the defects of current methods which were used to estimatethe relative importance of predictors in linear model,and intending to introduce four methodswhich are researched and proposed in the word: product mearsure,dominance analysis,proportionmarginal variance decomposition(PMVD) and relative weight. besides, systematic theoreticalanalysis and applied research are conducted in the thesis.Methods Based on the analysis of the traditional methods, preliminary discussion areconducted about the methods to estimate the relative importance of predictors in linear modelWhich includes product mearsure,dominance analysis,proportion marginal variancedecomposition(PMVD) and relative weight; besides, the corresponding computer program isdeveloped in software such as SAS or R, and foregin standard example is adopted to verify;meanwhile, Bootstrap simulation techniques are employed to explore its accuracy, and the specificsteps are as follows: the Bootstrap method are used to sample on actual data,evaluating the relativeimportance of predictors value in each sample,respectively.and obtanining the samplingdistribution of the estimated value,then establishing the confidence interval methods fourmethods,in order to assess the variablility of the estimation results.Results Among eatimation the importance of the facors imposing the predicting survivaltime of the liver surgery patients, the relative importance of each predictors in standard regressioncoefficients squared(β2)estimation are as follows: blood clotting, prognostic index, enzymefuction are respectively0.150,0.317,0.598and its Bootstrap95%CI are respectively (0.128,0.174),(0.266,0.374),(0.526,0.685); the relative importance of each predictors in squaredsemipartial correlation(r2y (xi x1Kxj))estimation are as follows: blood clotting, prognostic index,enzyme fuction are0.315,0.147,0.585and its Bootstrap95%CI are respectively (0.264,0.366),(0.125,0.169),(0.519,0.648); the relative importance of each predictors in productmearsure(βj ryxj)estimation are as follows: blood clotting, prognostic index, enzyme fuctionare respectively0.121,0.305,0.529and its Bootstrap95%CI are respectively (0.115,0.159), (0.270,0.342),(0.480,0.580); the relative importance of each predictors in PMVD(Pj))estimation are as follows: blood clotting, prognostic index, enzyme fuction arerespectively0.139,0.315,0.501and its Bootstrap95%CI are respectively (0.118,0.164),(0.279,0.354),(0.456,0.546); the relative importance of each predictors in dominanceanalysis(Dj)estimation are as follows: blood clotting, prognostic index, enzyme fuction arerespectively0.123,0.305,0.527and its Bootstrap95%CI are respectively (0.116,0.159),(0.270,0.341),(0.480,0.572); the relative importance of each predictors in relative weight(εj)estimation are as follows: blood clotting, prognostic index, enzyme fuction arerespectively0.124,0.305,0.526and its Bootstrap95%CI are respectively (0.117,0.158),(0.267,0.340),(0.481,0.570).Conclusions In this study, the fators imposing the predicting survival time of the liversurgery patients which are estiablished by the estimate methods include: blood clotting, prognosticindex and enzyme fuction. the fators which exert influence to different degrees with enzymefuction imposing the biggest effect followed by the prognostic index and blood clotting. Whenpredictor variables are correlated, the results which estimated by the four methods includingproduct mearsure, dominance analysis, proportion marginal variance decomposition(PMVD) andrelative weight are more accurate, reliable and truthful, which should be widely applied.

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