Maximally selected chi-square statistic corrected for logistic regression
碩士 === 國立中興大學 === 統計學研究所 === 100 === Epidemiologic studies concern the effect of an exposure, and a set of explanatory variables, on the outcome variable. When logistic regression model is used and some variables are dichotomized according to possible cutoff points to produce maximally selected test...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2012
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| Online Access: | http://ndltd.ncl.edu.tw/handle/93341098869296309746 |
| Summary: | 碩士 === 國立中興大學 === 統計學研究所 === 100 === Epidemiologic studies concern the effect of an exposure, and a set of explanatory variables, on the outcome variable. When logistic regression model is used and some variables are dichotomized according to possible cutoff points to produce maximally selected test statistics, the distribution of the test statistics under null hypothesis (of ‘no effect’) is proved to be not a chi-square distribution with 1 degree of freedom. It is a distribution of the supremum of the Brownian bridge with suitable correction. This study extends the problem to a logistic regression setting. We investigate the situation of independent explanatory variables towards the power of different tests. When there are correlations among variables, we propose a stepwise pseudo Gram-Schmidt orthogonalization process so that each individual regression parameters can have reasonable type I error. Several methods are proposed, and their powers are compared through simulations. We implement the proposed methods on an actual data set for illustration.
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