### Abstract

Assume y is a response variable, x is a risk factor of interest, and z's are covariates, or sometime called "confounders of x" if they are correlated with both x and y. If the covariates are numerous, then model selection procedures are applied on z's while x is usually forced into the model before or after the selection. In this situation, over-dispersion will occur to bias the inference on the relation between x and y. In a linear model, the over-dispersion comes from two sources: An underestimation of the mean-squared error, and a dependency between the estimator of the x-effect and its standard error. The author proposed a method that incorporates the ideas of Ye's generalized degree of freedom and Rosenbaum and Rubin's propensity score. The method reduces the bias and over-dispersion effect to acceptable levels. Data from the Georgia capital charging and sentencing study, which included 1077 observations and 295 covariates, were analyzed as an illustration.

Original language | English |
---|---|

Pages (from-to) | 197-214 |

Number of pages | 18 |

Journal | Computational Statistics and Data Analysis |

Volume | 43 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2003 Jun 28 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

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**Reducing over-dispersion by generalized degree of freedom and propensity score.** / Lian, Iebin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Reducing over-dispersion by generalized degree of freedom and propensity score

AU - Lian, Iebin

PY - 2003/6/28

Y1 - 2003/6/28

N2 - Assume y is a response variable, x is a risk factor of interest, and z's are covariates, or sometime called "confounders of x" if they are correlated with both x and y. If the covariates are numerous, then model selection procedures are applied on z's while x is usually forced into the model before or after the selection. In this situation, over-dispersion will occur to bias the inference on the relation between x and y. In a linear model, the over-dispersion comes from two sources: An underestimation of the mean-squared error, and a dependency between the estimator of the x-effect and its standard error. The author proposed a method that incorporates the ideas of Ye's generalized degree of freedom and Rosenbaum and Rubin's propensity score. The method reduces the bias and over-dispersion effect to acceptable levels. Data from the Georgia capital charging and sentencing study, which included 1077 observations and 295 covariates, were analyzed as an illustration.

AB - Assume y is a response variable, x is a risk factor of interest, and z's are covariates, or sometime called "confounders of x" if they are correlated with both x and y. If the covariates are numerous, then model selection procedures are applied on z's while x is usually forced into the model before or after the selection. In this situation, over-dispersion will occur to bias the inference on the relation between x and y. In a linear model, the over-dispersion comes from two sources: An underestimation of the mean-squared error, and a dependency between the estimator of the x-effect and its standard error. The author proposed a method that incorporates the ideas of Ye's generalized degree of freedom and Rosenbaum and Rubin's propensity score. The method reduces the bias and over-dispersion effect to acceptable levels. Data from the Georgia capital charging and sentencing study, which included 1077 observations and 295 covariates, were analyzed as an illustration.

UR - http://www.scopus.com/inward/record.url?scp=0037669059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037669059&partnerID=8YFLogxK

U2 - 10.1016/S0167-9473(02)00223-2

DO - 10.1016/S0167-9473(02)00223-2

M3 - Article

AN - SCOPUS:0037669059

VL - 43

SP - 197

EP - 214

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 2

ER -