解决Logistic回归中分离问题的统计方法比较

顾彩姣; 韩婷; 王慧; 王彤

doi:10.16462/j.cnki.zhjbkz.2016.03.023

解决Logistic回归中分离问题的统计方法比较

doi: 10.16462/j.cnki.zhjbkz.2016.03.023

顾彩姣¹,
韩婷^1,2,
王慧¹,
王彤^1, ,

1. 山西医科大学公共卫生学院卫生统计教研室, 山西太原 030001;
2. 太原市疾病预防与控制中心传染病防治科, 山西太原 030001

基金项目:

国家自然科学基金（81473073）

详细信息

作者简介:
顾彩姣(1990-),女,山西忻州人,在读硕士研究生。主要研究方向:多元统计及应用。

中图分类号: R195.1;R181
计量
- 文章访问数: 806
- HTML全文浏览量: 142
- PDF下载量: 72
- 被引次数: 0
出版历程
- 收稿日期: 2015-08-09
- 修回日期: 2016-01-17

A comparative study of methods for logistic regression with separated or nearly separated data

GU Cai-jiao¹,
HAN Ting^1,2,
WANG Hui¹,
WANG Tong^{1
, ,}

1. Department of Health Statistics, School of Public Health, Shanxi Medical University, Taiyuan 030001, China;
2. Department of Infectious Diseases Control and Prevention, Center for Disease Control and Prevention of Taiyuan, Taiyuan 030001, China

摘要

摘要: 目的介绍解决Logistic回归中分离问题的统计学方法并进行比较。方法用最大似然估计、确切Logistic估计及Firth惩罚最大似然估计对75名静脉注射吸毒者感染人类免疫缺陷病毒（human immunodeficiency virus,HIV）的情况及其影响因素进行分析，并比较其结果。结果确切Logistic回归及惩罚最大似然估计均得出有效参数估计，前者的可信区间比后者宽。结果显示民族对该市注射吸毒人群感染HIV的影响具有统计学意义,彝族的HIV感染显著高于汉族。结论当数据出现分离现象导致最大似然估计无效的情况下，确切Logistic及惩罚最大似然估计均能得出有效值，但由于前者计算复杂，可能出现过条件及条件似然退化等问题，推荐使用后者。
- Logistic模型 /
- 统计学 /
- 流行病学方法
Abstract: Objective To introduce a comparative study of methods for Logistic regression with separated or nearly separated data. Methods Human immunodeficiency virus (HIV) infection and its influential factors, 75 drug users were analyzed by maximum Likelihood estimate, exact Logistic regression and Firth's penalized maximum Likelihood estimate, then results of the three methods were compared. Results Both of penalized maximum Likelihood estimation and exact Logistic regression produced valid parameter estimates and confidence interval of the latter was wider. The results of penalized maximum Likelihood estimation and exact Logistic regression showed that race was significantly associated with HIV infection, and Yi people with HIV infection was higher than Han people. Conclusions The maximum Likelihood estimate for separated or nearly separated data is invalid. However, exact Logistic regression and Firth's penalized maximum Likelihood estimate can get valid estimates. Since exact Logistic regression have problems of complex calculations, over-conditioning and conditional distributions degenerated, Firth's penalized maximum Likelihood estimate is recommended to Logistic regression with separated or nearly separated data.
- Logistic regression /
- Statistics /
- Epidemiologic methods

HTML全文

参考文献(20)

Schaefer RL. Bias correction in maximum likelihood logistic regression [J]. Stat Med, 1983,2(1):71-78.

Cordeiro GM, McCullagh P. Bias correction in generalized linear models [J]. R Statist Soc, 1991,B53:629-643.

Bull SB, Greenwood CM, Hauck WW. Jackknife bias reduction for polychotomous logistic regression [J]. Stat Med, 1997,16(5):545-560.

Cordeiro GM, Cribari-neto F. On bias reduction in exponential and non-exponential family regression models [J]. Commu Stat, 1998, 27(2):485-500.

Allison PD. Convergence Failures in Logistic Regression [R]. Sas Global Forum, 2008.

Zamar D, McNeney B, Graham J. elrm: Software implementing exact-like inference for logistic regression models [J]. J Statist Software, 2007,21(3):1-18.

Firth D, Bias reduction. The Jeffreys prior and GLIM [J]. Lecture Notes in Statistics, 1992, 78:91-100.

Firth D. Generalized linear models and Jeffreys priors: an iterative weighted least-squares approach [J]. Comput Statist,1992,1:553-557.

Firth D. Bias reduction of maximum-likelihood-estimates [J]. Biometrika, 1993,80(1):27-38.

Albert A, Anderson JA. On the existence of maximum-likelihood estimates in logistic-regression models [J]. Biometrika,1984, 71:1-10.

Santner TJ, Duffy DE. A note on A. Albert and J.A. Anderson’s conditions for the existence of maximum likelihood estimates in logistic regression models [J]. Biometrika, 1986,73(3):755-758.

郑海燕,廖志远,刘四兰,等. Logistic回归系数可信区间估计及假设检验的三种方法比较 [J]. 数理医药学杂志, 2012,25(4):393-396.

李明丽,潘沛江,朱金辉,等. 新旧注射吸毒人群HIV传播因素研究 [J]. 中华疾病控制杂志, 2014,18(2):97-101.

Mehta CR, Patel NR. Exact logistic regression: theory and examples [J]. Stat Med, 1995, 14(19):2143-2160.

韩宏. 确切Logistic回归方法及其在医学遗传学领域的应用 [D]. 太原:山西医科大学, 2002.

王彤,韩宏. 确切Logistic回归方法及其医学遗传学应用 [J]. 中国卫生统计, 2003,20(3):147-150.

Heinze G, Schemper M. A solution to the problem of monotone likelihood in Cox regression [J]. Biometrics, 2001,57(1):114-119.

Heinze G. A comparative investigation of methods for logistic regression with separated or nearly separated data [J]. Stat Med, 2006, 25(24):4216-4226.

Bull SB, Mak C, Greenwood CMT. A modified score function estimator for multinomial logistic regression in small samples [J]. Comput Stat Data Anal, 2002,39(1):57-74.

Bull SB, Lewinger JP, Lee SSF. Confidence intervals for multinomial logistic regression in sparse data [J]. Stat Med, 2007,26:903-918.

施引文献

资源附件(0)

访问统计