TESTING GOODNESS-OF-FIT FOR A PARAMETRIC FAMILY OF LINK FUNCTIONS

• 成果类型: Article
• 署名作者: CHENG, KF; WU, JW
• 署名单位: Tamkang University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290868
• 发表日期: 1994
• 页码: 657-664
• 关键词: GENERALIZED LINEAR-MODELS; logistic-regression models; quasi-likelihood functions; graphical methods; CURVES

摘要

We concern ourselves with the methods for testing the overall goodness of fit of a parametric family of link functions used for modeling the conditional mean of the response variable Y given the covariates X = x is-an-element-of R(p). The null hypothesis is that the conditional mean function is a known functional depending on betax and a finite number of parameters theta = (theta1,..., theta(q)), where beta is a p-dimensional row vector of regression parameters and x is a column vector. The proposed test statistic is derived from an ''information'' equivalence result and a dimension-reduction technique. The new test is very simple in computation. Also, it is generally consistent against broad class of alternatives and, asymptotically, the null distribution is independent of the underlying distribution of Y, given X = x. Practical examples are given to show the advantage of the proposed test. Furthermore, power comparisons with the test used by Su and Wei are also performed to indicate the usefulness of the new test. Particularly, we find that the new test has good power performance in discriminating between the probit and logit links.