Homogeneity score tests with nuisance parameters

Abstract

For situations in which a parameter may be estimated from several independent data sets and there are no nuisance parameters, Mather (1935) proposed a homogeneity test based on efficient scores. The homogeneity score test can be extended to the nuisance parameter case using the theory of score, or Lagrange multiplier, tests. A modification of the extended homogeneity score test is presented, wherein a consistent but inefficient estimator of the parameter of interest may be substituted for the maximum likelihood estimator. Use of the modified procedure is illustrated in testing for a common logistic slope parameter in several 2xJ contingency tables.

Keywords:

• homogeneity test
• efficient score
• consistent estimator
• efficient estimator
• maximum likelihood estimator