Inferences for Selected Location Quotients with Applications to Health Outcomes
Abstract:The location quotient (LQ) is an index frequently used in geography and economics to measure the relative concentration of activities. This quotient is calculated in a variety of ways depending on which group is used as a reference. Here, we focus on a simultaneous inference for the ratios of the individual proportions to the overall proportion based on binomial data. This is a multiple comparison problem and inferences for LQs with adjustments for multiplicity have not been addressed before. The comparisons are negatively correlated. The quotients can be simultaneously tested against unity, and simultaneous confidence intervals can be constructed for the LQs based on existing probability inequalities and by directly using the asymptotic joint distribution of the associated test statistics. The proposed inferences are appropriate for analysis based on sample surveys. Two real data sets are used to demonstrate the application of multiplicity-adjusted LQs. A simulation study is also carried out to assess the performance of the proposed methods to achieve a nominal coverage probability. For the LQs considered, the coverage of the simple Bonferroni-adjusted Fieller intervals for LQs is observed to be almost as good as the coverage of the method that directly takes the correlations into account.
Document Type: Research Article
Affiliations: 1: Department of Mathematics and Statistics, South Dakota State University, South Dakota, U.S.A. 2: Institute of Biostatistics, Leibniz University of Hannover, Germany 3: Department of Economics and Finance, Middle Tennessee State University, Tennessee, U.S.A.
Publication date: July 1, 2010