Treatments for undefined log ratios in matching analyses

Abstract

A challenge in carrying out matching analyses is to deal with undefined log ratios. If any reinforcer or response rate equals zero, the logarithm of the ratio is undefined: data are unsuitable for analyses. There have been some tentative solutions, but they had not been thoroughly investigated. The purpose of this article is to assess the adequacy of five treatments: omit undefined ratios, use full information maximum likelihood, replace undefined ratios by the mean divided by 100, replace them by a constant 1/10, and add the constant .50 to ratios. Based on simulations, the treatments are compared on their estimations of variance accounted for, sensitivity, and bias. The results show that full information maximum likelihood and omiting undefined ratios had the best overall performance, with negligibly biased and more accurate estimates than mean divided by 100, constant 1/10, and constant .50. The study suggests that mean divided by 100, constant 1/10, and constant .50 should be avoided and recommends full information maximum likelihood to deal with undefined log ratios in matching analyses.