Comparisons of two‐part models with competitors

Abstract

Two‐part models arise when there is a clump of 0 observations in a distribution of continuous non‐negative responses. Several methods for comparing two such distributions are available. These include the straightforward application of the z‐test (or t‐test), the Wilcoxon–Mann–Whitney rank sum test, the Kolmogorov–Smirnov test, and three tests that use a 2 degree of freedom χ² test based on the sum of the test for equality of proportions and a conditional χ² test for the continuous responses. This conditional test may be the z‐test, the rank sum test, or the χ² corresponding to the Kolmogorov–Smirnov test. This study compares the size and power of several of these methods. All tests have the appropriate distribution under the null hypothesis if the distribution of the continuous part has finite moments. If it does not, the z‐test has no power to detect any alternatives. It is found that the 2 d.f. tests are superior to the others when the larger proportion of 0 values corresponds to the population with the larger mean. If the reverse holds, the difference in the proportion of zeros reinforces the difference in means and some single‐part models (the rank sum or Kolmogorov–Smirnov) do best. In those cases, the two‐part models are not far behind, although statistically significantly poorer with respect to power. Published in 2001 by John Wiley & Sons, Ltd.