A MANOVA test for multivariate lognormal observations with a spike at zero, with application to ecological niches of South Africa

We develop an asymptotic likelihood ratio test for multivariate lognormal data with a point mass at zero in each dimension. The test generalizes Wilks' lambda and Hotelling T-test to the case of semicontinuous data. Simulations show that the resulting test statistic attains the nominal Type I error rate and has good power for reasonable alternatives. We conclude with an application to exploration of ecological niches of trees of South Africa.