We propose a MANOVA test for semicontinuous data that is applicable also when the dimensionality exceeds the sample size. The test statistic is obtained as a likelihood ratio, where numerator and denominator are computed at the maxima of penalized likelihood functions under each hypothesis. Closed form solutions for the regularized estimators allow us to avoid computational overheads. We derive the null distribution using a permutation scheme. The power and level of the resulting test are evaluated in a simulation study. We illustrate the new methodology with two original data analyses, one regarding microRNA expression in human blastocyst cultures, and another regarding alien plant species invasion in the island of Socotra (Yemen).

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