Compositional data are positive multivariate data whose sum equals 1. A popular method to analyze such data is via log--ratio transformations, which are however not applicable when zero values are present. In this paper we present a conditional logistic normal distribution suitable for compositional data with structural zero values. The model is applicable to arbitrary dimensions and the EM algorithm guarantees a fast implementation. The model accepts predictors and we provide a residual analysis. We further provide principal component analysis and biplots for visualization of compositional data with zero values present. Simulation studies and real data examples illustrate the performance of the model, with and without covariates, and compare it to the Dirichlet analogue.

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