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The mode of a distribution provides a significant summary. A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes. Finite mixture of regression (FMR) models are frequently used to analyze data that arise from a heterogeneous population. This work develops a new data analysis tool called finite mixture of mode regression (FMMoR) in order to explore skewed data from several subpopulations. The main virtue of considering the FMMoR models for skewed data is that this class of models has a nice hierarchical representation which allows easy implementation of inferences. A productive clustering method via mode identification is applied to select the number of components. A modified expectation-maximization algorithm facilitated by the two-point step size gradient descent method (GDEM), simultaneously, is developed for the inference. The proposed methods are evaluated through some simulation studies and illustrated by a real dataset.

Estimation for finite mixture of mode regression models using skew-normal distribution