Identification of proportionality structure with two-part models using penalization

Data with a mixture distribution are commonly encountered. A special example is zero-inflated data, where a proportion of the responses takes zero values, and the rest are continuously distributed. Such data routinely arise in public health, biomedicine, and many other fields. Two-part modeling is a natural choice for zero-inflated data, where the first part of the model describes whether the responses are equal to zero, and the second part describes the continuously distributed responses. With two-part models, an interesting problem is to identify the proportionality structure of covariate effects. Such a structure can lead to more efficient estimates and also provide scientific insights into the underlying data-generating mechanisms. To identify the proportionality structure, we adopt a penalization method. Compared to the alternatives, notable advantages of this method include computational simplicity, solid statistical properties, and others. For inference, we adopt a bootstrap approach. The proposed method shows satisfactory performance in simulation and the analysis of two public health datasets.