Expanding on the zero-inflated Poisson model, the multiple-inflated Poisson model is applied to analyze count data with multiple inflated values. The existing studies on the multiple-inflated Poisson model determined the inflated values by inspecting the histogram of count response and fitting the model with different combinations of inflated values, which leads to relatively complicated computations and may overlook some real inflated points. We address a two-stage inflated values selection method, which takes all values of count response as potential inflated values and adopts the adaptive lasso regularization on the mixing proportion of those values. Numerical studies demonstrate the excellent performance both on inflated values selection and parameters estimation. Moreover, a specially designed simulation, based on the structure of data from a randomized clinical trial of an HIV sexual risk education intervention, performs well and ensures our method could be generalized to the real situation. An empirical analysis of a clinical trial dataset is used to elucidate the multiple-inflated Poisson model.
Keywords: Adaptive lasso; count data; inflated values selection; mixture model; multiple inflated values.