Bayesian Inference for Finite Mixture Regression Model Based on Non-Iterative Algorithm

Finite mixtures normal regression (FMNR) models are widely used to investigate the relationship between a response variable and a set of explanatory variables from several unknown latent homogeneous groups. However, the classical EM algorithm and Gibbs sampling to deal with this model have several weak points. In this paper, a non-iterative sampling algorithm for fitting FMNR model is proposed from a Bayesian perspective. The procedure can generate independently and identically distributed samples from the posterior distributions of the parameters and produce more reliable estimations than the EM algorithm and Gibbs sampling. Simulation studies are conducted to illustrate the performance of the algorithm with supporting results. Finally, a real data is analyzed to show the usefulness of the methodology.

Heterogeneous Association of Chinese Adolescents’ Engaged Living With Problematic Internet Use: A Mixture Regression Analysis

The present study explored heterogeneity in the association between engaged living (i.e., social integration and absorption) and problematic Internet use (PIU). This study included 641 adolescents from four junior-senior high schools of Guangzhou, China. Besides the standard linear regression analysis, mixture regression analysis was conducted to detect certain subgroups of adolescents, based on their divergent association between engaged living and PIU. Sex, age, and psychological need were further compared among the latent subgroups. The results showed that a mixture regression model could account for more variance of PIU than a traditional linear regression model, and identified three subgroups based on their class-specific regression of PIU to engaged living. For the High-PIU class, lower social integration and higher absorption were associated with increased PIU; for the Medium-PIU class, only high social integration was linked with the increase of PIU. For the Low-PIU class, no relation between engaged living and PIU were found. Additionally, being male or having a lower level of satisfied psychological needs increased the link between engaged living and PIU. The results indicated a heterogeneous relationship between engaged living and PIU among adolescents, and prevention or intervention programs should be tailored specifically to subgroups with moderate or high levels of PIU and to those with lower levels of psychological needs’ satisfaction, as identified by the mixture regression model.

Modeling Recovery Rates of Small- and Medium-Sized Entities in the US

A sound statistical model for recovery rates is required for various applications in quantitative risk management, with the computation of capital requirements for loan portfolios as one important example. We compare different models for predicting the recovery rate on borrower level including linear and quantile regressions, decision trees, neural networks, and mixture regression models. We fit and apply these models on the worldwide largest loss and recovery data set for commercial loans provided by GCD, where we focus on small- and medium-sized entities in the US. Additionally, we include macroeconomic information via a predictive Crisis Indicator or Crisis Probability indicating whether economic downturn scenarios are expected within the time of resolution. The horserace is won by the mixture regression model which regresses the densities as well as the probabilities that an observation belongs to a certain component.