Modelling household finances: A Bayesian approach to a multivariate two-part model

Deep Tobit networks: A novel machine learning approach to microeconometrics

Tobit models (also called as "censored regression models" or classified as "sample selection models" in microeconometrics) have been widely applied to microeconometric problems with censored outcomes. However, due to their linear parametric settings and restrictive normality assumptions, the traditional Tobit models fail to capture the pervading nonlinearities and thus may be inadequate for microeconometric analysis with large-scale datasets. This paper proposes two novel deep neural networks for Tobit problems and explores machine learning approaches in the context of microeconometric modeling. We connect the censored outputs in Tobit models with some deep learning techniques, which are thought to be unrelated to microeconometrics, and use the rectified linear unit activation and a particularly designed network structure to implement the censored output mechanisms and realize the underlying econometric conceptions. The benchmark Tobit-I and Tobit-II models are then reformulated as two carefully designed deep feedforward neural networks named deep Tobit-I network and deep Tobit-II network, respectively. A novel significance testing method is developed based on the proposed networks. Compared with the traditional models, our networks with deep structures can effectively describe the underlying highly nonlinear relationships and achieve considerable improvements in fitting and prediction. With the novel testing method, the proposed networks enable highly accurate and sophisticated econometric analysis with minimal random assumptions. The encouraging numerical experiments on synthetic and realistic datasets demonstrate the utility and advantages of the proposed method.

A two-part mixed-effects model for analyzing clustered time-to-event data with clumping at zero

BACKGROUND AND OBJECTIVE

In longitudinal epidemiological studies consisting of a baseline stage and a follow-up stage, observations at the baseline stage may contain a countable proportion of negative responses. The time-to-event outcomes of those observations corresponding to negative responses at baseline can be denoted as zeros, which are excluded from standard survival analysis. Consequently, some important information on these subjects is therefore lost in the analysis. Furthermore, subjects are often clustered within hospitals, communities or health service centers, resulting in correlated observations. The framework of the two-part model has been developed and utilized widely to analyze semi-continuous data or count data with excess zeros, but its application to clustered time-to-event data with clumping at zero remains sparse.

METHODS

A two-part mixed-effects modeling approach was proposed. A logistic mixed-effects regression model was used in the first part to determine factors associated with the prevalence of the baseline event of interest. Parametric frailty models (including Weibull, exponential, log-logistic and log-normal) were used in the second part to assess associations between exposures and time-to-event outcomes. Correlated random effects were incorporated within the two regression models to accommodate the inherent correlation within each clustering unit and the correlation between the two parts. As an illustrative example, the method was applied to exclusive breastfeeding data from a community-based prospective cohort study in Nepal.

RESULTS

A significantly positive correlation between the baseline prevalence of exclusive breastfeeding and exclusive breastfeeding duration was confirmed (ρ = 0.67, P < 0.001). The correlated two-part model outperformed the independent two-part model (likelihood ratio test statistic = 8.6, df = 1, P = 0.003).

CONCLUSIONS

The proposed approach makes full use of all available information at baseline and during the follow-up, compared to the conventional survival analysis. In addition to breastfeeding studies, the method can be applied to other research areas where clustered time-to-event data with clumping at zero arise.

A Bayesian approach of analysing semi-continuous longitudinal data with monotone missingness

There is a rich literature on the analysis of longitudinal data with missing values. However, the analysis becomes complex for semi-continuous (zero-inflated) longitudinal response with missingness. In this article, we propose a partially varying coefficients regression model for analysing such data. We use a two-part model, where in the first part we propose a latent dynamic model for accounting a ‘zero’ or a ‘non-zero’ response, and in the second part we use another dynamic model for estimating the mean trajectories of non-zero responses. Two dynamic models are linked through subject-specific random effects. The missing covariates are imputed repeatedly based on their respective posterior predictive distributions and the missing responses are imputed using the working model under different identifying restrictions. We analyse data from the Health and Retirement Study (HRS) for aged individuals and develop a dynamic model for predicting out-of-pocket medical expenditures (OOPME) containing excess zeros. The operating characteristics of the proposed model are investigated through extensive simulation studies.