Robust Modeling Using Non-Elliptically Contoured Multivariate t Distributions

Models based on multivariate t distributions are widely applied to analyze data with heavy tails. However, all the marginal distributions of the multivariate t distributions are restricted to have the same degrees of freedom, making these models unable to describe different marginal heavy-tailedness. We generalize the traditional multivariate t distributions to non-elliptically contoured multivariate t distributions, allowing for different marginal degrees of freedom. We apply the non-elliptically contoured multivariate t distributions to three widely-used models: the Heckman selection model with different degrees of freedom for selection and outcome equations, the multivariate Robit model with different degrees of freedom for marginal responses, and the linear mixed-effects model with different degrees of freedom for random effects and within-subject errors. Based on the Normal mixture representation of our t distribution, we propose efficient Bayesian inferential procedures for the model parameters based on data augmentation and parameter expansion. We show via simulation studies and real examples that the conclusions are sensitive to the existence of different marginal heavy-tailedness

Qualitative Evaluation of Associations by the Transitivity of the Association Signs

We say that the signs of association measures among three variables {X, Y, Z} are transitive if a positive association measure between the variable X and the intermediate variable Y and further a positive association measure between Y and the endpoint variable Z imply a positive association measure between X and Z. We introduce four association measures with different stringencies, and discuss conditions for the transitivity of the signs of these association measures. When the variables follow exponential family distributions, the conditions become simpler and more interpretable. Applying our results to two data sets from an observational study and a randomized experiment, we demonstrate that the results can help us to draw conclusions about the signs of the association measures between X and Z based only on two separate studies about {X, Y} and {Y, Z}.Comment: Statistica Sinica 201

Principal causal effect identification and surrogate endpoint evaluation by multiple trials

Principal stratification is a causal framework to analyze randomized experiments with a post-treatment variable between the treatment and endpoint variables. Because the principal strata defined by the potential outcomes of the post-treatment variable are not observable, we generally cannot identify the causal effects within principal strata. Motivated by a real data set of phase III adjuvant colon clinical trials, we propose approaches to identifying and estimating the principal causal effects via multiple trials. For the identifiability, we remove the commonly-used exclusion restriction assumption by stipulating that the principal causal effects are homogeneous across these trials. To remove another commonly-used monotonicity assumption, we give a necessary condition for the local identifiability, which requires at least three trials. Applying our approaches to the data from adjuvant colon clinical trials, we find that the commonly-used monotonicity assumption is untenable, and disease-free survival with three-year follow-up is a valid surrogate endpoint for overall survival with five-year follow-up, which satisfies both the causal necessity and the causal sufficiency. We also propose a sensitivity analysis approach based on Bayesian hierarchical models to investigate the impact of the deviation from the homogeneity assumption

Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments

Two-stage randomized experiments are becoming an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two-stage randomized experiments. Under the randomization-based framework, we propose unbiased point estimators of direct and spillover effects, construct conservative variance estimators, develop hypothesis testing procedures, and derive sample size formulas. We also establish the equivalence relationships between the randomization-based and regression based methods. We theoretically compare the two-stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the analysis of the data from a field experiment on a job placement assistance program

Numerical simulation of mould filling process for pressure plate and valve handle in LFC

In lost foam casting (LFC), the distribution of polymer beads during the bead filling process is not uniform, and the collision between polymer beads determines the distribution of two-phase flow of gas and solid. The interaction between the gas and solid phases reveals as coupling effect of the force that gas exerts on particles or vice versa, or that among particles. The gas-solid flow in filling process is nonlinearity, which makes the coupling effect an essential point to carry out a simulation properly. Therefore, information of each particle’s motion is important for acquiring the law of filling process. In bead filling process, compressed air is pressed into mold cavity, and discharged from gas vent, creating a pressure difference between outer and inner space near the gas vent. This pressure difference directly changes the spatial distribution and motion trace of gas and solid phases. In this paper, Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD) are employed to simulate the fluid dynamic character based on Newton’s Third Law of Motion. The simulation results of some casting products such as pressure plate and valve handle are compared with the result obtained from practical experiment in order to test the feasibility of DEM. The comparison shows that this DEM method can be a very promising tool in the mould filling simulation of beads’ movement

Principal Stratification with Continuous Post-Treatment Variables: Nonparametric Identification and Semiparametric Estimation

Causal inference is often complicated by post-treatment variables, which appear in many scientific problems, including noncompliance, truncation by death, mediation, and surrogate endpoint evaluation. Principal stratification is a strategy that adjusts for the potential values of the post-treatment variables, defined as the principal strata. It allows for characterizing treatment effect heterogeneity across principal strata and unveiling the mechanism of the treatment on the outcome related to post-treatment variables. However, the existing literature has primarily focused on binary post-treatment variables, leaving the case with continuous post-treatment variables largely unexplored, due to the complexity of infinitely many principal strata that challenge both the identification and estimation of causal effects. We fill this gap by providing nonparametric identification and semiparametric estimation theory for principal stratification with continuous post-treatment variables. We propose to use working models to approximate the underlying causal effect surfaces and derive the efficient influence functions of the corresponding model parameters. Based on the theory, we construct doubly robust estimators and implement them in an R package

Research on Continuous Use of B2B Platform in Chinese Intelligent Engineering Companies Based on the Theory of Resource Complementary

What factors affect the continuous use of B2B platforms by intelligent engineering companies is an important issue. Based on the theory of resource complementarity, a model of influencing factors for intelligent engineering companies to continue using the B2B platform is constructed, and four influencing factors including the complementary resources given by the platform, the complementary resources given by the company, interaction quality, and exploration and exploitation capability are analyzed. Using SmartPLS 3.0 to analyze 217 survey data, the results show that the complementary resources given by the platform and companies have positive impact on the interaction quality, and the complementary resources given by the platform have positive effect on the exploration and exploitation capabilities. Interaction quality has positive impact on the company’s continuous use intention of the B2B platform. The complementary resources given by the company have no positive impact on the exploration and exploitation capabilities, and the exploration and exploitation capabilities have no positive impact on the company’s continuous use intention of the B2B platform. Finally, some suggestions are proposed to increase the company’s continuous use intention of B2B platform