Testing for heteroskedasticity in the tobit and probit models

Non-constant variance across observations (heteroskedasticity) results in the maximum likelihood estimators of tobit and probit model parameters being inconsistent. Some of the available tests for constant variance across observations (homoskedasticity) are discussed and examined in a small Monte Carlo experiment.     

Discrimination between two binary data models: sequentially designed experiments

In this paper we propose a sequential procedure to design optimum experiments for discriminating between two binary data models. For the problem to be fully specified, not only the mode1link functions should be provided but also their associated linear predictor structures. Further, we suppose that one of the models is true, albeit it is not known which of them. Under these assumptions the procedure consists of making sequential choices of single experimental units to discriminate between the rival models as efficiently as possible. Depending on whether the models are nested or not, alternative methods are proposed.

To illustrate the procedure, a simulation study for the classical case of pro bit versus logit model is presented. It enables us to estimate the total sample sizes required to gain a certain power of discrimination and compare them to sample sizes for methods that were previously suggested in the literature.     

Bias corrected estimation for generalized probit regression with covariate measurement error and censored responses

In this paper, we propose a bias corrected estimate of the regression coefficient for the generalized probit regression model when the covariates are subject to measurement error and the responses are subject to interval censoring. The main improvement of our method is that it reduces most of the bias that the naive estimates have. The great advantage of our method is that it is baseline and censoring distribution free, in a sense that the investigator does not need to calculate the baseline or the censoring distribution to obtain the estimator of the regression coefficient, an important property of Cox regression model. A sandwich estimator for the variance is also proposed. Our procedure can be generalized to general measurement error distribution as long as the first four moments of the measurement error are known. The results of extensive simulations show that our approach is very effective in eliminating the bias when the measurement error is not too large relative to the error term of the regression model.     

家庭金融服务获得性对收入流动性的影响

伴随普惠金融的发展及金融精准扶贫政策的实施,广大居民家庭参与金融市场的广度和深度不断提升,家庭金融服务获得性对居民家庭收入分配影响日益凸显。使用中国家庭金融调查(CHFS)数据,运用收入转移矩阵和有序probit模型,研究家庭金融服务获得性对收入流动性的影响。研究结果表明,家庭金融服务获得性提高对低收入家庭向上流动具有积极影响,对高收入家庭向下流动具有抑制作用。进一步分城乡样本、面板数据等进行稳健性检验,验证实证结果的可靠性。鉴于提高家庭金融服务获得性对于促进微观收入流动性、缓解社会收入阶层固化具有积极作用,政府应继续推进普惠金融发展,降低融资成本;优化金融资源区域配置;加强金融教育,保护弱势金融群体。     

The one-step-late PXEM algorithm

The EM algorithm is a popular method for computing maximum likelihood estimates or posterior modes in models that can be formulated in terms of missing data or latent structure. Although easy implementation and stable convergence help to explain the popularity of the algorithm, its convergence is sometimes notoriously slow. In recent years, however, various adaptations have significantly improved the speed of EM while maintaining its stability and simplicity. One especially successful method for maximum likelihood is known as the parameter expanded EM or PXEM algorithm. Unfortunately, PXEM does not generally have a closed form M-step when computing posterior modes, even when the corresponding EM algorithm is in closed form. In this paper we confront this problem by adapting the one-step-late EM algorithm to PXEM to establish a fast closed form algorithm that improves on the one-step-late EM algorithm by insuring monotone convergence. We use this algorithm to fit a probit regression model and a variety of dynamic linear models, showing computational savings of as much as 99.9%, with the biggest savings occurring when the EM algorithm is the slowest to converge.     

Modified Profile Likelihood for Fixed-Effects Panel Data Models

We show how modified profile likelihood methods, developed in the statistical literature, may be effectively applied to estimate the structural parameters of econometric models for panel data, with a remarkable reduction of bias with respect to ordinary likelihood methods. Initially, the implementation of these methods is illustrated for general models for panel data including individual-specific fixed effects and then, in more detail, for the truncated linear regression model and dynamic regression models for binary data formulated along with different specifications. Simulation studies show the good behavior of the inference based on the modified profile likelihood, even when compared to an ideal, although infeasible, procedure (in which the fixed effects are known) and also to alternative estimators existing in the econometric literature. The proposed estimation methods are implemented in an R package that we make available to the reader.     

大学生体育用品的品牌选择及其影响因素研究——基于陕西21所高校大学生的调查分析

基于陕西21所高校1 000名大学生体育用品品牌选择的李克特量表调查数据,研究了大学生体育用品的品牌选择倾向及其影响因素。研究发现:品牌的高知名度和代言人的高知名度,能够给大学生选择时带来积极影响;体育用品美观性对大学生体育品牌选择具有重要的正面影响,而产品质量、产品售后服务水平等方面对大学生体育用品品牌选择影响不显著;价格水平对大学生体育品牌选择具有显著的负影响;家庭背景与锻炼习惯会对大学生体育用品品牌选择有重要的差异化影响。     

A Comparison of Methods of Benchmark-Dose Estimation for Continuous Response Data

Methods of quantitative risk assessment for toxic responses that are measured on a continuous scale are not well established. Although risk-assessment procedures that attempt to utilize the quantitative information in such data have been proposed, there is no general agreement that these procedures are appreciably more efficient than common quantal dose–response procedures that operate on dichotomized continuous data. This paper points out an equivalence between the dose–response models of the nonquantal approach of Kodell and West⁽¹⁾ and a quantal probit procedure, and provides results from a Monte Carlo simulation study to compare coverage probabilities of statistical lower confidence limits on dose corresponding to specified additional risk based on applying the two procedures to continuous data from a dose–response experiment. The nonquantal approach is shown to be superior, in terms of both statistical validity and statistical efficiency.     

Determinants of workplace health program participation among non,low, and incentive-achieving participants

The authors used a cross-sectional survey and zero-inflated ordered probit modeling to investigate individual psychosocial-, interpersonal-, organizational-, and community-level determinants distinguishing nonparticipants, low-level participants, and incentive-achieving participants in a single, university-based worksite health program (WHP) that uses insurance premium reductions to incentivize participation. Results from 319 employees suggested two nonparticipant groups. Persons without employer-sponsored insurance, those with negative participation perceptions, and men were more likely to be “never” participants; those who had never met the incentive were potential future participants. Increased confidence was related to incentive achievement; stress was associated with low participation. No interpersonal, organizational, or community factors were significant. When structuring incentives, WHPs should consider determinants of participation, vis-à-vis the incentive.