Estimation of reliability under ordered restriction on the parameters

This paper deals with the estimation of reliability for a strength-stress model under ordered restriction on the parameters. It is assumed that components have exponential distributions and are arranged in a parallel system and the failure of one component, results in increasing the failure rate of the remaining components. Results are derived when (i) the ordering of the means is taken into account and when (ii) the ordering of the means is ignored. Simulation studies are carried out to compare the results. It is noticed that, in almost all cases, in case (i) the estimates are closer to the true value with smaller mean squared error (MSE) and smaller’ standard deviation than in case (ii). Thus when the ordering of the means is present in the model, such information should be incorporated in the estimation of reliability.     

The nested joint clustering via Dirichlet process mixture model

This article focuses on the clustering problem based on Dirichlet process (DP) mixtures. To model both time invariant and temporal patterns, different from other existing clustering methods, the proposed semi-parametric model is flexible in that both the common and unique patterns are taken into account simultaneously. Furthermore, by jointly clustering subjects and the associated variables, the intrinsic complex shared patterns among subjects and among variables are expected to be captured. The number of clusters and cluster assignments are directly inferred with the use of DP. Simulation studies illustrate the effectiveness of the proposed method. An application to wheal size data is discussed with an aim of identifying novel temporal patterns among allergens within subject clusters.     

The Muscatine children's obesity data reanalysed using pattern mixture models

A set of longitudinal binary, partially incomplete, data on obesity among children in the USA is reanalysed. The multivariate Bernoulli distribution is parameterized by the univariate marginal probabilities and dependence ratios of all orders, which together support maximum likelihood inference. The temporal association of obesity is strong and complex but stationary. We fit a saturated model for the distribution of response patterns and find that non-response is missing completely at random for boys but that the probability of obesity is consistently higher among girls who provided incomplete records than among girls who provided complete records. We discuss the statistical and substantive features of, respectively, pattern mixture and selection models for this data set.     

RANDOMISATION AND THE 1975 SENATE BALLOT DRAW

“So the last shall be first, and the first last; for many be called, but few chosen.” Matthew 20:16 The “random” draw for positions on the Senate ballot papers in the 1975 election resulted in an apparently non-random ordering, to the possible advantage of one particular party. This paper assesses the statistical significance of the 1975 draw and looks at possible causes of the evident non-randomness. A simplified yet realistic mathematical model is used to describe conditions under which the so-called donkey vote can have an effect on the final outcome of the election, thereby confirming the widely-held belief that the order of parties on the Senate ballot paper is relevant. We examine other Senate elections between 1949 and 1983 for the existence of relevant non-randomness similar to the 1975 result. Finally, we report briefly on our submission to the 1983 Joint Select Committee on Electoral Reform, which led to an improvement in the randomisation procedure.     

Comparisons among regression estimators under the generalized mean square error criterion

It is not always prossible to establish a preference ordering among regression estimators in terms of the generalized mean square error criterion. In the paper, we determine when it is feasible to use this criteion to couduct comparisons among ordinary least squares, principal components, ridge regression, and shrunken least squares estimators.     

Natural cubic splines for the analysis of Alzheimer's clinical trials

Mixed model repeated measures (MMRM) is the most common analysis approach used in clinical trials for Alzheimer's disease and other progressive diseases measured with continuous outcomes over time. The model treats time as a categorical variable, which allows an unconstrained estimate of the mean for each study visit in each randomized group. Categorizing time in this way can be problematic when assessments occur off-schedule, as including off-schedule visits can induce bias, and excluding them ignores valuable information and violates the intention to treat principle. This problem has been exacerbated by clinical trial visits which have been delayed due to the COVID19 pandemic. As an alternative to MMRM, we propose a constrained longitudinal data analysis with natural cubic splines that treats time as continuous and uses test version effects to model the mean over time. Compared to categorical-time models like MMRM and models that assume a proportional treatment effect, the spline model is shown to be more parsimonious and precise in real clinical trial datasets, and has better power and Type I error in a variety of simulation scenarios.     

Local functional data model for characterizing shape variation of similar curves

“Similar curves” in the present article refers to a family of curves whose major shape are similar, but who have variation coming from curve-specific sources. The goal here is to develop a general methodology to describe small changes among similar curves. Previous methods mainly focus on dimension reduction through FPCA, which are not appropriate for quantifying local variation. Here, we consider a local functional data model which divides data into segments adaptively and models each segment with a shape invariant model. Such model has great flexibility in characterizing local variation of curves, as illustrated by simulation and real data examples.     

课程网站的用户使用意愿研究

课程网站是信息技术在教育教学中的重要应用,可以有效提高教学质量,但目前却存在用户持续使用率低等问题。鉴此,从用户角度出发,基于技术接受模型和交互理论,探讨影响课程网站用户使用意愿的因素,并运用结构方程模型对研究假设进行验证。研究发现:课程网站的使用意愿受使用态度、交互性、主观规范三大因素的影响显著,感知有用性和感知娱乐性未对使用意愿产生直接的显著影响,由此提出增强课程网站用户使用意愿的对策建议,以期能够充分发挥课程网站在教学工作中的作用。     

大学生创业自我效能、行为控制知觉与创业意向的实证研究

采用结构方程模型,对河北、天津4所高校640名在校大学生进行调查研究,发现创业自我效能对创业意向的显著正向影响及其机制,以及行为控制知觉作为中介变量对创业自我效能影响创业意向过程中所发挥的作用,揭示了行为控制知觉的部分中介作用机制。根据模型研究结果,就提高创业意向的途径、方法,围绕创业教育、自我强化和社会环境劝导进行了探讨。     

Unbiased tests for some one-sided testing problems

Unbiased tests are found for various testing problems. In the first model considered we test homogeneity of k + 1 independent one-parameter exponential family populations vs. the tree-top ordering alternative. The tree-top alternative is appropriate for one-sided comparisons for treatments with a control. In the next set of models normality is assumed. In one such model k independent populations have different unknown means but have an unknown common variance. An independent estimate of the variance exists. We test homogeneity of means against the alternative of no homogeneity. We also consider the alternative of an ordering of the means as well as the tree-top ordering. The final model considered is when we take a random sample from a multivariate normal population with unknown mean vector and an unknown covariance matrix of the intraclass type. We test the hypothesis that the mean vector is the zero vector against the one-sided alternative that each mean is nonnegative (with at least one positive).     

On the Comparison of Two Ordinal Responses

Responses of two groups, measured on the same ordinal scale, are compared through the column effect association model, applied on the corresponding 2 × J contingency table. Monotonic or umbrella shaped ordering for the scores of the model are related to stochastic or umbrella ordering of the underlying response distributions, respectively. An algorithm for testing all possible hypotheses of stochastic ordering and deciding on an appropriate one is proposed.     

Study Design in Causal Models

The causal assumptions, the study design and the data are the elements required for scientific inference in empirical research. The research is adequately communicated only if all of these elements and their relations are described precisely. Causal models with design describe the study design and the missing‐data mechanism together with the causal structure and allow the direct application of causal calculus in the estimation of the causal effects. The flow of the study is visualized by ordering the nodes of the causal diagram in two dimensions by their causal order and the time of the observation. Conclusions on whether a causal or observational relationship can be estimated from the collected incomplete data can be made directly from the graph. Causal models with design offer a systematic and unifying view to scientific inference and increase the clarity and speed of communication. Examples on the causal models for a case–control study, a nested case–control study, a clinical trial and a two‐stage case–cohort study are presented.     

汽车4S店顾客满意度模型及其实证研究——以天津丰田汽车4S店为例

构建了以感知硬件质量和感知软件质量为外生变量,以感知价值和顾客满意为中介变量,以重复购买意向和正面口碑相传为结果变量的汽车4S店顾客满意度模型,并对其进行实证检验,研究发现:感知硬件质量对购后行为意向没有显著的直接影响,而是通过感知价值和顾客满意间接作用于购后行为意向;感知软件质量只对重复购买意向有显著的直接正向影响,同时也会通过感知价值和顾客满意对购买行为意向产生间接的作用;感知硬件质量对顾客满意的作用力最强;汽车的外观设计与感知硬件质量的相关性最强;供应的零配件质量与感知软件质量的相关性最强。     

Mean residual life ordering

A new partial ordering among life distributions in terms of their mean residual life is introduced. This ordering is weaker than the hazard rate ordering but it is stronger than the variability ordering. Characterizations of the DMRL and NBUE distribution are given.     

Multivariate models for correlated count data

In this study, we deal with the problem of overdispersion beyond extra zeros for a collection of counts that can be correlated. Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions have been considered. First, we propose a multivariate count model in which all counts follow the same distribution and are correlated. Then we extend this model in a sense that correlated counts may follow different distributions. To accommodate correlation among counts, we have considered correlated random effects for each individual in the mean structure, thus inducing dependency among common observations to an individual. The method is applied to real data to investigate variation in food resources use in a species of marsupial in a locality of the Brazilian Cerrado biome.     

Evidence of bias in the Eurovision song contest: modelling the votes using Bayesian hierarchical models

The Eurovision Song Contest is an annual musical competition held among active members of the European Broadcasting Union since 1956. The event is televised live across Europe. Each participating country presents a song and receive a vote based on a combination of tele-voting and jury. Over the years, this has led to speculations of tactical voting, discriminating against some participants and thus inducing bias in the final results. In this paper we investigate the presence of positive or negative bias (which may roughly indicate favouritisms or discrimination) in the votes based on geographical proximity, migration and cultural characteristics of the participating countries through a Bayesian hierarchical model. Our analysis found no evidence of negative bias, although mild positive bias does seem to emerge systematically, linking voters to performers.     

On estimation and testing arising from order restricted balanced mixed model

The randomized complete block design is one of the most widely used experimental designs to systematically control the variability arising from known nuisance sources. The balanced mixed effects model is usually appropriate for such an experiment when the blocks used in the experiment are randomly chosen. In applications with k increasing or decreasing treatment levels, there is sometimes prior knowledge about the ordering of the treatment effects. The most commonly seen orderings include simple ordering, simple tree ordering and umbrella orderings with known or unknown peaks. A natural question is how to incorporate the prior ordering information in estimating the parameters in a balanced mixed effects model so that the estimated treatment effects are consistent with the prior information and the estimated variances of the block effects and experiment errors are nonnegative. In this paper we derive the maximum likelihood estimators of the parameters in a balanced mixed model subject to any partial ordering of the treatment effects, which includes the usual maximum likelihood estimators as a special case. An example is provided to illustrate the results.     

Semiparametric regression estimation for longitudinal data in models with martingale difference error's structure

An inherent characteristic of longitudinal data is the dependence among the observations within the same subject. For exhibiting dependencies among the observations within the same subject, this paper considers a semiparametric partially linear regression model for longitudinal data based on martingale difference error's structure. We establish a strong consistency for the least squares estimator of a parametric component and the estimator of a non-parametric function under some mild conditions. A simulation study shows the performance of the proposed estimator in finite samples.     

Two-Part Models for Analysis of Agatston Scores with Possible Proportionality Constraints

ABSTRACT

Logit-linear and probit-linear two-part models can be used to analyze data that are a mixture of zeros and positive continuous responses. The slopes in the linear part of a model can be constrained to be proportional to the slopes in the logit or probit part. In this article, it is shown that implementing such a constraint will decrease (in Loewner ordering) the asymptotic covariance matrix of the maximum likelihood estimates. A case study is provided using coronary artery calcification data from the Multi-Ethnic Study of Atherosclerosis.     

A Conditional Autoregressive Gaussian Process for Irregularly Spaced Multivariate Data with Application to Modelling Large Sets of Binary Data

A Gaussian conditional autoregressive (CAR) formulation is presented that permits the modelling of the spatial dependence and the dependence between multivariate random variables at irregularly spaced sites so capturing some of the modelling advantages of the geostatistical approach. The model benefits not only from the explicit availability of the full conditionals but also from the computational simplicity of the precision matrix determinant calculation using a closed form expression involving the eigenvalues of a precision matrix submatrix. The introduction of covariates into the model adds little computational complexity to the analysis and thus the method can be straightforwardly extended to regression models. The model, because of its computational simplicity, is well suited to application involving the fully Bayesian analysis of large data sets involving multivariate measurements with a spatial ordering. An extension to spatio-temporal data is also considered. Here, we demonstrate use of the model in the analysis of bivariate binary data where the observed data is modelled as the sign of the hidden CAR process. A case study involving over 450 irregularly spaced sites and the presence or absence of each of two species of rain forest trees at each site is presented; Markov chain Monte Carlo (MCMC) methods are implemented to obtain posterior distributions of all unknowns. The MCMC method works well with simulated data and the tree biodiversity data set.