Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL

Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).

INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS

This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available.

Optimal Credibility Estimation of Random Parameters in Hierarchical Random Effect Linear Model

In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases. This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.

涉海产业类企业融资效率及影响因素测评研究——基于DEA-Random Effects Models的经验数据

为发展壮大涉海产业类企业并带动海洋产业发展以实现海洋强国战略,有必要对涉海产业类企业融资效率状况进行准确定位并采取相应策略。以企业融资效率理论为基础,运用DEA模型评价涉海产业类企业融资效率及并运用随机效应面板数据模型检验其影响因素。检验结果发现,2008-2013年间涉海产业类企业融资效率整体上处于低效水平,其主要影响因素有宏观经济形势、行业竞争程度、企业规模大小和公司治理机制。企业融资效率与宏观经济形势、行业竞争程度和公司治理机制显著正相关,与企业规模大小显著负相关。这说明涉海产业类企业还有大幅度提高融资效率的空间,政策建议是引导资本市场支持海洋资源开发利用,保持稳定增长的整体经济环境,促进垄断竞争性涉海产业类企业理性投融资,缓解中小型涉海产业类企业融资难困境和深化国有控股涉海产业类企业改革。

INFLUENCE ANALYSIS IN NONLINEAR MODELS WITH RANDOM EFFECTS

In this paper,a unified diagnostic method for the nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991 is presented.It is shown that the case deletion model is equivalent to the mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented. A numerical example illustrates that the method is available.

Bootstrap inference of the skew-normal two-way classification random effects model with interaction

In this paper,we consider the statistical inference problems for the fixed effect and variance component functions in the two-way classification random effects model with skewnormal errors.Firstly,the exact test statistic for the fixed effect is constructed.Secondly,using the Bootstrap approach and generalized approach,the one-sided hypothesis testing and interval estimation problems for the single variance component,the sum and ratio of variance components are discussed respectively.Further,the Monte Carlo simulation results indicate that the exact test statistic performs well in the one-sided hypothesis testing problem for the fixed effect.And the Bootstrap approach is better than the generalized approach in the one-sided hypothesis testing problems for variance component functions in most cases.Finally,the above approaches are applied to the real data examples of the consumer price index and value-added index of three industries to verify their rationality and effectiveness.

Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the Bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.

Comparison of REML and MINQUE for Estimated Variance Components and Predicted Random Effects

Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included. Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets. Results showed that MINQUE and REML methods performed equally regarding bias, Type I error, and power. Jackknife-based MINQUE and REML greatly improved power compared to non-Jackknife based linear mixed model approaches. Results also showed that MINQUE is more time-saving compared to REML, especially with the use of resampling techniques and large data set analysis. Results from the actual cotton data analysis were in agreement with our simulated results. Therefore, Jackknife-based MINQUE approaches could be recommended to achieve desirable power with reduced time for a large data analysis and model simulations.

Inference Based on Empirical Likelihood for Varying Coefficient Model with Random Effect

In this article, we develop a statistical inference technique for the unknown coefficient functions in the varying coeffi- cient model with random effect. A residual-adjusted block empirical likelihood (RABEL) method is suggested to inves- tigate the model by taking the within-subject correlation into account. Due to the residual adjustment, the proposed RABEL is asymptotically chi-squared distribution. We illustrate the large sample performance of the proposed method via Monte Carlo simulations and a real data application.

Automatic Variable Selection for Single-Index Random Effects Models with Longitudinal Data

We consider the problem of variable selection for the single-index random effects models with longitudinal data. An automatic variable selection procedure is developed using smooth-threshold. The proposed method shares some of the desired features of existing variable selection methods: the resulting estimator enjoys the oracle property;the proposed procedure avoids the convex optimization problem and is flexible and easy to implement. Moreover, we use the penalized weighted deviance criterion for a data-driven choice of the tuning parameters. Simulation studies are carried out to assess the performance of our method, and a real dataset is analyzed for further illustration.

Estimation in Nonlinear Models with Random Effects

本文首次给出了非线性随机效应模型参数估计弱相合性的必要条件，并证明了在一定正则条件下估计的强相合性和渐近正态性，推广了ＢｒｅｓｌｏｗａｎｄＣａｌｙｔｏｎ（１９９３），ＬｅａｎｄＮｅｌｄｅｒ（１９９６）的结果．

Additive Hazards Regression with Random Effects for Clustered Failure Times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.

Testing for Random Effects in Linear Mixed Models for Longitudinal Data under Moment Conditions

In this paper, we consider whether the random effect exists in linear mixed models （LMMs） when only moment conditions are assumed. Based on the estimators of parameters and their asymptotic properties, a Wald-type test is constructed. It is consistent against global alternatives and is sensitive to the local alternatives converging to the null hypothesis at parametric rates, a fastest possibly rate for goodness-of-fit testing. Moreover, a simulation study shows the performance of the test is good. The procedure also applies to a real data.

Accessing Individual Students Academic Performance Using Random Effect Analysis(Multilevel Analysis)

Sometimes,people with interest in measuring quality of education take intoaccountlevel in academic performance and various associated factors.Usually,an aver-age academic performance is an accustomed way of assessment;however,this studyexamines on individual basis different factors that might have an impact on the acad-emic performance of undergraduate students.Data on the semester weighted averageof class of 2012 mathematics students were acquired from the Quality Assurance andPlanning Unit and the Examination Office of the Department of Mathematics,KwameNkrumah University of Science and Technology.The main factors considered for thisresearch were entry age,gender,entry aggregate,Ghana education service gradedlevel of senior high school attended and geographical location.The statistical methodconsidered was random effect.Since the interaction or variation around the slope washighly insignificant,the random intercept model was the better alternative ahead ofthe random intercept and slope model.Statistically,not all the parameter estimatesare significant at a=0.05 level of significance.It was observed that the differencein geographical location was not significant in the main effect model.Hence where astudent comes from has no influence on their academic performance.However,entryaggregate,entry age and gender were all significant.Nevertheless,the geographical location with regard to the Northern Belt was significant in the linear trend with astandard deviation of approximately 0.712.

Bootstrap Inference on the Variance Component Functions in the Two-Way Random Effects Model with Interaction

In this paper,using the Bootstrap approach and generalized approach,the authors consider the one-sided hypothesis testing problems for variance component functions in the two-way random effects model.Firstly,the test statistics and confidence intervals for the sum of variance components are constructed.Next,the one-sided hypothesis testing problems for the ratio of variance components are also discussed.The Monte Carlo simulation results indicate that the Bootstrap approach is better than the generalized approach in most cases.Finally,the above approaches are applied to the real data examples of mice blood p H and molded plastic part’s dimensions.

A random effects generalized linear model for reliability compositive evaluation

This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments. The relevant algorithms are also provided. Simulation results manifest the soundness and effectiveness of the proposed model.

Total ionizing dose and synergistic effects of magnetoresistive random-access memory

A magnetoresistive random-access memory(MRAM) device was irradiated by ^(60) Co c-rays and an electron beam.The synergistic effect of this on the MRAM was tested with an additional magnetic field during irradiation,from which the total ionizing dose(TID) and the synergistic damage mechanism of MRAM were analyzed.In addition,DC,AC,and functional parameters of the memory were tested under irradiation and annealing via a very large-scale integrated circuit test system.The radiation-sensitive parameters were obtained through analyzing the data.Because of the magnetic field applied on the MRAM while testing the synergistic effects,shallow trench isolation leakage and Frenkel–Poole emission due to synergistic effects were smaller than that of TID,and hence radiation damage of the synergistic effects was also lower.

RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD AND ITS VERIFICATION FOR EFFECTIVE PROPERTIES OF COMPOSITE MATERIALS

The present study aims at developing a new method-RandomMicrostructure Finite Element Method (RMFEM) for the effectiveproperties of com- Posite materials. In this method, a randommicrostructure Model is used to simulate the microstructure of thereal composite materials. The physical fields in such a randomMicrosturucture model under specified boundary and initial Conditionsare analyzed by finite element method.