高校教师工资影响因素分析

文章以某地区若干高校教师月平均工资为研究对象,随机抽取500名教师为样本,对于一些定性的解释变量采用虚拟变量的形式与工资进行回归分析,通过拟合线性回归模型及对其参数和整体方程的检验,分析出年龄、学历、职务等定性的解释变量对高校教师工资的影响程度。     

空间回归模型估计中的最小二乘法

空间回归模型由于引入了空间地理信息而使得其参数估计变得复杂,因为主要采用最大似然法,致使一般人认为在空间回归模型参数估计中不存在最小二乘法。通过分析空间回归模型的参数估计技术,研究发现,最小二乘法和最大似然法分别用于估计空间回归模型的不同的参数,只有将两者结合起来才能快速有效地完成全部的参数估计。数理论证结果表明,空间回归模型参数最小二乘估计量是最佳线性无偏估计量。空间回归模型的回归参数可以在估计量为正态性的条件下而实施显著性检验,而空间效应参数则不可以用此方法进行检验。     

Beta-Binomial回归模型及其应用

在成败型试验中或满意度支持率调查中,Beta-Binomial分布常被用来刻画具有偏大离差的计数型比例数据,由此提出Beta-Binomial回归模型,研究参数的最大似然估计方法并基于Newton-Raphson算法给出参数估计的迭代方法;重点讨论模型中回归参数和相关性参数存在的检验问题,提出Score检验方法并通过数值模拟研究Score检验统计量的检验功效问题;实例分析证明Beta-Binomial回归模型的有用性。     

一元线性回归分析中三种检验的等价性研究

在研究两个变量是否线性相关时,要对线性相关系数进行统计检验;在建立线性回归模型时,既要对回归模型中的参数进行统计检验,又要对模型本身进行统计检验。然而,在一元线性回归分析中,尽管对变量线性相关性的检验、模型参数和模型本身检验的目的各不相同,所选统计量也不同,但是,三种检验却具有检验效果的等价性。文章将对此进行研究、证明。     

纵向数据下半参数回归模型估计的强相合性

一、引言半参数回归模型最早由Engle等在研究气候条件对电力需求影响这一实际问题提出,它既有参数分量,又含有非参数分量,兼顾了这两种模型的优点。因而它比经典的线性或非参数回归模型更具有灵活性和适用性。关于半参数回归模型的研究工作,     

半参数Beta回归模型在数据挖掘中的应用

回归分析是数据挖掘中重要的方法之一。文章研究了基于半参数Beta回归模型结合惩罚样条估计的数据挖掘方法。当数据中因变量的数据取值为(0,1)区间(或某个区间)时,利用半参数Beta回归模型进行数据挖掘,不仅具有很好的解释效果,而且能挖掘出隐含在数据内部的有用信息。实验结果验证了研究方法的有效性。     

缺失偏态数据下线性回归模型的统计推断

研究缺失偏态数据下线性回归模型的参数估计问题,针对缺失偏态数据,为克服样本分布扭曲缺点和提高模型的回归系数、尺度参数和偏度参数的估计效果,提出了一种适合偏态数据下线性回归模型中缺失数据的修正回归插补方法.通过随机模拟和实例研究,并与均值插补、回归插补、随机回归插补方法比较,结果表明所提出的修正回归插补方法是有效可行的.     

联合均值和散度逆高斯回归模型的参数估计

逆高斯回归模型可用于分析正偏态数据,人们通常研究解释变量对其均值参数的影响,但往往忽略了对其散度参数的影响,文章则基于解释变量对均值和散度都有影响的前提,针对联合均值和散度逆高斯回归模型,探讨模型参数的极大似然估计问题。MM算法在优化问题上具有分离参数、降低目标函数的维度、简化求解过程等优点,将MM算法应用于联合均值和散度逆高斯回归模型,能将多元似然函数彻底分解为一系列一元函数之和,从而绕开了参数估计中的矩阵求逆问题。模拟研究表明,当数据量达到100时就能得到很好的估计效果;实证分析表明,理论研究在实际应用中具有可行性。     

线性GMDH参数模型的无偏估计研究

 多元线性回归分析中,参数无偏性是参数估计方法的一个重要指标。本文对线性GMDH参数模型建立多元线性模型进行了研究,得到以下结论：一,在满足经典线性回归模型的假设条件下,其参数估计量具有无偏的性质;二,在满足其它假设条件下,可以在样本量少于待估参数的情况下建模,估计的参数也是无偏的;三,用参数GMHD方法建模时,它对完全多重共线性是免疫的。     

基于傅里叶变换的时变参数回归模型:估计、设定检验和实证应用

回归模型参数的时变性会严重影响模型的拟合程度和预测效果。基于卡尔曼滤波的时变参数模型需要估计很多的参数,因而造成效率损失。基于傅里叶变换建立一个简单的变系数回归模型,给出估计方法并证明参数收敛于真实值,并给出了模型设定检验的方法。通过蒙特卡洛模拟表明:新建立的时变参数回归模型能很好地处理连续的、随机的和跳跃的时变参数模型。最后,将新建立的方法应用于研究股市联动关系,发现:不考虑系数的时变性可能给出误导性结论,考虑时变性能捕捉更为丰富的联动特征。     

ADE-4: a multivariate analysis and graphical display software

We present ADE-4, a multivariate analysis and graphical display software. Multivariate analysis methods available in ADE-4 include usual one-table methods like principal component analysis and correspondence analysis, spatial data analysis methods (using a total variance decomposition into local and global components, analogous to Moran and Geary indices), discriminant analysis and within/between groups analyses, many linear regression methods including lowess and polynomial regression, multiple and PLS (partial least squares) regression and orthogonal regression (principal component regression), projection methods like principal component analysis on instrumental variables, canonical correspondence analysis and many other variants, coinertia analysis and the RLQ method, and several three-way table (k-table) analysis methods. Graphical display techniques include an automatic collection of elementary graphics corresponding to groups of rows or to columns in the data table, thus providing a very efficient way for automatic k-table graphics and geographical mapping options. A dynamic graphic module allows interactive operations like searching, zooming, selection of points, and display of data values on factor maps. The user interface is simple and homogeneous among all the programs; this contributes to making the use of ADE-4 very easy for non- specialists in statistics, data analysis or computer science.     

A log-linear regression model for the odd Weibull distribution with censored data

We introduce the log-odd Weibull regression model based on the odd Weibull distribution (Cooray, 2006). We derive some mathematical properties of the log-transformed distribution. The new regression model represents a parametric family of models that includes as sub-models some widely known regression models that can be applied to censored survival data. We employ a frequentist analysis and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to assess global influence. Further, for different parameter settings, sample sizes and censoring percentages, some simulations are performed. In addition, the empirical distribution of some modified residuals are given and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to check the model assumptions. The extended regression model is very useful for the analysis of real data.     

Confidence intervals for finite difference solutions

Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it is only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential equations. In line with this very recent trend, we show how certain commonly used finite difference schemes for numerical solutions of ordinary and partial differential equations can be considered in a regression setting. Focusing on this regression framework, we apply a simple Bayesian strategy to obtain confidence intervals for the finite difference solutions. We apply this framework on several examples to show how the confidence intervals are related to truncation error and illustrate the utility of the confidence intervals for the examples considered.     

The log-odd log-logistic Weibull regression model: modelling,estimation, influence diagnostics and residual analysis

In applications of survival analysis, the failure rate function may frequently present a unimodal shape. In such cases, the log-normal and log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the odd log-logistic Weibull distribution is proposed for modelling data with a decreasing, increasing, unimodal and bathtub failure rate function as an alternative to the log-Weibull regression model. For censored data, we consider a classic method to estimate the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals is determined and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the new regression model applied to censored data. We analyse a real data set using the log-odd log-logistic Weibull regression model.     

Regression analysis and ratio analysis for domains: A randomization-theory approach

In most surveys, inference for domains poses a difficult problem because of data shortage. This paper presents a probability sampling theory approach to some common types of statistical analysis for domains of a surveyed population. Simple and multiple regression analysis, and analysis of ratios are considered. Two new methods are constructed and explored which can improve substantially over the common method based on sample-weighted sums of squares and products. These new methods use auxiliary variables whose importance depends on the extent to which they succeed in explaining certain patterns in the regression residuals. The theoretical conclusions are supported by empirical results from Monte Carlo experiments.     

New regression model with four regression structures and computational aspects

A new general class of exponentiated sinh Cauchy regression models for location, scale, and shape parameters is introduced and studied. It may be applied to censored data and used more effectively in survival analysis when compared with the usual models. For censored data, we employ a frequentist analysis for the parameters of the proposed model. Further, for different parameter settings, sample sizes, and censoring percentages, various simulations are performed. The extended regression model is very useful for the analysis of real data and could give more adequate fits than other special regression models.     

Bayesian inference for bivariate generalized linear models in diagnosing renal arterial obstruction

Generalized linear models are well-established generalizations of the linear models used for regression and analysis of variance. They allow flexible mean structures and general distributions, other than the linear link and normal response assumed in regression. Further enhancements using ideas from multivariate analysis improve power and precision by modelling dependencies between response variables. This paper focuses on the specific case of regression models for bivariate Bernoulli responses and investigates their analysis using a Bayesian approach. The important problem of renal arterial obstruction is considered, as a medical application of these models.     

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.     

The exponentiated power exponential regression model with different regression structures: application in nursing data

We define the exponentiated power exponential distribution and propose a regression model with different systematic structures based on the new distribution. We show that the new regression model can be applied to dispersion data since it represents a parametric family of models that includes as sub-models some widely-known regression models. It then can be used more effectively in the analysis of real data. We use maximum likelihood estimation and derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. Some global-influence measurements are also investigated and simulation studies are performed to evaluate the accuracy of the estimates. We provide an application of the regression model with four systematic structures to nursing activities score data in the Unit of the Medical Clinic of University of São Paulo (USP) Hospital.     

Simplifying Regression Models Using Dimensional Analysis

Dimensional analysis can make a contribution to model formulation when some of the measurements in the problem are of physical factors. The analysis constructs a set of independent dimensionless factors that should be used as the variables of the regression in place of the original measurements. There are fewer of these than the originals and they often have a more appropriate interpretation. The technique is described briefly and its proposed role in regression discussed and illustrated with examples. We conclude that dimensional analysis can be effective in the preliminary stages of regression analysis whendeveloping formulations involving continuous variables with several dimensions.