多重共线性的诊断方法

在对经济现象作建模分析与预测过程中,常常会遇到多重共线问题。基于多重共线的病态模型预测完全失效,文章就多重共线的诊断理论方法作了阐述,尤其是对多重共线影响点的诊断方法作了介绍,特别是对Walker法与主成分法对多重共线影响点的诊断作了比较。     

列昂节夫逆阵在解决多重共线问题中的应用

本文先论述多重共线的危害,然后介绍了几种常用的发现和检验多重共线的方法,并提出一种新的解决方法-利用列昂节夫逆阵整合解释变量的方法.     

关于投入产出分析中消耗系数的研究

投入产出分析方法是一种重要的经济数量分析方法,它主要是通过计算有关系数以分析经济系统中各部分之间的技术经济联系和预测国民经济平衡关系的发展变化,直接消耗系数、完全消耗系数和完全需求系数是其中最重要的三个系数,是其它各种系数的基础。在有关投入产出分析方法的各种     

国民经济部门的投入产出分析

投入产出分析,又称投入产出法,是由美国经济学家W.列昂惕夫于1931年首先提出来的,它是通过国民经济中各部门间投入与产出的对应关系来研究经济结构之间依存关系的方法。随着投入产出法的完善,它得到越来越广泛地应用,大到国家、地区,小到企业都可以用投入产出表及数学模型进行经济分析、经济预测、编制经济计划。一、投入产出分析1、技术经济联系分析部门间技术经济联系分析的指标是直接消耗系数与完全消耗系数。直接消耗系数又称投入系数或技术系数,是指某部门生产单位产品对本部门及其它某一部门产品的直接消耗量,它反映了国民经济中有直…     

一种消除变量间相关性的模型聚类方法

欧氏距离条件下的聚类分析没有考虑指标间的相关性,基于模型的聚类方法存在多重共线性影响参数稳定性等问题,针对上述问题,文章在欧式距离条件下对变量间具有相关性的数据样本进行聚类分析时,先构建变量间相关性结构的回归相关模型,再通过差分分析对变量间的多重共线进行消除,然后做聚类分析.并以1996-2011年9个省份城市教育投入情况进行聚类分析,结果表明,给出的聚类方法是有效的.     

灰色多元线性回归模型及其应用

基于灰色关联法和灰色聚类法诊断、解决多重共线问题;利用GM(1,1)模型对原始数据序列进行修正,降低随机波动的干扰;据修正变量数据建立灰色多元线性回归模型,并将其运用于具体实例取得满意的预测效果。该模型对处理数据贫乏、波动较大的样本效果显著。     

产业关联测度方法及其应用问题探析

投入产出法作为从技术经济角度进行产业关联研究的重要工具,其分析基础是:在一定的值域内,某种产品的产出量与相关的投入(各种中间投入和最初投入)量之间是成线性比例的①。各种消耗系数就是刻划这种数量关系的主要工具。如所周知,最基本的产业关联分析测度是直接消耗系数,由此可推导或派生出几乎所有的其他分析系数。通常将直接消耗系数矩阵定义为:A=(aij)n×n=X^q-1(其中,X为中间流量矩阵,q为总产出向量),则有如下的完全消耗系数矩阵和完全需求系数矩阵(列昂节夫逆矩阵)②:B=(I-A)-1-I=(bij)n×n C=(I-A)-1=B I=(cij)n×n借助于这些…     

完全需求系数的真实内涵：代数解法

一、前言完全需求系数也叫最终产品系数,或Leontief逆阵系数,是投入产出分析中主要的系数之一,在投入产出分析方法中具有核心地位和作用,正确理解其含义对于学好投入产出分析方法是非常重要的。在目前各种关于投入产出的教材和书籍中,都是在完全消耗系数的基础上引出完全需求系     

基于多重尝试Metropolis算法的非线性DSGE模型贝叶斯推断

本文提出一种改进的多重尝试Metropolis算法,用于非线性动态随机一般均衡模型的贝叶斯参数估计和模型选择。多重尝试策略通过每次迭代抽取多个尝试点的方法来提高算法的混合速率,新方法中提出使用近似的方法提高计算速度,并通过接收概率调整偏差。数值实验表明新方法在相同的计算时间内具有更高的估计效率。最后,本文比较了具有不同货币政策设定的模型对中国经济数据的拟合效果,发现中国数据更加支持具有时变通胀目标的模型。     

年缴m次保费的一种估算法

随着我国寿险保险公司现行缴费方式的灵活多样化,给精算工作增加了不少工作量,针对这一情况,文章讨论寿险中的年缴m次保费的一种近似估算法,给出了各种缴费方式下的转换系数与精度估计,在保持一定精度的条件下,通过模拟运算表明这种估算法是十分有用的,因而具有推广的价值。     

Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors

One important component of model selection using generalized linear models (GLM) is the choice of a link function. We propose using approximate Bayes factors to assess the improvement in fit over a GLM with canonical link when a parametric link family is used. The approximate Bayes factors are calculated using the Laplace approximations given in [32], together with a reference set of prior distributions. This methodology can be used to differentiate between different parametric link families, as well as allowing one to jointly select the link family and the independent variables. This involves comparing nonnested models and so standard significance tests cannot be used. The approach also accounts explicitly for uncertainty about the link function. The methods are illustrated using parametric link families studied in [12] for two data sets involving binomial responses. The first author was supported by Sonderforschungsbereich 386 Statistische Analyse Diskreter Strukturen, and the second author by NIH Grant 1R01CA094212-01 and ONR Grant N00014-01-10745.     

Detecting influential observations in Liu and modified Liu estimators

In regression, detecting anomalous observations is a significant step for model-building process. Various influence measures based on different motivational arguments are designed to measure the influence of observations through different aspects of various regression models. The presence of influential observations in the data is complicated by the existence of multicollinearity. The purpose of this paper is to assess the influence of observations in the Liu [9] and modified Liu [15] estimators by using the method of approximate case deletion formulas suggested by Walker and Birch [14]. A numerical example using a real data set used by Longley [10] and a Monte Carlo simulation are given to illustrate the theoretical results.     

Number of predictors and multicollinearity: What are their effects on error and bias in regression?

The present Monte Carlo simulation study adds to the literature by analyzing parameter bias, rates of Type I and Type II error, and variance inflation factor (VIF) values produced under various multicollinearity conditions by multiple regressions with two, four, and six predictors. Findings indicate multicollinearity is unrelated to Type I error, but increases Type II error. Investigation of bias suggests that multicollinearity increases the variability in parameter bias, while leading to overall underestimation of parameters. Collinearity also increases VIF. In the case of all diagnostics however, increasing the number of predictors interacts with multicollinearity to compound observed problems.     

A useful approach to identify the multicollinearity in the presence of outliers

The presence of outliers in the data sets affects the structure of multicollinearity which arises from a high degree of correlation between explanatory variables in a linear regression analysis. This affect could be seen as an increase or decrease in the diagnostics used to determine multicollinearity. Thus, the cases of outliers reduce the reliability of diagnostics such as variance inflation factors, condition numbers and variance decomposition proportions. In this study, we propose to use a robust estimation of the correlation matrix obtained by the minimum covariance determinant method to determine the diagnostics of multicollinearity in the presence of outliers. As a result, the present paper demonstrates that the diagnostics of multicollinearity obtained by the robust estimation of the correlation matrix are more reliable in the presence of outliers.     

Variable selection in linear regression based on ridge estimator

In this article, we consider the problem of variable selection in linear regression when multicollinearity is present in the data. It is well known that in the presence of multicollinearity, performance of least square (LS) estimator of regression parameters is not satisfactory. Consequently, subset selection methods, such as Mallow's Cp, which are based on LS estimates lead to selection of inadequate subsets. To overcome the problem of multicollinearity in subset selection, a new subset selection algorithm based on the ridge estimator is proposed. It is shown that the new algorithm is a better alternative to Mallow's Cp when the data exhibit multicollinearity.     

MulticolIinearity Problems in Modeling Time Series With Trading-Day Variation

This article discusses the multicollinearity problems associated with the estimation of time series models influenced by trading-day variation. An analysis of the design matrix is performed, and measures of the degree of multicollinearity are computed. The characteristics of the design matrix of a popular parameterization are also analyzed, and it is shown that in some cases use of this reparameterization significantly alleviates the multicollinearity problem.     

Nonparametric Decomposition of Time Series Data with Inputs

The backfitting algorithm commonly used in estimating additive models is used to decompose the component shares explained by a set of predictors on a dependent variable in the presence of linear dependencies (multicollinearity) among the predictors. Simulated and actual data show that the backfitting methods are superior in terms of predictive ability as the degree of multicollinearity worsens. Furthermore, the additive smoothing splines are especially superior when the linear model yield inadequate fit to the data and the predictors exhibit extreme multicollinearity.     

New shrinkage-type estimators in a linear regression model when multicollinearity is severe

For the linear regression model y=Xβ+e with severe multicollinearity, we put forward three shrinkage-type estimators based on the ordinary least-squares estimator including two types of independent factor estimators and a seemingly convex combination. The simulation study shows that the new estimators are not good enough when multicollinearity is mild to moderate, but perform very well when multicollinearity is severe to very severe.     

A graphical evaluation of logistic ridge estimator in mixture experiments

In comparison to other experimental studies, multicollinearity appears frequently in mixture experiments, a special study area of response surface methodology, due to the constraints on the components composing the mixture. In the analysis of mixture experiments by using a special generalized linear model, logistic regression model, multicollinearity causes precision problems in the maximum-likelihood logistic regression estimate. Therefore, effects due to multicollinearity can be reduced to a certain extent by using alternative approaches. One of these approaches is to use biased estimators for the estimation of the coefficients. In this paper, we suggest the use of logistic ridge regression (RR) estimator in the cases where there is multicollinearity during the analysis of mixture experiments using logistic regression. Also, for the selection of the biasing parameter, we use fraction of design space plots for evaluating the effect of the logistic RR estimator with respect to the scaled mean squared error of prediction. The suggested graphical approaches are illustrated on the tumor incidence data set.     

Robust Linearized Ridge M-estimator for Linear Regression Model

In the multiple linear regression, multicollinearity and outliers are commonly occurring problems. They produce undesirable effects on the ordinary least squares estimator. Many alternative parameter estimation methods are available in the literature which deals with these problems independently. In practice, it may happen that the multicollinearity and outliers occur simultaneously. In this article, we present a new estimator called as Linearized Ridge M-estimator which combats the problem of simultaneous occurrence of multicollinearity and outliers. A real data example and a simulation study is carried out to illustrate the performance of the proposed estimator.