Linear versus logistic regression when the dependent variable is a dichotomy

The article argues against the popular belief that linear regression should not be used when the dependent variable is a dichotomy. The relevance of the statistical arguments against linear analyses, that the tests of significance are inappropriate and that one risk getting meaningless results, are disputed. Violating the homoscedasticity assumption seems to be of little practical importance, as an empirical comparison of results shows nearly identical outcomes for the two kinds of significance tests. When linear analysis of dichotomous dependent variables is seen as acceptable, there in many situations exist compelling arguments of a substantive nature for preferring this approach to logistic regression. Of special importance is the intuitive meaningfulness of the linear measures as differences in probabilities, and their applicability in causal (path) analysis, in contrast to the logistic measures.     

成分数据偏最小二乘 Logistic回归模型及其应用

成分数据由于存在定和约束和多重共线性，在进行传统的logistic回归建模时遇到了困难。本文在对称logratio变换和偏最小二乘logistic回归技术的基础上，提出了成分数据偏最小二乘logistic回归模型，较好地解决了成分数据的logistic回归建模问题。应用此方法，本文研究了中国三次产业就业结构与人民生活水平之间的关系。结果表明，该模型在有关结构问题的logistic回归建模中具有很好的适用性。     

Dynamic logistic regression and variable selection: Forecasting and contextualizing civil unrest

Civil unrest can range from peaceful protest to violent furor, and researchers are working to monitor, forecast, and assess such events to allocate resources better. Twitter has become a real-time data source for forecasting civil unrest because millions of people use the platform as a social outlet. Daily word counts are used as model features, and predictive terms contextualize the reasons for the protest. To forecast civil unrest and infer the reasons for the protest, we consider the problem of Bayesian variable selection for the dynamic logistic regression model and propose using penalized credible regions to select parameters of the updated state vector. This method avoids the need for shrinkage priors, is scalable to high-dimensional dynamic data, and allows the importance of variables to vary in time as new information becomes available. A substantial improvement in both precision and F1-score using this approach is demonstrated through simulation. Finally, we apply the proposed model fitting and variable selection methodology to the problem of forecasting civil unrest in Latin America. Our dynamic logistic regression approach shows improved accuracy compared to the static approach currently used in event prediction and feature selection.     

成都市房价影响因素的回归分析与事后模拟

运用SPSS软件,以GDP、市区居民人均可支配收入、住宅投资完成额、住宅施工面积、住宅竣工面积和市区人口为自变量,采用1997～2005年9年的数据,建立了多元线性回归模型,对成都市房价这一因变量进行了模拟分析。模型通过各种检验,得出了影响成都市住房价格最重要的因素是市区人口和住宅施工面积这一结论;最后,并运用模型做了事后模拟,其结果比较接近市场价格。     

R＆D与企业规模关系模型再研究

关于R＆D活动与企业规模的关系之前已做过不少的研究。本文从新的视角重新检验两者之间的关系，通过一个非线性函数研究R＆D与企业规模的关系。企业规模变量不是作为一个独立的解释变量，而是作为调节变量。2001-2008年沪深两市上市的制造业公司数据为研究面板数据。研究结果表明，R＆D与企业规模呈现一个近似“U型”关系。     

Control variate method for stationary processes

The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent. Then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator. It is shown that this estimator improves the sample mean in the sense of mean square error. Also this analysis is extended to the case when the mean dynamics is of the form of regression. Then we propose a control variate estimator for the regression coefficients which improves the least squares estimator (LSE). Numerical studies will be given to see how our estimator improves the LSE.     

On direction of dependence

Under the assumption of the existence of linear relationship between two random variables, new formulas are introduced to express the coefficient of correlation. One of these formulas, the fourth power of the correlation coefficient is used to determine the direction of dependency between two random variables. Also an interpretation of the correlation coefficient as an asymmetric function of kurtosis coefficient and skewness coefficient of dependent variable and independent variable is provided. In the absent of the intercept in linear regression, the correlation coefficient is also expressed as a ratio of coefficients of variation between independent and dependent variables.     

Asymptotic theory for nonparametric regression with spatial data

Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss the application of our conditions to spatial autoregressive models, and models defined on a regular lattice.     

Interval censored regression with fixed effects

This paper considers identification and estimation of a fixed-effects model with an interval-censored dependent variable. In each time period, the researcher observes the interval (with known endpoints) in which the dependent variable lies but not the value of the dependent variable itself. Two versions of the model are considered: a parametric model with logistic errors and a semiparametric model with errors having an unspecified distribution. In both cases, the error disturbances can be heteroskedastic over cross-sectional units as long as they are stationary within a cross-sectional unit; the semiparametric model also allows for serial correlation of the error disturbances. A conditional-logit-type composite likelihood estimator is proposed for the logistic fixed-effects model, and a composite maximum-score-type estimator is proposed for the semiparametric model. In general, the scale of the coefficient parameters is identified by these estimators, meaning that the causal effects of interest are estimated directly in cases where the latent dependent variable is of primary interest (e.g., pure data-coding situations). Monte Carlo simulations and an empirical application to birthweight outcomes illustrate the performance of the parametric estimator.     

基于逐步回归法的皖西物流需求研究

影响区域物流需求的因素有经济总量、贸易水平等经济指标。文中选取皖西地区2001～2012年期间GDP、全社会固定资产投资、进出口总额、城镇居民人均可支配收入、社会消费品零售总额为自变量,以货运周转量代替物流需求量为因变量,通过SPSS软件用逐步回归法对皖西物流需求情况进行多元线性回归分析,得出全社会固定资产投资及城镇居民人均可支配收入对货运周转量有显著影响,并提出建议。     

Linear mixed-effects model for longitudinal complex data with diversified characteristics

The increasing richness of data encourages a comprehensive understanding of economic and financial activities, where variables of interest may include not only scalar (point-like) indicators, but also functional (curve-like) and compositional (pie-like) ones. In many research topics, the variables are also chronologically collected across individuals, which falls into the paradigm of longitudinal analysis. The complicated nature of data, however, increases the difficulty of modeling these variables under the classic longitudinal framework. In this study, we investigate the linear mixed-effects model (LMM) for such complex data. Different types of variables are first consistently represented using the corresponding basis expansions so that the classic LMM can then be conducted on them, which generalizes the theoretical framework of LMM to complex data analysis. A number of simulation studies indicate the feasibility and effectiveness of the proposed model. We further illustrate its practical utility in a real data study on Chinese stock market and show that the proposed method can enhance the performance and interpretability of the regression for complex data with diversified characteristics.     

A distribution-free least squares estimator for censored linear regression models

This paper describes a method for estimating simultaneously the parameter vector of the systematic component and the distribution function of the random component of a censored linear regression model. The estimator is obtained by minimizing the sum of the squares of the differences between the observed values of the dependent variable and the corresponding expected values of this variable according to the estimated parameter vector and distribution function. The resulting least squares parameter estimator incorporates information on the distribution of the random component of the regression model that is available from the estimation sample. Hence, it may often be more efficient than are parameter estimators that do not use such information. The results of numerical experiments with the least squares estimator tend to support this hypothesis.     

广西北部湾经济区物流需求预测分析

随着中国-东盟自由贸易区的建立,我国与东南亚各国的经济往来更加频繁,货物流量大大增加,因此对广西北部湾经济区物流需求量进行预测分析显得尤为重要,准确的预测结果可以为广西北部湾经济区的经济发展提供参考依据.文章采用简单实用的线性回归分析方法,利用2000-2010年时间序列数据,把广西物流总额设为因变量Y,把广西GDP、广西物流总费用设为自变量X1、X2,通过建立简单、可行的物流需求预测模型,求得2011年广西的物流总额,为分析物流供需平衡提供了可以量化的数据.     

The financial and green effects of cultural values on mission drifts in European social enterprises

The sustainable social enterprises (SEs) literature shows that SEs have to simultaneously pursue economic, social, and environmental aims. However, tensions between these objectives can make this a challenging task and lead towards mission drift. This work investigates if the cultural dimension can forecast the mission drift. We empirically analyze this relationship in three stages. In the first stage, we identify a homogeneous dataset of 287 sustainable SEs from seven EU countries from 2011 to 2020. Then, in the second stage, we apply the data envelopment analysis (DEA) methodology to calculate the efficiency of the SEs. An efficient SE has to simultaneously achieve social, environmental, and economic aims. We calculate a proxy of the mission drift and generate a dichotomous category variable that assigns value 1 to the SE not affected by mission drift, 0 otherwise. In the last stage, we implement the 2SLS logistic regression between the variable that identifies the SEs affected by mission drift and three cultural dimensions: avoidance of uncertainty, masculinity, and short-term orientation.     

房价影响因素的实证分析——以青岛市为例

运用SPSS软件,以人口、人均GDP、住房销售面积和房地产开发投资为自变量,采用2000～2009年10年的数据,建立了多元线性回归模型,对青岛市房价这一因变量进行了模拟分析。模型通过各种检验,得出了影响青岛市住房价格最重要的因素是市区人口这一结论,说明青岛市有效的需求增大,是抬高住房价格十分重要的因素,这在一定层面上说明了青岛的住宅市场的价格是比较正常的价格。     

Estimation of a linear regression under microaggregation with the response variable as a sorting variable

Microaggregation is a popular statistical disclosure control technique for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. However, while reducing the disclosure risk of data files, the technique also affects the results of statistical analyses. The paper deals with the impact of microaggregation on a multiple linear regression in continuous variables. We show that parameter estimates are biased if the dependent variable is used to form the groups. Using this result, we develop a consistent estimator that removes the aggregation bias, and derive its asymptotic covariance matrix.     

Graphical Tools for Detecting Departures from Linear Mixed Model Assumptions and Some Remedial Measures

We review some results on the analysis of longitudinal data or, more generally, of repeated measures via linear mixed models starting with some exploratory statistical tools that may be employed to specify a tentative model. We follow with a summary of inferential procedures under a Gaussian set‐up and then discuss different diagnostic methods focusing on residual analysis but also addressing global and local influence. Based on the interpretation of diagnostic plots related to three types of residuals (marginal, conditional and predicted random effects) as well as on other tools, we proceed to identify remedial measures for possible violations of the proposed model assumptions, ranging from fine‐tuning of the model to the use of elliptically symmetric or skew‐elliptical linear mixed models as well as of robust estimation methods. We specify many results available in the literature in a unified notation and highlight those with greater practical appeal. In each case, we discuss the availability of model diagnostics as well as of software and give general guidelines for model selection. We conclude with analyses of three practical examples and suggest further directions for research.     

Optimal regression designs for prediction when prior knowledge is available

Summary Using Bayesian decision theory, the problem of how to choose an optimal regression design is considered when there is prior knowledge about the regression parameters available and the data are to be analyzed so that a future value of the dependent variable can be predicted.     

Specification error in multinomial logit models: Analysis of the omitted variable bias

In this article, we analyze the omitted variable bias problem in the multinomial logistic probability model. Sufficient, as well as necessary, conditions under which the omitted variable will not create asymptotically biased coefficient estimates for the included variables are derived. Conditional on the response variable, if the omitted explanatory and the included explanatory variable are independent, the bias will not occur. Bias will occur if the omitted relevant variable is independent with the included explanatory variable. The coefficient of the included variable plays an important role in the direction of the bias.     

Identifiability of mean‐reverting measurement error with instrumental variable

In the context where one main regressor is measured with error and at least one instrumental variable is available for the correction of measurement error, this paper provides, to the best of our knowledge, a first point‐identification result on the variance of measurement error, the variance of latent variable, and their covariance. We show that the parameters are identified if the regression model is not de facto linear. We illustrate the method in an application to identify mean‐reverting measurement error, a typical issue in reported income where the measurement error of income is negatively correlated with the true income.