RIDGE ESTIMATORS FOR PROBIT REGRESSION: WITH AN APPLICATION TO LABOUR MARKET DATA

In this paper we propose ridge regression estimators for probit models since the commonly applied maximum likelihood (ML) method is sensitive to multicollinearity. An extensive Monte Carlo study is conducted where the performance of the ML method and the probit ridge regression (PRR) is investigated when the data are collinear. In the simulation study we evaluate a number of methods of estimating the ridge parameter k that have recently been developed for use in linear regression analysis. The results from the simulation study show that there is at least one group of the estimators of k that regularly has a lower mean squared error than the ML method for all different situations that have been evaluated. Finally, we show the benefit of the new method using the classical Dehejia and Wahba dataset which is based on a labour market experiment.     

Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High-Dimension Regime

In this study, we suggest pretest and shrinkage methods based on the generalised ridge regression estimation that is suitable for both multicollinear and high-dimensional problems. We review and develop theoretical results for some of the shrinkage estimators. The relative performance of the shrinkage estimators to some penalty methods is compared and assessed by both simulation and real-data analysis. We show that the suggested methods can be accounted as good competitors to regularisation techniques, by means of a mean squared error of estimation and prediction error. A thorough comparison of pretest and shrinkage estimators based on the maximum likelihood method to the penalty methods. In this paper, we extend the comparison outlined in his work using the least squares method for the generalised ridge regression.     

Estimation employing a priori information within mass appraisal and hedonic pricing models

Both statistical appraisal and hedonic pricing models decompose houses into a set of individual characteristics. Regression estimates yield the contribution of each characteristic to total value. Unfortunately, straightforward application of OLS may produce untenable results such as implausible coefficient magnitudes or incorrect signs. Often the suspected cause is multicollinearity. This article examines the effect on estimation efficiency of differing levels of multicollinearity, R², and a priori information in the form of sub-market cost data, by comparing inequality restricted least squares (IRLS) with OLS in a series of Monte Carlo experiments. The IRLS procedure investigated here hybridizes the statistical market approach implemented by OLS, and the more traditional cost approach. The experiments show dramatic gains in estimation efficiency from exploiting a priori information through IRLS.     

基于岭回归的海南人均GDP与三大产业关系研究

以海南省人均GDP为衡量经济发展水平指标变量,建立其关于三次产业增加值的多元线性回归模型,进行结构性分析。为了克服多重共线性的影响和数据容量少的缺陷,建立了岭回归模型,对海南人均GDP进行边际分析;从数据的不光滑特征出发,对原始数据进行对数变换,建立了分段回归模型,对海南人均GDP进行弹性分析。从定量角度阐述了三次产业在海南经济发展中的地位和作用,为决策部门相关政策的制定提供一定参考。     

Threats to the Validity of Logistics and Supply Chain Management Research

To increase the relevance of logistics and supply chain academic research, this paper recommends the development and testing of middle‐range theory and practice‐level theory. Yet, there are a number of research issues that arise when academic researchers test middle‐range and practice‐level theory, both in measuring constructs and in testing theoretical relationships between constructs. Concerning the measurement of constructs, this paper recommends that academic researchers pay more attention to content validity and undertake rigorous processes to ensure content validity. In addition, academic researchers need to more explicitly define constructs as either reflective or formative. If the construct is defined as formative, then the traditional statistical approaches to validate these measurement scales are not recommended. The appropriate use of employing single‐item measures for concrete constructs is discussed. In regard to conducting hypothesis tests, research issues associated with multicollinearity and omitted variable bias are discussed. Relative weight analysis is ideal for testing theoretical models and research hypotheses when survey data are obtained, multicollinearity is present, and there are a large number of independent variables predicting a dependent variable. Thus, relative weight analysis is ideal for testing research hypotheses in logistics and supply chain management.     

Improving the validity of theory testing in logistics research using correlated components regression

The purpose of this logistics research methods article is to empirically test and introduce correlated components regression (CCR) as a new statistical technique that will improve the accuracy and validity in testing logistics theoretical models and hypothesised relationships. The purpose of the current study is to use CCR analysis as technique to address multicollinearity. Customer satisfaction data with parcel carriers is analysed with using CCR and multiple regression. To determine the best regression model of these two approaches, cross-validation R² values are used. In addition, comparisons are made to examine the standardised beta coefficients from both methods and to assess the possible impact from high levels of multicollinearity. Findings of the analysis suggest that CCR has a significantly higher cross-validation R² value and thus is determined the best model of these two approaches.     

The effect of response scaling on the detection of linear dependencies among multiresponse data

Summary Box and Draper (1965) introduced a criterion for the estimation of parameters from a multiresponse model. This criterion can lead to misleading results in the presence of linear relationships among the responses. Box et al. (1973) proposed a procedure for detecting the existence of such relationships when the multiresponse data are subject to round-off errors. The procedure is applicable only when the round-off errors are identically distributed as uniform random variates. In many situations, however, the round-off errors can vary considerably. For example, the responses may have distinct physical meanings, and hence distinct scales of measurement with possibly widely different orders of magnitude. This article extends Box et al.’s procedure to cover these situations. Two examples are given to illustrate the implementation of the proposed methodology.     

基于技术进步的浙江省能源消费回弹效应研究

基于技术进步对经济增长的贡献和环境负荷分解模型,对浙江省1990年以来技术进步对GDP增长的贡献、能源消费回弹效应及能源回弹量进行实证分析。其中,对技术进步的测定采用城镇单位在岗职工工资总额和农村居民纯收入作为劳动因素,以期更合理地体现劳动对经济增长的贡献,同时对多元回归模型的多重共线性进行滞后差分变换,以期得到更为精确的实证数据。     

Determinants of Domestic Travel Expenditure in South Korea

Summary

This study examines factors affecting domestic Korean tourist expenditure per person. Independent variables include family size, Per Capita Gross National Product (GNP), number of cars, number of working hours, number of years of education, previous year's domestic travel expenditure, and exchange rate. A 21-year historical data were used in the study. Two estimation methods, principal components regression and ridge regression, were employed in this study to eliminate the problems of multicollinearity caused by Ordinary Least Squares (OLS) method. The empirical results show that number of working hours, family size, and number of years of education turned out to be important factors affecting domestic travel expenditure.     

Multicollinearity: How common factors cause Type 1 errors in multivariate regression

Research Summary : In multivariate regression analyses of correlated variables, we sometimes observe pairs of estimated beta coefficients large in absolute magnitude and opposite in sign. T‐statistics are also large, suggesting meaningful findings. I found 64 recently published Strategic Management Journal articles with results exhibiting these characteristics. In this article, I demonstrate that such results may be Type 1 errors (false positives): If regressors are correlated via an unobservable common factor, estimated beta coefficients will misleadingly tend toward infinite magnitudes in opposite directions, even if the variables’ real effects are small and of the same sign. Diagnostics such as Variance Inflation Factors (VIF) will misleadingly validate Type 1 errors as legitimate results. After establishing general results via mathematical analysis and simulation, I provide guidelines for detection and mitigation. Managerial Summary : This article demonstrates mathematically how regression analyses with correlated independent variables may generate beta coefficients of opposite sign to the variables’ true effects. To assess the likelihood of this possibility, I propose that: if (a) absolute correlation of two independent variables is about ±0.3 or more (smaller correlations may be problematic for large data sets), (b) the two variables have beta coefficients of opposite sign, if correlated positively, and of the same sign, if correlated negatively, and (c) the bivariate correlation of one independent variable with the dependent variable is of the opposite sign from the beta coefficient, then the beta might be a false positive. To facilitate such analysis, authors should provide complete correlation tables, including dependent variables, interaction terms, and quadratic terms.