scholarly journals A Monte Carlo Study for Dealing with Multicollinearity and Autocorrelation Problems in Linear Regression Using Two Stage Ridge Regression Method

2021 ◽  
Vol 9 (5) ◽  
pp. 630-638
Author(s):  
Hussein Eledum ◽  
Hytham Hussein Awadallah
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Ridge Regression ◽  
Monte Carlo Study ◽  
Regression Method ◽  
Two Stage

scholarly journals Linear regression with many controls of limited explanatory power

2021 ◽  
Vol 12 (2) ◽  
pp. 405-442 ◽  
Author(s):  
Chenchuan (Mark) Li ◽  
Ulrich K. Müller
Keyword(s):  
Monte Carlo ◽  
Linear Regression ◽  
Linear Regression Model ◽  
Asymptotic Efficiency ◽  
Explanatory Power ◽  
Monte Carlo Study ◽  
Inference Procedure ◽  
Quadratic Mean ◽  
Additional Information ◽  
Control Coefficients

We consider inference about a scalar coefficient in a linear regression model. One previously considered approach to dealing with many controls imposes sparsity, that is, it is assumed known that nearly all control coefficients are (very nearly) zero. We instead impose a bound on the quadratic mean of the controls' effect on the dependent variable, which also has an interpretation as an R 2‐type bound on the explanatory power of the controls. We develop a simple inference procedure that exploits this additional information in general heteroskedastic models. We study its asymptotic efficiency properties and compare it to a sparsity‐based approach in a Monte Carlo study. The method is illustrated in three empirical applications.

Metric Conjoint Segmentation Methods: A Monte Carlo Comparison

1996 ◽  
Vol 33 (1) ◽  
pp. 73-85 ◽  
Author(s):  
Marco Vriens ◽  
Michel Wedel ◽  
Tom Wilms
Keyword(s):  
Monte Carlo ◽  
Degrees Of Freedom ◽  
Goodness Of Fit ◽  
Latent Class ◽  
Predictive Accuracy ◽  
Monte Carlo Study ◽  
Error Variance ◽  
Two Stage ◽  
Parameter Recovery ◽  
Segmentation Methods

The authors compare nine metric conjoint segmentation methods. Four methods concern two-stage procedures in which the estimation of conjoint models and the partitioning of the sample are performed separately; in five, the estimation and segmentation stages are integrated. The methods are compared conceptually and empirically in a Monte Carlo study. The empirical comparison pertains to measures that assess parameter recovery, goodness-of-fit, and predictive accuracy. Most of the integrated conjoint segmentation methods outperform the two-stage clustering procedures under the conditions specified, in which a latent class procedure performs best. However, differences in predictive accuracy were small. The effects of degrees of freedom for error and the number of respondents were considerably smaller than those of number of segments, error variance, and within-segment heterogeneity.

scholarly journals METODE MODIFIED JACKKNIFE RIDGE REGRESSION DALAM PENANGANAN MULTIKOLINIERITAS (STUDI KASUS INDEKS PEMBANGUNAN MANUSIA DI JAWA TENGAH)

2021 ◽  
Vol 10 (1) ◽  
pp. 104-113
Author(s):  
Arya Huda Arrasyid ◽  
Dwi Ispriyanti ◽  
Abdul Hoyyi
Keyword(s):  
Linear Regression ◽  
Human Development ◽  
Ridge Regression ◽  
Human Development Index ◽  
Mean Squared Error ◽  
Regression Method ◽  
Linear Regression Method ◽  
Development Index ◽  
Regression Parameters ◽  
Years Of Schooling

The human development index is a value where the value showed the measure of living standards comparison in a region. The Human Development Index is influenced by several factors, one of them is the education factor that is the average years of schooling and expected years of schooling. A statistical method to find the correlation between the independent variable and the dependent variable can be conducted using the linear regression method. Linear regression requires several assumptions, one of which is the multicollinearity assumption. If the multicollinearity assumption is not fulfilled, another alternative is needed to estimate the regression parameters. One method that can be used to estimate regression parameters is the ridge regression method with an ordinary ridge regression estimator. Ordinary ridge regression then developed more into several methods, such as generalized ridge regression, jackknife ridge regression, and modified jackknife ridge regression method. The generalized Ridge Regression method causes a reduction to variance in linear regression, while the jackknife ridge regression method is obtained by resampling jackknife process on the generalized ridge regression method. Modified jackknife ridge regression is a combination of generalized ridge regression and jackknife ridge regression method. In this journal, the three ridge regression methods will be compared based on the Mean Squared Error obtained in each method. The results of this study indicate that the jackknife ridge regression method has the smallest MSE value. Keywords: Generalized Ridge Regression, Jackknife Ridge Regression, Modified Jackknife Ridge Regression, Multicolinearity  

scholarly journals Feasible Generalized Stein-Rule Restricted Ridge Regression Estimators

2017 ◽  
Vol 13 (1) ◽  
pp. 77-97
Author(s):  
Nimet Özbay ◽  
Issam Dawoud ◽  
Selahattin Kaçıranlar
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Ridge Regression ◽  
Simulation Experiment ◽  
Regression Estimators ◽  
Coefficient Vector ◽  
General Linear Regression Model

Abstract Several versions of the Stein-rule estimators of the coefficient vector in a linear regression model are proposed in the literature. In the present paper, we propose new feasible generalized Stein-rule restricted ridge regression estimators to examine multicollinearity and autocorrelation problems simultaneously for the general linear regression model, when certain additional exact restrictions are placed on these coefficients. Moreover, a Monte Carlo simulation experiment is performed to investigate the performance of the proposed estimator over the others.

A Clusterwise Regression Method for Simultaneous Fuzzy Market Structuring and Benefit Segmentation

1991 ◽  
Vol 28 (4) ◽  
pp. 385-396 ◽  
Author(s):  
Michel Wedel ◽  
Jan-Benedict E. M. Steenkamp
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Regression Method ◽  
Number Of Clusters ◽  
Preference Analysis ◽  
Clusterwise Regression ◽  
Benefit Segmentation ◽  
Degree Of Membership ◽  
The Cross

A generalized algorithm for fuzzy clusterwise regression (GFCR) is proposed that incorporates both benefit segmentation and market structuring within the framework of preference analysis. The method simultaneously estimates the models relating preferences to product dimensions within each of a number of clusters, and the degree of membership of brands and of subjects in those clusters. The performance of GFCR is assessed in a Monté Carlo study. An application to data on preferences for brands of margarine and butter is reported, the cross-validity of GFCR is assessed, and it is compared empirically with Kamakura's method. Managerial and research implications are discussed.

Analyzing Observed Composite Differences Across Groups

Methodology ◽  
2013 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Holger Steinmetz
Keyword(s):  
Monte Carlo ◽  
Structural Equation Modeling ◽  
Measurement Invariance ◽  
Structural Equation ◽  
Monte Carlo Study ◽  
Equation Modeling ◽  
Factor Loadings ◽  
Latent Mean Differences ◽  
Partial Invariance ◽  
Mean Differences

Although the use of structural equation modeling has increased during the last decades, the typical procedure to investigate mean differences across groups is still to create an observed composite score from several indicators and to compare the composite’s mean across the groups. Whereas the structural equation modeling literature has emphasized that a comparison of latent means presupposes equal factor loadings and indicator intercepts for most of the indicators (i.e., partial invariance), it is still unknown if partial invariance is sufficient when relying on observed composites. This Monte-Carlo study investigated whether one or two unequal factor loadings and indicator intercepts in a composite can lead to wrong conclusions regarding latent mean differences. Results show that unequal indicator intercepts substantially affect the composite mean difference and the probability of a significant composite difference. In contrast, unequal factor loadings demonstrate only small effects. It is concluded that analyses of composite differences are only warranted in conditions of full measurement invariance, and the author recommends the analyses of latent mean differences with structural equation modeling instead.

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