Metode Boostrap dan Jackknife dalam Mengestimasi Parameter Regresi Linear Ganda (Kasus: Data Kemiskinan Kota Makassar Tahun 2017)

Abstrak Metode kuadrat terkecil merupakan metode standar untuk mengestimasi nilai parameter model regresi linear. Metode tersebut dibangun berdasarkan asumsi error bersifat identik dan independen, serta berdistribusi normal. Apabila asumsi tidak terpenuhi maka metode ini tidak akurat. Alternatif untuk mengatasi hal tersebut adalah dengan menggunakan metode resampling. Adapun metode resampling yang digunakan dalam penelitian ini yaitu metode bootstrap dan Jackknife. Terlebih dahulu dilakukan estimasi nilai parameter regresi untuk analisis data kemiskinan Kota Makassar Tahun 2017. Data tersebut merupakan data sekunder diperoleh dari BAPPEDA Kota Makassar. Dari uji asumsi klasik diperoleh bahwa model tidak bersifat homoskedastis dan residual tidak berdistribusi normal sehingga model regresi yang diperoleh tidak dapat dipertanggungjawabkan. Metode bootstrap dan jackknife yang dikenalkan disini menggunakan program R untuk mencari nilai bias dan nilai standar errornya. Estimasi parameter model regresi linear berganda dari metode resampling bootstrap dengan B=200 dan B=500 serta metode resampling jackknife Terhapus-1 diperoleh model regresi. Hasil yang didapat dalam penelitian ini, metode jackknife merupakan metode yang efisien dibandingkan dengan metode bootstrap, hal ini didukung dengan kecilnya tingkat standar error dan nilai biasnya yang dihasilkan. Kata Kunci: Regrei, Resampling, Bootsrap, JaccknifeAbstract. The Ordinary least squares method is a standard method for estimating the parameter values of a linear regression model. The method is built based on error assumptions that are identical and independent, and are normally distributed. If the assumptions are not met, this method is not accurate. The alternative to overcome this is to use the resampling method. The resampling method used in this study is bootstrap and jackknife methods. First, estimation of regression parameter values for analysis of poverty data in Makassar City in 2017. The data is secondary data obtained from the BAPPEDA of Makassar City. From the classic assumption test, it is obtained that the model is not homosexedastic and residual is not normally distributed so that the regression model obtained cannot be accounted for. Bootstrap and jackknife methods are introduced here using the R program to find the value of the bias and the standard error values. Parameter estimation of multiple linear regression models from Bootstrap resampling method with B= 200, B= 500 and jackknife deleted-1 resampling method obtained regression models. The results obtained in this study, Jackknife method is an efficient method compared with the bootstrap method, and this is supported by the small standard level error and bias in resulting value.Keywords: regression, resampling, bootstrap, jackknife.

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A Comparative Analysis on Some Estimators of Parameters of Linear Regression Models in Presence of Multicollinearity

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2018/v2i228773 ◽

2018 ◽

pp. 1-8

Author(s):

Warha, Abdulhamid Audu ◽

Yusuf Abbakar Muhammad ◽

Akeyede, Imam

Keyword(s):

Linear Regression ◽

Least Squares ◽

Regression Models ◽

Mean Squared Error ◽

Least Squares Method ◽

Ordinary Least Squares ◽

Least Square ◽

Linear Regression Models ◽

Independent Variables ◽

Different Levels

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators’ criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at different levels of multicollinearity and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity was increased.

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Estimation in Dynamic Linear Regression Models with Infinite Variance Errors

Econometric Theory ◽

10.1017/s0266466600007982 ◽

1993 ◽

Vol 9 (4) ◽

pp. 570-588 ◽

Cited By ~ 28

Author(s):

Keith Knight

Keyword(s):

Asymptotic Behavior ◽

Linear Regression ◽

Regression Model ◽

Linear Regression Model ◽

Regression Models ◽

Infinite Variance ◽

Linear Regression Models ◽

Asymptotically Normal ◽

Second Moments ◽

True Values

This paper considers the asymptotic behavior of M-estimates in a dynamic linear regression model where the errors have infinite second moments but the exogenous regressors satisfy the standard assumptions. It is shown that under certain conditions, the estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n−½ rate.

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Brazilian Articles in Top-Tier Dental Journals and Influence of International Collaboration on Citation Rates

Brazilian Dental Journal ◽

10.1590/0103-6440201902826 ◽

2019 ◽

Vol 30 (4) ◽

pp. 307-316 ◽

Cited By ~ 3

Author(s):

Ana Paula R Gonçalves ◽

Bruna L Porto ◽

Bruna Rodolfo ◽

Clovis M Faggion Jr ◽

Bernardo A. Agostini ◽

...

Keyword(s):

Linear Regression ◽

Regression Model ◽

International Collaboration ◽

Linear Regression Model ◽

Regression Models ◽

Dental Materials ◽

Original Research ◽

Linear Regression Models ◽

Article Type ◽

Multilevel Linear Regression

Abstract This study investigated the presence of co-authorship from Brazil in articles published in top-tier dental journals and analyzed the influence of international collaboration, article type (original research or review), and funding on citation rates. Articles published between 2015 and 2017 in 38 selected journals from 14 dental subareas were screened in Scopus. Bibliographic information, citation counts, and funding details were recorded for all articles (N=15619). Collaboration with other top-10 publishing countries in dentistry was registered. Annual citations averages (ACA) were calculated. A linear regression model assessed differences in ACA between subareas. Multilevel linear regression models evaluated the influence of article type, funding, and presence of international collaboration in ACA. Brazil was a frequent co-author of articles published in the period (top 3: USA=25.5%; Brazil=13.8%; Germany=9.2%) and the country with most publications in two subareas. The subjects with the biggest share of Brazil are Operative Dentistry/Cariology, Dental Materials, and Endodontics. Brazil was second in total citations, but fifth in citation averages per article. From the total of 2155 articles co-authored by Brazil, 74.8% had no co-authorship from other top-10 publishing countries. USA (17.8%), Italy (4.2%), and UK (3.2%) were the main co-author countries, but the main collaboration country varied between subjects. Implantology and Dental Materials were the subjects with most international co-authorship. Review articles and articles with international collaboration were associated with increased citation rates, whereas the presence of study funding did not influence the citations.

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Analysis of SF-6D Health State Utility Scores: Is Beta Regression Appropriate?

Healthcare ◽

10.3390/healthcare8040525 ◽

2020 ◽

Vol 8 (4) ◽

pp. 525

Author(s):

Samer A Kharroubi

Keyword(s):

Linear Regression ◽

Regression Model ◽

Random Effects ◽

Regression Models ◽

Mean Squared Error ◽

Health State Utility ◽

Beta Regression ◽

Health State ◽

Linear Regression Models ◽

Utility Scores

Background: Typically, modeling of health-related quality of life data is often troublesome since its distribution is positively or negatively skewed, spikes at zero or one, bounded and heteroscedasticity. Objectives: In the present paper, we aim to investigate whether Bayesian beta regression is appropriate for analyzing the SF-6D health state utility scores and respondent characteristics. Methods: A sample of 126 Lebanese members from the American University of Beirut valued 49 health states defined by the SF-6D using the standard gamble technique. Three different models were fitted for SF-6D via Bayesian Markov chain Monte Carlo (MCMC) simulation methods. These comprised a beta regression, random effects and random effects with covariates. Results from applying the three Bayesian beta regression models were reported and compared based on their predictive ability to previously used linear regression models, using mean prediction error (MPE), root mean squared error (RMSE) and deviance information criterion (DIC). Results: For the three different approaches, the beta regression model was found to perform better than the normal regression model under all criteria used. The beta regression with random effects model performs best, with MPE (0.084), RMSE (0.058) and DIC (−1621). Compared to the traditionally linear regression model, the beta regression provided better predictions of observed values in the entire learning sample and in an out-of-sample validation. Conclusions: Beta regression provides a flexible approach to modeling health state values. It also accounted for the boundedness and heteroscedasticity of the SF-6D index scores. Further research is encouraged.

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On the least trimmed squares estimators for JS circular regression model

Kuwait Journal of Science ◽

10.48129/kjs.v48i3.10004 ◽

2021 ◽

Vol 48 (3) ◽

Author(s):

Shokrya Saleh Alshqaq ◽

Keyword(s):

Linear Regression ◽

Regression Model ◽

Regression Models ◽

Real Data ◽

Linear Regression Models ◽

Least Trimmed Squares ◽

Leverage Points ◽

Circular Regression ◽

Robust Linear Regression

The least trimmed squares (LTS) estimation has been successfully used in the robust linear regression models. This article extends the LTS estimation to the Jammalamadaka and Sarma (JS) circular regression model. The robustness of the proposed estimator is studied and the used algorithm for computation is discussed. Simulation studied, and real data show that the proposed robust circular estimator effectively fits JS circular models in the presence of vertical outliers and leverage points.

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PERILAKU KECURANGAN AKADEMIK MAHASISWA AKUNTANSI : DIMENSI FRAUD PENTAGON (STUDI KASUS PADA MAHASISWA PRODI AKUNTANSI UKRIDA)

Jurnal Akuntansi Bisnis ◽

10.30813/jab.v12i2.1786 ◽

2019 ◽

Vol 12 (2) ◽

Author(s):

Kennedy Fadersair ◽

Subagyo Subagyo

Keyword(s):

Linear Regression ◽

Regression Model ◽

Regression Models ◽

Sampling Method ◽

Accounting Students ◽

Linear Regression Models ◽

Purposive Sampling ◽

Academic Fraud

ABSTRACT: This research examined factors that influence the behaviour of student’s cheating by using the concept of fraud pentagon consisting of pressure, opportunity, rationalization, competence and arrogance. In collecting data using questionnaires with purposive sampling method. The regression model used in this study is the linear regression models with SPSS 24. Participants in this study were 122 accounting students in Faculty of Economics and Business Christian Krida Wacana University. The result of this research shows that simultaneously fraud pentagon have significant effect to student’s academic fraud behavior. Partially, pressure and competence have positive significant effect to student’s academic fraud behavior. Arrogance have negative significant effect to student’s academic fraud behavior. Rationalization and opportunity did not influence. Keyword : academic fraud, pressure, opportunity, rasionalization, capability,arrogance. ABSTRAK: Penelitian ini untuk menguji faktor-faktor yang berpengaruh terhadap perilaku kecurangan akademik mahasiswa menggunakan konsep fraud pentagon, yaitu tekanan, kesempatan, rasionalisasi, kemampuan dan arogansi. Dalam pengumpulan data menggunakan kuesioner dengan metode purposive sampling. Model regresi yang digunakan dalam penelitian ini adalah model regresi linear berganda dengan bantuan SPSS 24. Sampel Penelitian sebanyak 122 mahasiswa Program Studi Akuntansi Fakultas Ekonomi dan Bisnis Universitas Kristen Krida Wacana. Hasil penelitian ini secara simultan menunjukkan bahwa fraud pentagon beperngaruh secara signifikan. Secara parsial menunjukkan bahwa tekanan dan kemampuan berpengaruh signifikan positif terhadap perilaku kecurangan akademik. Arogansi berpengaruh signifikan negatif terhadap perilaku kecurangan akademik. Rasionalisasi dan kesempatan tidak berpengaruh signifikan. Kata kunci : kecurangan akademik, tekanan, kesempatan, rasionalisasi, kemampuan, arogansi.

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Significant non-linearity in nitrous oxide chamber data and its effect on calculated annual emissions

Biogeosciences Discussions ◽

10.5194/bgd-6-115-2009 ◽

2009 ◽

Vol 6 (1) ◽

pp. 115-141 ◽

Cited By ~ 13

Author(s):

P. C. Stolk ◽

C. M. J. Jacobs ◽

E. J. Moors ◽

A. Hensen ◽

G. L. Velthof ◽

...

Keyword(s):

Nitrous Oxide ◽

Linear Regression ◽

Regression Model ◽

Linear Regression Model ◽

Regression Models ◽

Goodness Of Fit ◽

Surface Fluxes ◽

Linear Regression Models ◽

Open Questions ◽

Non Linear

Abstract. Chambers are widely used to measure surface fluxes of nitrous oxide (N2O). Usually linear regression is used to calculate the fluxes from the chamber data. Non-linearity in the chamber data can result in an underestimation of the flux. Non-linear regression models are available for these data, but are not commonly used. In this study we compared the fit of linear and non-linear regression models to determine significant non-linearity in the chamber data. We assessed the influence of this significant non-linearity on the annual fluxes. For a two year dataset from an automatic chamber we calculated the fluxes with linear and non-linear regression methods. Based on the fit of the methods 32% of the data was defined significant non-linear. Significant non-linearity was not recognized by the goodness of fit of the linear regression alone. Using non-linear regression for these data and linear regression for the rest, increases the annual flux with 21% to 53% compared to the flux determined from linear regression alone. We suggest that differences this large are due to leakage through the soil. Macropores or a coarse textured soil can add to fast leakage from the chamber. Yet, also for chambers without leakage non-linearity in the chamber data is unavoidable, due to feedback from the increasing concentration in the chamber. To prevent a possibly small, but systematic underestimation of the flux, we recommend comparing the fit of a linear regression model with a non-linear regression model. The non-linear regression model should be used if the fit is significantly better. Open questions are how macropores affect chamber measurements and how optimization of chamber design can prevent this.

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