PL EN


Preferences help
enabled [disable] Abstract
Number of results
2019 | 116 | 245-252
Article title

The Best Model of LASSO With The LARS (Least Angle Regression and Shrinkage) Algorithm Using Mallow’s Cp

Content
Title variants
Languages of publication
EN
Abstracts
EN
Multicollinearity often occurs in regression analysis. Multicollinearity is a condition of correlation between independent variables which is a problem. One method that can overcome multicollinearity is the LASSO (Least Absolute Shrinkage and Selection Operator) method. LASSO is able to help to shrink multicollinearity and improve the accuracy of linear regression models. Estimators of LASSO parameters can be solved by the LARS (Least Angle Regression and Shrinkage) algorithm by algorithm which calculates the correlation vector, the largest absolute correlation value, equiangular vector, inner product vector, and determines the LARS algorithm limiter for LASSO. Selecting the best model using the Mallow’s C_p statistics. The smallest Mallow’s C_p value will be selected as the best model. LASSO method with a more detailed procedure with LARS algorithm and selecting the best model using the Mallow’s C_p statistics is discussed in this paper.
Keywords
Discipline
Year
Volume
116
Pages
245-252
Physical description
Contributors
  • Master Program in Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia
  • Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia
  • Department of Marine Science, Faculty of Fishery and Marine Science, Universitas Padjadjaran, Indonesia
References
  • [1] M. Alauddin, H.S. Nghiemb, Do Instructional Attributes Pose Multicollinearity Problems ? An Empirical Exploration. Economic Analysis and Policy 40(3) (2010) 351-361.
  • [2] Z.Y. Algamal, M.H. Lee, Penalized logistic regression with the adaptive LASSO for gene selection in high-dimensional cancer classification. Expert Systems with Applications 42 (2015) 9326–9332.
  • [3] S. Chand, S. Ahmad, M. Batool, Solution path ef fi ciency and oracle variable selection by Lasso-type methods. Chemometrics and Intelligent Laboratory Systems 183 (2018) 140-146.
  • [4] H. Chen, X. Yaoxin, The Study of Credit Scoring Model Based on Group Lasso. Procedia Computer Science 122 (2017) 677–684.
  • [5] S. Chen, C.H.Q. Ding, B. Luo, Linear Regression Based Projections for Dimensionality Reduction. Information Sciences 467 (2018) 74-86.
  • [6] M.D. Dyar, M.L. Carmosino, E.A. Breves, M.V. Ozanne, S.M. Clegg, R.C. Wiens, Comparison of Partial Least Squares and Lasso Regression Techniques as Applied to Laser-Induced Breakdown Spectroscopy of Geological Samples. Spectrochimica Acta Part B: Atomic Spectroscopy 70 (2012) 51-67.
  • [7] B. Efron, T. Hastie, I. Johnstone, R. Tibshirani, Least Angle Regression. Annals of Statistics 32(2) (2004) 407-499.
  • [8] P. Gauthier, W. Scullion, A. Berry, Sound Quality Prediction Based on Systematic Metric Selection and Shrinkage : Comparison of Stepwise , Lasso , and Elastic-Net Algorithms and Clustering Preprocessing. Journal of Sound and Vibration 400 (2017) 134-53.
  • [9] O. Hössjer. On the coefficient of determination for mixed regression models. Journal of Statistical Planning and Inference 138 (2008) 3022–3038.
  • [10] E. Iturbide, J. Cerda, M. Graff. A Comparison between LARS and LASSO for Initialising the Time-Series Forecasting Auto-Regressive Equations. Procedia Technology 7 (2013) 282–288.
  • [11] N.H. Jadhav, D.N. Kashid, S.R. Kulkarni, Subset selection in multiple linear regression in the presence of outlier and multicollinearity. Statistical Methodology 19 (2014) 44–59.
  • [12] M. Jansen, Generalized Cross Validation in Variable Selection with and without Shrinkage. Journal of Statistical Planning and Inference 159 (2015) 90-104.
  • [13] Kazemi, A. Mohamed, H. Shareef, H. Zayandehroodi, Optimal Power Quality Monitor Placement Using Genetic Algorithm and Mallow ’ s Cp. International Journal of Electrical Power and Energy Systems 53 (2013) 564–575.
  • [14] Katrutsa, V. Strijov, Comprehensive study of feature selection methods to solve multicollinearity problem according to evaluation criteria. Expert Systems With Applications 76 (2017) 1–11.
  • [15] Kim, J. Lee, H. Yang, W. Bae, Case influence diagnostics in the lasso regression. Journal of the Korean Statistical Society 44 (2015) 271–279.
  • [16] J. Kuan, Regression analysis estimation of stature from foot length. Cognitive Systems Research 52 (2018) 251–260.
  • [17] M.H. Kutner, C.J. Nachtsheim, J. Neter, Applied Linear Regression Models. 4th ed. New York: McGraw-Hill Companies, Inc (2004).
  • [18] S. Lee, C. Jun, Fast Incremental Learning of Logistic Model Tree Using Least Angle Regression. Expert Systems With Applications 97 (2018) 137-145.
  • [19] V. Lorchirachoonkul, J. Jitthavech, A Modified Cp Statistic in a System-of-Equations Model. Journal of Statistical Planning and Inference 142(8) (2012) 2386–2394
  • [20] L.E. Melkumovaa, S.Y. Shatskikhb, Comparing Ridge and LASSO estimators for data analysis. Procedia Engineering 201 (2017) 746-755.
  • [21] R. Miyashiro, Y. Takano, Subset Selection by Mallow’s Cp: A Mixed Integer Programming Approach. Expert Systems With Applications 42(1) (2015) 325-331.
  • [22] K. Nakamura, T. Yasutaka, T. Kuwatani, T. Komai, Development of a predictive model for lead, cadmium and fluorine soil–water partition coefficients using sparse multiple linear regression analysis. Chemosphere 186 (2017) 501-509.
  • [23] H. Ogasawara, Accurate distributions of Mallows’ Cp and its unbiased modifications with applications to shrinkage estimation. Journal of Statistical Planning and Inference 184 (2016) 105-116.
  • [24] S.D Permai, H. Tanty, Linear Regression Model Using Bayesian Approach for Energy Linear Regression Model Using Bayesian Approach for Energy Performance of Residential Building Performance of Residential Building. Procedia Computer Science 135 (2018) 671-677.
  • [25] O. Renaud, M. Victoria-Feser, A robust coefficient of determination for regression. Journal of Statistical Planning and Inference 140 (2010) 1852-1862.
  • [26] G. Sermpinis, S. Tsoukas, P. Zhang, Modelling Market Implied Ratings Using LASSO Variable Selection Techniques. Journal of Empirical Finance 48 (2018) 19-35.
  • [27] X. Shi, Y. Huang, J. Huang, S. Ma, A Forward and Backward Stagewise algorithm for nonconvex loss functions with adaptive Lasso. Computational Statistics and Data Analysis 124 (2018) 235–252.
  • [28] H. Tong, M. Ng, Analysis of Regularized Least Squares for Functional Linear Regression Model. Journal of Complexity 49 (2018) 85-94.
  • [29] Torres-barr, C.M. Alaız, J.R. Dorronsoro, ν-SVM Solutions of Constrained Lasso and Elastic Net. Neurocomputing 275(31) (2017) 1921-1931.
  • [30] R. Tibshirani, Regression Shrinkage and Selection via the LASSO. Journal of Royal Statistical Society, Series B 58(1) (1996) 267-288.
  • [31] S. Wang, B. Ji, J. Zhao, W. Liu, T. Xu, Predicting Ship Fuel Consumption Based on LASSO Regression. Transportation Research Part D: Transport and Environment 65 (2017) 817-824.
  • [32] L. Zhang, K. Li, Forward and Backward Least Angle Regression for Nonlinear. Automatica 53 (2015) 94-102.
  • [33] X. Zhou, X. Huang, Reliability Analysis of Slopes Using UD-Based Response Surface Methods Combined with LASSO. Engineering Geology 233(31) (2018) 111-123.
Document Type
short_communication
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-bce3d866-732e-4ee4-972d-ba9d366b6d0d
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.