ASSESSMENT OF THE CONSISTENCY OF A CLUSTER LINEAR REGRESSION MODEL
Authors:
1.
Irkutsk State University of Railway Transport
(Doctor of Technical Sciences, Professor; Professor of the Department of Information Systems and Information Security)
Irkutsk, Irkutsk region, Russian Federation
Irkutsk, Irkutsk region, Russian Federation
2.
Irkutsk State University of Railway Transport
Type:
Article
Pages:
from 88
to 91
Status:
In work
Language:
Russian
Keywords:
CLUSTER LINEAR REGRESSION MODEL, CONSISTENCY, LEAST ABSOLUTE VALUE METHOD, LINEAR BOOLEAN PROGRAMMING PROBLEM, CHEMICAL INDUSTRY, AVERAGE AND MAXIMUM RELATIVE APPROXIMATION ERRORS, BIAS CRITERION
Abstract (English):
The paper provides a brief overview of publications on various aspects of construction, research and application of cluster linear regression in the framework of applied regression analysis. In particular, the following are considered: a procedure for testing data to determine an acceptable level of their clustering; a family of mixture models with random covariates embedded in a linear cluster-weighted model; a procedure for functional clustering for classifying daily load curves; analysis of clustered data using partial linear regression models; an adaptive convex clustering method for simultaneously performing data segmentation and model fitting for generalized linear models; efficient computational algorithms for bootstrapping linear regression models with clustered data. The paper presents a form of the linear Boolean programming problem to which the problem of estimating the parameters of cluster linear regression can be reduced if the Manhattan distance is taken as the distance between the calculated and actual values of the dependent variable. It is proposed to use the bias criterion used as an external one in the group argument accounting method as the main criterion for assessing the consistency of the cluster linear model. When assessing consistency, it is also possible to use the average and maximum relative approximation errors calculated for each cluster. It is noted that the use of cluster linear regression for spatial data has a greater applied significance than for time series, as is done in the work, since clustering of such data opens up wide opportunities in solving a wide range of practical problems of analysis and forecasting, and its results are well interpretable. A cluster linear model of the development of the chemical industry of the Russian Federation is constructed, and its consistency is assessed.
The paper provides a brief overview of publications on various aspects of construction, research and application of cluster linear regression in the framework of applied regression analysis. In particular, the following are considered: a procedure for testing data to determine an acceptable level of their clustering; a family of mixture models with random covariates embedded in a linear cluster-weighted model; a procedure for functional clustering for classifying daily load curves; analysis of clustered data using partial linear regression models; an adaptive convex clustering method for simultaneously performing data segmentation and model fitting for generalized linear models; efficient computational algorithms for bootstrapping linear regression models with clustered data. The paper presents a form of the linear Boolean programming problem to which the problem of estimating the parameters of cluster linear regression can be reduced if the Manhattan distance is taken as the distance between the calculated and actual values of the dependent variable. It is proposed to use the bias criterion used as an external one in the group argument accounting method as the main criterion for assessing the consistency of the cluster linear model. When assessing consistency, it is also possible to use the average and maximum relative approximation errors calculated for each cluster. It is noted that the use of cluster linear regression for spatial data has a greater applied significance than for time series, as is done in the work, since clustering of such data opens up wide opportunities in solving a wide range of practical problems of analysis and forecasting, and its results are well interpretable. A cluster linear model of the development of the chemical industry of the Russian Federation is constructed, and its consistency is assessed.
Keywords:
CLUSTER LINEAR REGRESSION MODEL, CONSISTENCY, LEAST ABSOLUTE VALUE METHOD, LINEAR BOOLEAN PROGRAMMING PROBLEM, CHEMICAL INDUSTRY, AVERAGE AND MAXIMUM RELATIVE APPROXIMATION ERRORS, BIAS CRITERION
CLUSTER LINEAR REGRESSION MODEL, CONSISTENCY, LEAST ABSOLUTE VALUE METHOD, LINEAR BOOLEAN PROGRAMMING PROBLEM, CHEMICAL INDUSTRY, AVERAGE AND MAXIMUM RELATIVE APPROXIMATION ERRORS, BIAS CRITERION
