Inference of Linear Regression Model with Systematic Measurement Errors in the Response Variable

2021 ◽  
Vol 23 (6) ◽  
pp. 2607-2617
Author(s):  
Juwon Song
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Measurement Errors ◽  
Systematic Measurement ◽  
Response Variable

scholarly journals Selection of Appropriate Model for Quality of Life Data of Strabismus Patients Despite Censorship

2021 ◽  
Author(s):  
Zahra Ghassemi ◽  
Mehdi Yaseri ◽  
Mostafa Hosseini
Keyword(s):  
Quality Of Life ◽  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Linear Regression Model ◽  
Multiple Linear Regression Model ◽  
Tobit Model ◽  
P Value ◽  
Response Variable

Introduction: Previous studies on the quality of life of strabismus patients have not examined the existence of censoring to express the relation between the response variable and its predictors. Methods & Materials: The information used in this study is a conducted cross-sectional study in 2012. The sample size is 90 children in the age range (4-18) years and with congenital strabismus. We used the RAND Health Insurance Study questionnaire with ten subscales to evaluate the quality of life, which was increased to 11 dimensions by adding some items related to eye alignment concerns introduced by Archer et al. The demographic profile is also recorded by 13 other questions. We have expressed the relationship between the independent and response variables in each of the 11 dimensions of the questionnaire and the overall quality of life score by fitting the multiple linear regression model. Then we fitted the two models of classic Tobit and CLAD, which are for censoring, to all dimensions of the questionnaire. Results: We showed that in fitting the models to the overall quality of life scale variable, the best model is the multiple linear regression. Because the response variable was normal, and there was no censoring (ceiling and floor effect). However, in the depression subscale, due to the high censoring (28.89% of the ceiling effect) and the almost normal distribution of the response variable (p-value of skewness< 0.05), the appropriate model according to the criteria is the classic Tobit (AIC = 546.33). That is, the classic Tobit model is the best alternative to the multiple linear regression model in the presence of censoring. But these conditions did not exist in all variables. In the subscale, there was a severe censoring performance constraint (67.78% of the ceiling effect). When censoring is high, the distribution of the response variable becomes very skewed, and the distribution of response variables deviates drastically from normal. The distribution of the performance constraint variable was very skewed (p-value <0.001). Here the RMSE standard scale for the classic Tobit model was 28.74, which is much higher than the standard scale for the multiple linear regression model (14.23). The best model for the high censoring was CLAD. Conclusion: To use the appropriate statistical method in the analysis, one must look at how the response variable is distributed. The multiple linear regression model is very widely used, but in the presence of censoring, the use of this model gives skewed results. In this case, the classic Tobit model and its derived model, CLAD, are replaced. The nonparametric CLAD model calculates accurate estimates with minimum defaults and censoring.

Regression models

2020 ◽  
pp. 65-92
Author(s):  
Bendix Carstensen
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Generalized Linear Models ◽  
Linear Regression Model ◽  
Regression Models ◽  
Linear Models ◽  
General Linear Model ◽  
Simple Linear Regression ◽  
Response Variable ◽  
Quantitative Response

This chapter evaluates regression models, focusing on the normal linear regression model. The normal linear regression model establishes a relationship between a quantitative response (also called outcome or dependent) variable, assumed to be normally distributed, and one or more explanatory (also called regression, predictor, or independent) variables about which no distributional assumptions are made. The model is usually referred to as 'the general linear model'. The chapter then differentiates between simple linear regression and multiple regression. The term 'simple linear regression' covers the regression model where there is one response variable and one explanatory variable, assuming a linear relationship between the two. The chapter also discusses the model formulae in R; generalized linear models; collinearity and aliasing; and logarithmic transformations.

Effects of measurement errors in predictor selection of linear regression model

2007 ◽  
Vol 52 (2) ◽  
pp. 1183-1195 ◽  
Author(s):  
Kimmo Vehkalahti ◽  
Simo Puntanen ◽  
Lauri Tarkkonen
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Measurement Errors ◽  
Selection Of

scholarly journals Prediction in a Hybrid of Fuzzy Linear Regression with Symmetric Parameter Model and Fuzzy C-Means Method Using Simulation Data

2018 ◽  
Vol 7 (4.30) ◽  
pp. 419
Author(s):  
Muhammad Ammar Shafi ◽  
Mohd Saifullah Rusiman ◽  
Kavikumar Jacob ◽  
Nor Shamsidah Amir Hamzah ◽  
Norziha Che Him ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Mean Square Error ◽  
Hybrid Model ◽  
Linear Regression Model ◽  
Measurement Errors ◽  
Mean Square ◽  
Fuzzy Linear Regression ◽  
Simulation Data ◽  
Fuzzy Linear Regression Model

The objective of fuzzy linear regression model (FLRM) to predict the dependent variable and independent variables in vague phenomenon. In this study, several models such as fuzzy linear regression model (FLRM), fuzzy linear regression with symmetric parameter (FLWSP) and a hybrid model have been applied to be evaluated by 1000 rows in 1 simulation data. Moreover, the hybrid method was applied between fuzzy linear regression with symmetric parameter (FLRWSP) and fuzzy c-mean (FCM) method to get the effective prediction in a new model and best result in this study. To improve the accuracy of evaluating and predicting, this study employ two measurement error of cross validation statistical technique which are mean square error (MSE) and root mean square error (RMSE). The simulation result suggests that comparison among models using two measurement errors should be to determine the best results. Finally, this study notes that the new hybrid model of FLRWSP and FCM is verified to be a good model with the least value of MSE and RMSE measurement errors.

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