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Showing 34 results for Regression
Parvin Sarbakhsh, Dr Yadollah Mehrabi, Dr Ali Akbar Khadem Maboudi, Dr Farzad Hadaegh,
Volume 16, Issue 1 (9-2011)
Abstract
Regression is one of the most important statistical tools in data analysis and study of the relationship between predictive variables and the response variable. in most issues, regression models and decision tress only can show the main effects of predictor variables on the response and considering interactions between variables does not exceed of two way and ultimately three-way, due to complexity of such interactions.
To consider such interactions in the regression models, instead of individual variables in the model, we can construct a combination of them and use this combination as a new independent variable into the model
Logic regression is a generalized regression and classification method that in this model, predictive variables are Boolean combinations that are made of the original binary variables.
Annealing algorithm is used to find such combinations and their coefficients. randomization test or “null model test” is an overall test for signal in the data.also, cross-validation test can be used to determine the size of the logic tree model with the best predictive capability.
As an example, we applied Logic Regression to predict diabetes in TLGS study.
Mrs Maryam Hadipour, Mrs Razieh Jafaraghaiee, Ms Ghassem Yadegarfar, Ms Avat Feizi, Ms Farid Abolhasani,
Volume 17, Issue 1 (9-2012)
Abstract
In recent years, multilevel regression models were intensely developed in many fields like medicine, psychology economic and the others. Such models are applicable for hierarchical data that micro levels are nested in macros.
For modeling these data, when response is not normality distributed, we use generalized multilevel regression models.
In this paper, at first, multilevel ordinal logistic regression models and some estimation methods are explained.
So their applications are investigated in the effect of patient’s environment on economic burden of diabetes type 2.
Ms Adele Ossareh, Dr Firoozeh Rivaz,
Volume 18, Issue 1 (9-2013)
Abstract
In this paper, four approaches are presented to the problem of fitting a linear regression model in the presence of spatially misaligned data. These approaches are plug-in method, simulation, regression calibration and maximum likelihood. In the first two approaches, with modeling the correlation between the explanatory variable, prediction of explanatory variable is determined at sites corresponding to response variable. Then the model is fitted using the predictions as a covariate in regression model. It is shown that this creates Berkson error and this error leads to bias in estimation of the slope of regression model. To adjust the bias, regression calibration approach is provided. In the maximum likelihood approach, misaligned data is used directly, and the regression model parameters are estimated. In fact, it is not required to predict explanatory variable at sites corresponding to response. Unfortunately, the maximum likelihood estimator properties can not be accurately assessed due to lack of analytical form. In a simulation study, the performance of all these approaches is assessed under several spatial models for explanatory variable. It is observed that regression calibration can significantly reduce the bias of slope of regression line compared to other methods. Moreover, Nominal coverage of confidence interval of slope of regression line is notable by this method.
Dr Yadollah Mehrabi, Parvin Sarbakhsh, Dr Farid Zayeri, Dr Maryam Daneshpour,
Volume 19, Issue 2 (2-2015)
Abstract
Logic regression is a generalized regression and classification method that is able to make Boolean combinations
as new predictive variables from the original binary variables. Logic regression was introduced for case control or
cohort study with independent observations. Although in various studies, correlated observations occur due to different
reasons, logic regression have not been studied in theory and application to analyze of correlated observations
and longitudinal data.
Due to the importance of identifying and considering the interactions between variables in longitudinal studies,
in this paper we propose Transition Logic Regression as an extension of Logic Regression to binary longitudinal
data. AIC of the models are used as score function of Annealing algorithm. In order to assess the performance of
the method, simulation study is done in various conditions of sample size, first order dependency and interaction
effect. According to results of simulation study, by increasing the sample size, percentage of identification of true
interactions and MSE of estimations get better. As an application, we assess interaction effect of some SNPs on
HDL level over time in TLGS study using our proposed model.
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Volume 20, Issue 1 (4-2015)
Abstract
The problem of sample size estimation is important in medical applications, especially in cases of expensive measurements
of immune biomarkers. This paper describes the problem of logistic regression analysis with the sample
size determination algorithms, namely the methods of univariate statistics, logistics regression, cross-validation and
Bayesian inference. The authors, treating the regression model parameters as multivariate variable, propose to estimate
the sample size using the distance between parameter distribution functions on cross-validated data sets.
Herewith, the authors give a new contribution to data mining and statistical learning, supported by applied mathematics.
Miss Azade Ghazanfari Hesari, ,
Volume 20, Issue 2 (10-2015)
Abstract
One of the most important problem in any statistical analysis is the existence of unexpected observations. Some
observations are not a part of the study and are known as outliers. Studies have shown that the outliers affect to the
performance of statistical standard methods in models and predictions. The point of this work is to provide a couple
of statistical package in R software to identify outliers in circular-circular regression which is written by the author,
we introduce a brief explanation about the circular data and circular regression, then the packages in R for circular
regression introduced. After wand, the functions in the package CircOutlier will be described.
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Volume 21, Issue 1 (9-2016)
Abstract
In this paper, collinearity in regression models is introduced and then the procedures on how to " remove it" are studied. Moreover preliminary definitions have been given. And the end of this paper, collinearity in regression model will be recognition and a solution will be introduced for remove it.
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Volume 21, Issue 1 (9-2016)
Abstract
In this paper, we have studied the analysis an interval linear regression model for fuzzy data.
In section one, we have introduced the concepts required in this thesis and then we illustrated linear regression fuzzy sets and some primary definitions. In section two, we have introduced various methods of interval linear regression analysis. In section three, we have implemented numerical examples of the chapter two. Finally, we have improved some methods of interval linear regression analysis that considered in section four. We will showed performance of three methods by several examples. All computations of examples are done by alabama package by R software.
Ali Aghmohammadi, Sakine Mohammadi,
Volume 21, Issue 2 (3-2017)
Abstract
Dynamic panel data models include the important part of medicine, social and economic studies. Existence of the lagged dependent variable as an explanatory variable is a sensible trait of these models. The estimation problem of these models arises from the correlation between the lagged depended variable and the current disturbance. Recently, quantile regression to analyze dynamic panel data has been taken in to consideration. In this paper, quantile regression model by adding an adaptive Lasso penalty term to the random effects for dynamic panel data is introduced by assuming correlation between the random effects and initial observations. Also, this model is illustrated by assuming that the random effects and initial values are independent. These two models are analyzed from a Bayesian point of view. Since, in these models posterior distributions of the parameters are not in explicit form, the full conditional posterior distributions of the parameters are calculated and the Gibbs sampling algorithm is used to deduction. To compare the performance of the proposed method with the conventional methods, a simulation study was conducted and at the end, applications to a real data set are illustrated.
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Volume 21, Issue 2 (3-2017)
Abstract
In this paper a new weighted fuzzy ridge regression method for a given set of crisp input and triangular fuzzy output values is proposed. In this regard, ridge estimator of fuzzy parameters is obtained for regression model and its prediction error is calculated by using the weighted fuzzy norm of crisp ridge coefficients. . To evaluate the proposed regression model, we introduce the fuzzy coefficient of determination (FCD). Fuzzy regression is compared with its ridge version by using mean predict error and FCD, numerically. It is evident from comparison results the proposed fuzzy ridge regression is superior to the non-ridge counterpar
S. Mahmoud Taheri,
Volume 22, Issue 2 (3-2018)
Abstract
There are two main approches to the fuzzy regression (more precisely: regression in fuzzy environment): the least of sum of distances (including two methods of least squared errors and least absolute errors) and the possibilistic method (the method of least whole vaguness under some restrictions). Beside, some heuristic methods have been proposed to deal with fuzzy regression. Some of them are based on a combination of two mentioned approaches. Some of them are based on computational algorithmes. A few of heuristic methods use the fuzzy inference systems. Also, there are some methods based on clustering, artificial neural networks, evolutionary algorithms, and nonparametric procedures.
In this paper, a history and basic ideas of the two main approaches to fuzzy regression are reveiwed, and some heuristic methods in this topic are investigated. Moreover, 10 criterion are proposed by which one can evaluate and compare fuzzy regression models.
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Volume 22, Issue 2 (3-2018)
Abstract
Robust regression is an appropriate alternative for ordinal regression when outliers exist in a given data set. If we have fuzzy observations, using ordinal regression methods can't model them; In this case, using fuzzy regression is a good method. When observations are fuzzy and there are outliers in the data sets, using robust fuzzy regression methods are appropriate alternatives. In this paper, we propose a fuzzy least square regression analysis. When independent variables are crisp, the dependent variable is fuzzy number and outliers are present in the data set. In the proposed method, the residuals are ranked as the comparison of fuzzy sets. In the proposed method, the residuals are ranked as the comparison of fuzzy sets, and the weight matrix is defined by the membership function of the residuals. Weighted fuzzy least squares estimators (WFLSE) are obtained by using weight matrix. Two examples are discussed and results of these examples are presented. Finally, we compare this proposed method with ordinal least squares method using the goodness of fit indices.
Ms Sara Jazan, Dr Seyyed Morteza Amini,
Volume 22, Issue 2 (3-2018)
Abstract
One of the factors affecting the statistical analysis of the data is the presence of outliers. The methods which are not affected by the outliers are called robust methods. Robust regression methods are robust estimation methods of regression model parameters in the presence of outliers. Besides outliers, the linear dependency of regressor variables, which is called multicollinearity, the large number of regressor variables with respect to sample size, specially in high dimensional sparse models, are problems which result in efficiency reduction of inferences in classical regression methods. In this paper, we first study the disadvantages of classical least squares regression method, when facing with outliers, multicollinearity and sparse models. Then, we introduce and study robust and penalized regression methods, as a solution to overcome these problems. Furthermore, considering outliers and multicollinearity or sparse models, simultaneously, we study penalized-robust regression methods. We examine the performance of different estimators introdused in this paper, through three different simulation studies. A real data set is also analyzed using the proposed methods.
Dr Fatemeh Hosseini, Dr Omid Karimi, Ms Ahdiyeh Azizi,
Volume 23, Issue 1 (9-2018)
Abstract
Often in practice the data on the mortality of a living unit correlation is due to the location of the observations in the study. One of the most important issues in the analysis of survival data with spatial dependence, is estimation of the parameters and prediction of the unknown values in known sites based on observations vector. In this paper to analyze this type of survival, Cox regression model with piecewise exponential function used as a hazard and spatial dependence as a Gaussian random field and as a latent variable is added to the model. Because there is no closed form for posterior distribution and full conditional distributions, also long computing for Markov chain Monte Carlo algorithms, to analyze the model are used the approximate Bayesian methods.
A practical example of how to implement an approximate Bayesian approach is presented.
Javad Ahmadi, ,
Volume 23, Issue 2 (3-2019)
Abstract
A simultaneous confidence band gives useful information on the reasonable range of the unknown regression model. In this note, when the predictor variables are constrained to a special ellipsoidal region, hyperbolic and constant width confidence bonds for a multiple linear regression model are compared under the minimum volome confidence set (MVCS) criterion. The size of one speical angle that determines the size of the predictor variable region is used to find out which band is better than the other. When the angle and consquently the size of the predictor variable region is small, the constant width band is better than the hyperbolic band.
When the angle hence the size of the predictor variable regoin is large, the hyperbolic band is considerably better than the constant width band.
Mrs Azam Rastin, Dr Mohmmadreza Faridrohani, Dr Amirabbas Momenan, Dr Fatemeh Eskandari, Dr Davood Khalili,
Volume 23, Issue 2 (3-2019)
Abstract
Cardiovascular diseases (CVDs) are the leading cause of death worldwide. To specify an appropriate model to determine the risk of CVD and predict survival rate, users are required to specify a functional form which relates the outcome variables to the input ones. In this paper, we proposed a dimension reduction method using a general model, which includes many widely used survival models as special cases.
Using an appropriate combination of dimension reduction and Cox Proportional Hazards model, we found a method which is effective for survival prediction.
Seyedeh Mona Ehsani Jokandan, Behrouz Fathi Vajargah,
Volume 24, Issue 2 (3-2020)
Abstract
In this paper, the difference between classical regression and fuzzy regression is discussed. In fuzzy regression, nonphase and fuzzy data can be used for modeling. While in classical regression only non-fuzzy data is used.
The purpose of the study is to investigate the possibility of regression method, least squares regression based on regression and linear least squares linear regression method based on fuzzy weight calculation for non-fuzzy input and fuzzy output using symmetric triangular fuzzy numbers. Further reliability, confidence intervals and fitness fit criterion is presented for choosing the optimal model.
Finally, by providing examples of the behavior of the proposed methods, the optimality of the regression hybrid model is shown by the least linear fuzzy squares.
Akram Heidari Garmianaki, Mehrdad Niaparast,
Volume 24, Issue 2 (3-2020)
Abstract
In the present era, classification of data is one of the most important issues in various sciences in order to
detect and predict events. In statistics, the traditional view of these classifications will be based on classic
methods and statistical models such as logistic regression. In the present era, known as the era of explosion
of information, in most cases, we are faced with data that cannot find the exact distribution. Therefore, the
use of data mining and machine learning methods that do not require predetermined models can be useful.
In many countries, the exact identification of the type of groundwater resources is one of the important
issues in the field of water science. In this paper, the results of the classification of a data set for groundwater resources were compared using regression, neural network, and support vector machine.
The results of these classifications showed that machine learning methods were effective in determining the exact type of springs.
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Volume 24, Issue 2 (3-2020)
Abstract
The minimum density power divergence method provides a robust estimate in the face of a situation where the dataset includes a number of outlier data.
In this study, we introduce and use a robust minimum density power divergence estimator to estimate the parameters of the linear regression model and then with some numerical examples of linear regression model, we show the robustness of this estimator in the face of a dataset which includes a number of outliers.
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Volume 24, Issue 2 (3-2020)
Abstract
Sometimes, in practice, data are a function of another variable, which is called functional data. If the scalar response variable is categorical or discrete, and the covariates are functional, then a generalized functional linear model is used to analyze this type of data. In this paper, a truncated generalized functional linear model is studied and a maximum likelihood approach is used to estimate the model parameters. Finally, in a simulation study and two practical examples, the model and methods presented are implemented.
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