Fuzzy Logistic Regression Analysis Using the Least Squares Method
Zahra Behdani
1
(گروه آمار- دانشکده علوم پایه- دانشگاه صنعتی خاتم الانبیاء)
Majid Darehmiraki
2
(Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Khouzestan, Iran)
کلید واژه: Least square, Distance measure, Logistic regression.,
چکیده مقاله :
One of the most efficient statistical tools for modeling the relationship between a dependent variable and several independent variables is regression. In practice, observations relating to one or more variables, or the relationship between variables, may be vague or non-specific. In such cases, classic regression methods will not have enough capability to model data, and one of the alternative methods is regression in a fuzzy environment. The fuzzy logistic regression model provides a framework in the fuzzy environment to investigate the relationship between a binary response variable and a set of covariates. The purpose of this paper is to attempt to develop a fuzzy model that is based on the idea of the possibility of success. These possibilities are characterized {by several} linguistic phrases, including low, medium, and high, among others. Next, we {use a set of precise explanatory variable observations to model the logarithm transformation of "possibilistic odds." We assume that the model's parameters are triangular fuzzy numbers.} We use the least squares method in fuzzy linear regression to estimate the parameters of the provided model. We compute three types of goodness-of-fit criteria to evaluate the model. Ultimately, we model suspected cases of Systemic Lupus Erythematosus (SLE) disease based on significant risk factors to identify the model's application. We do this due to the widespread use of logistic regression in clinical studies and the prevalence of ambiguous observations in clinical diagnosis. Furthermore, to assess the prevalence of diabetes in the community, we will collect a sample of plasma glucose levels, measured two hours after a meal, from each participant in a clinical survey. The proposed model has the potential to rationally replace an ordinary model in modeling the clinically ambiguous condition, according to the findings.
چکیده انگلیسی :
One of the most efficient statistical tools for modeling the relationship between a dependent variable and several independent variables is regression. In practice, observations relating to one or more variables, or the relationship between variables, may be vague or non-specific. In such cases, classic regression methods will not have enough capability to model data, and one of the alternative methods is regression in a fuzzy environment. The fuzzy logistic regression model provides a framework in the fuzzy environment to investigate the relationship between a binary response variable and a set of covariates. The purpose of this paper is to attempt to develop a fuzzy model that is based on the idea of the possibility of success. These possibilities are characterized {by several} linguistic phrases, including low, medium, and high, among others. Next, we {use a set of precise explanatory variable observations to model the logarithm transformation of "possibilistic odds." We assume that the model's parameters are triangular fuzzy numbers.} We use the least squares method in fuzzy linear regression to estimate the parameters of the provided model. We compute three types of goodness-of-fit criteria to evaluate the model. Ultimately, we model suspected cases of Systemic Lupus Erythematosus (SLE) disease based on significant risk factors to identify the model's application. We do this due to the widespread use of logistic regression in clinical studies and the prevalence of ambiguous observations in clinical diagnosis. Furthermore, to assess the prevalence of diabetes in the community, we will collect a sample of plasma glucose levels, measured two hours after a meal, from each participant in a clinical survey. The proposed model has the potential to rationally replace an ordinary model in modeling the clinically ambiguous condition, according to the findings.
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