In this paper, we consider the issue of data classification in which the response (dependent) variable is two (or multi) valued and the predictor (independent) variables are ordinary variables. The errors could be nonprecise and Random. In this case, the response variable is also a fuzzy Random variable. Based on this and Logistic Regression, we formulate a Model and find the estimation of the coefficients using the least squares method. We will describe the results with an example of one independent Random variable. Finally, we provide recurrence relations for the estimation of parameters. This relation can be used in machine learning and big data classification.

Generalized linear mixed Models (GLMMs) are common methods for the analysis of clustered data. In many longitudinal and hierarchical epidemiological frameworks, accurate measurements of variables are invalid or expensive to be obtained and there might be situations that both the response and covariate variables are likely to be mismeasured. Insensitivity of errors in either covariate or response variable is, not always plausible. With nonlinear Regression Models for the outcome process, classification errors for binary responses and measurement error in covariates basically needs to be accounted for in order to make conclusive inferences. In this article, we provide an approach to simultaneously adjust for non-differential misclassification in the correlated binary response and classical measurement error in the covariates, using the multivariate Gauss-Hermite quadrature technique for the approximation of the likelihood function. Simulation studies are then conducted to inform the Effects of correcting for measurement error and misclassification on the estimation of Regression parameters. The application of the multivariate Gauss-Hermite quadrature method in the conjunction of measurement error and misclassification problems is further highlighted with real-world data based on a multilevel study of contraceptive methods used by women in Bangladesh.

Background & Objectives: Logistic Regression is a general Model for medical and epidemiological data analysis. Recently few researchers have directed their studies to analysis of Logistic Regression with missing value at covariate variable. While the missing is a major threat in results authenticity of data set, in many studies the researchers face data with missing value and it is difficult to avoid such a case in studies.Material & Methods: Satten and Carroll, in the case of completely observed value of covariate variable and some covariate variable with missing at Random mechanism (MAR), introduced a special likelihood function for parameters estimation of Logistic Regression Model. In this research the above- mentioned likelihood function has been used in Bayesian analysis for parameters estimation of Logistic Regression Model and the conclusions are compared with the Multiple Imputation method and Complete Case method.Results: The above-mentioned methods were applied on both simulation data and dentistry data and concluded that The parameters estimation from SCMCMC method had less variance in comparison with parameters estimation from Multiple Imputation and Complete Case methods.Conclusion: After comparison of the three mentioned methods results it had been concluded that if the mechanism is of missing at Random the application of Bayesian analysis with MCMC causes to more accurate estimation and shorter Confidence Intervals than the Multiple Imputation method and Complete Case.

This study aimed to estimate the genetic parameters of body weight traits in Markhoz goats, using B-spline Random Regression Models. The data used in this study included 19549 records collected during 29 years (1992-2021) in Markhoz goat Breeding Research Station, located in Sanandaj, Iran. The Model used to analyze data included fixed Effects (year of birth, sex, type of birth and age of dam) and Random Effects including direct additive genetic, maternal additive genetic, permanent environmental and maternal permanent environmental assuming homogeneous and heterogeneous residual variance during the time. Akaike (BIC) and Bayesian (BIC) information criteria were used to compare the Models and bspq.4.4.4.4 was selected as the best Model. The direct heritability values for birth, 3-month, 6-month, 9-month and 12-month weights were estimated to be 0.14, 0.16, 0.08, 0.28 and 0.26, respectively. Genetic correlation between body weights at birth and 3-month, birth and 6-month, birth and 9-month, birth and 12-month, 3-month and 6-month, 3-month and 9-month, 3-month and 12-month, 6-months and 9-month and 9-month and 12-month were 0.22, 0.38, 0.21, 0.56, -0.26, 0.30, 0.62, 0.86 and 0.77, respectively. The highest phenotypic correlation was between the weight of 9-month and 12-month (0.82) and the lowest correlation was between birth weight and 3-month and 6-month (0.12). The results showed that the 9-month weight is a good criterion for selection in Markhoz goats.

Background & Aim: One of the basic assumptions in simple linear Regression Models is the statistical independence of observations. Sometimes this assumption is not true for study subject and consequently the use of general Regression Models may not be appropriate. In this case, one of the leading methods is the use of multilevel Models. The present study utilizes multivariate Logistic Regression Model using a multilevel Model to exhibit the chance of having elbow, wrist and knee disorders over the past year based on elbow, wrist and disorders during the past week. Methods & Materials: This study is a cross-sectional study that was carried out from April 2015 to May 2016 in Mobarakeh Steel Company, Isfahan. The study population includes 300 male employees of Mobarakeh Steel Company, with a mean age of 41. 40± 8. 17 years and an average working experience of 16. 0± 7. 66 years. Data were analyzed using SPSS (version 24) and MLwiN software. Results: Based on this study, results obtained from single variable and multivariable Regression were different. Conclusion: Based on this study, it can be suggested that multivariable Regression cause a better and more accurate deduction compared to single variable method.

In many applications we have to encountered with bounded dependent variables. Beta Regression Model can be used to deal with these kinds of response variables. In this paper we aim to study spatially correlated responses in the unit interval. Initially we introduce spatial beta generalized linear mixed Model in which the spatial correlation is captured through a Random effect. Then the performances of the proposed Model is evaluated via a simulation study, implementing Bayesian approach for parameter estimation.Finally the application of this Model on two real data sets about migration rate and divorce rate in Iran are presented.

This paper investigates non linear Effects of income on health expenditure (as out of pocket payment). The explanatory variables in health expenditure equation include urbanization, age, insurance, employment of household's head, the number of people employed, earned income and the number of persons aged fewer than 12 and over 60 years in the household. Database used was chosen from the household income & expenditure surveys in 1386. Database contains 31277 rural and urban households. Linear and non-linear econometric Models based on Logistic smooth transition Regression (STR) are estimated. One of the most important findings is that health spending shows asymmetric behavior relative to household income or total expenditure (as a transition variable) so that the impact of explanatory variables on health expenditure in the high and low income regime is different. Also the results show that health expenditure is a necessary good for households, because the coefficient of the logarithm of income in the demand function is positive and much smaller than unity. In addition, out of pocket payments for health care services in high income groups are more than low income ones. Based on the results, with increased urbanization and for high aged people (beyond sixty years of old), health expenditure increase but if family members are covered by insurance, out of pocket payment for health expenses will reduce. So, it is important to develop the social security system and increase its efficiency to cover more health expenditure, especially for poorer households which lead to justice in health areas and increase in welfare of society.

The optimal criteria are used to find the optimal design in the studied Model. These kinds of Models are included the paired comparison Models. In these Models, the optimal criteria (D-optimality) determine the optimal paired comparison. In this paper, in addition to introducing the quadratic Regression Model with Random Effects, the paired comparison Models were presented and the optimal design has been calculated for them.

Following a Bayesian statistical inference paradigm, we provide an alternative methodology for analyzing a multivariate Logistic Regression. We use a multivariate normal prior in the Bayesian analysis. We present a unique Bayes estimator associated with a prior which is admissible. The Bayes estimators of the coefficients of the Model are obtained via MCMC methods. The proposed procedure is illustrated by analyzing a data set which has previously been analyzed by various authors. It is shown that our Model is more precise and computationally less taxing.