In certain statistical process control applications, quality of a process or product can be characterized by a function between response variable and one or more independent variables. This function commonly referred to as profile. Response variable can be continuous or discrete. All of the research assumes that the response variable is continuous. Whereas, some of the potential applications of profile monitoring are cases where the output can be modeled using polytomous (especially Multinomial) or binary logistic regression models. Polytomous response variables, especially Multinomial variables, can have various applications especially in service industry. In this paper, we propose some methods for monitoring a profile when the process output is a Multinomial response variable. Multinomial logistic regression (OLR) provides the basis for our profile model. Performances of the proposed methods in terms of the signal probability for different out-of-control scenarios are compared based on simulation studies.

Inspired by the interactive discrete choice logit models [Aggarwal, 2019], this paper presents the advanced families of discrete choice models, such as nested logit, mixed logit, and Probit models to consider the interaction among the attributes. Besides the DM’ s attitudinal character is also taken into consideration in the computation of choice probabilities. The proposed choice models make use of Choquet integal and the recent attitudinal Choquet integral. The models are termed as Choquet nested logit (CNL), Choquet mixed Multinomial logit (CMMNL), and Choquet Multinomial Probit (CMP). These are further extended to represent the DM’ s attitudinal character, and termed as attitudinal CNL, attitudinal CMMNL, and attitudinal CMP.

Background & Aim: Questionnaires are used mostly as a tool in medical research. Due to the different varieties of questionnaires, we may face different score distributions. In many cases multiple linear regression assumptions are violated. Beta-binomial regression model has the high flexibility and compatibility with this situation. In previous studies there were no comparison between beta-binomial accuracy and other models to fitting quality of life data. So in this study, our aim is to compare the accuracy of models to prediction. Methods & Materials: In this cross-sectional study we collected the quality of life data from 511 healthy women in Qazvin, Iran. The data were used to compare accuracy of betabinomial model and with some other models. Since beta-binomial considers the discrete response variable, so it should be compared with other similar models which are mostly used such as Multinomial, dirichlet-Multinomial and ordinal regression models. The main method that we used in our study was cross-validation to determine the accuracy of different models. To compare the different aspects, vast variety of situations were made and considered. Results: Regarding to the accuracy of models that were obtained by cross-validation in different situations, beta-binomial model had better accuracy among all models. Conclusion: According to the results, we have concluded that beta-binomial model is more accurate in prediction and fitting to the quality of data than the other models. The main advantages of this model are its simplicity, more efficacy and accuracy than the similar models.

In certain statistical process control applications, quality of a process or product can be characterized by a function commonly referred to as profile. Some of the potential applications of profile monitoring are cases where quality characteristic of interest is modelled using binary, Multinomial or ordinal variables. In this paper, profiles with Multinomial response are studied. For this purpose, Multinomial log it regression (MLR) is considered as the basis. Then, the MLR is converted to Poisson GLM with log link. Two methods including Multivariate exponentially weighted moving average (MEWMA) statistics, and Likelihood ratio test (LRT) statistics are proposed to monitor MLR profiles in phase II. Performances of these three methods are evaluated by average run length criterion (ARL). A case study from alloy fasteners manufacturing process is used to illustrate the implementation of the proposed approach. Results indicate satisfactory performance for the proposed method.

Introduction Statistical shape analysis is one of the fields of multivariate statistics, where the main focus is on the geometric structures of objects. This analysis method is widely used in many scientific fields, such as medicine and morphology. One of the tools for diagnosing diseases or determining animal species is the images and the shapes extracted from them. Introducing methods of classifying shapes can be a solution to determine the class of each observation. Usually, in regression modelling, explanatory and dependent variables are quantitative. However, one may want to measure the relationship between an explanatory variable (with continuous values) and a dependent variable with qualitative values. One option is to use the Multinomial logistic regression model. Therefore, a semiparametric Multinomial logistic regression model to classify shape data is introduced in this paper. Material and Methods The power-divergence criterion is a measure for hypothesis testing in Multinomial data. This criterion is used to define the kernel function of explanatory variables. The model is a Multinomial logistic regression model based on kernel function as a function of explanatory variables and an intercept. Since the shapes’,geometric structure and size play a key role in the classification of shapes, the kernel function is determined based on the shape distances. The smoothing parameter was estimated using the least square cross-validation method. Also, the estimation of model parameters was done using the neural network method. Results and Discussion The shape space is a manifold, but most of the methods presented in the literature for classifying shapes were done in the shape tangent space or used linear transformations. Since mapping from the manifold to linear space decreases data information, applying tangent space and linear spaces will reduce classification accuracy. Therefore, the shape space is used to classify the shape data. The performance of the model in a simulation study and two real data sets were investigated in the paper. The two real data sets used in this paper are taken from the shape package in R software. The first data set is related to schizophrenia patients and people as control, and the second one is associated with the skull of three species of apes of two sexes. The classification of these data showed an accuracy of 82% and 84%, respectively. Also, a comparison was made with the previous methods based on a real data set, which showed the proper performance of our approach compared to the other two techniques. Conclusion Since in the nonparametric kernel function, suitable distances of the shape space were used, the introduced method performs better than those based on Euclidean spaces. Also, the ability to use other shape distances, such as partial, full Procrustes and Riemannian distances, makes the model more flexible in classifying different types of shape data. On the other hand, sizeand-shape distance can be used in the kernel function to classify data whose size plays a key role in their geometric structure. Furthermore, since few statistical distributions have been introduced in the shape space, nonparametric methods can be helpful in the analysis of shape data. However, using nonparametric methods in the shape space is time-consuming from the point of view of computer calculations.

Organic agriculture is one of the sustainable farming systems that emphasizes economic, social, and environmental aspects to achieve sustainability targets. This study aims to identify the economic, social, and environmental factors affecting organic product production from the perspective of experts and 150 farmers in Jiroft County. The results revealed that low government financial support for organic farmers (average rating of 3.8133) is the most effective factor, while lack of adequate marketability (average rating of 2.6733) is the least effective factor among the barriers to achieving organic agriculture. from the farmers' perspective. According to experts, organic farming serves as a tool for improving public health conditions, (average rank of 11.66), which it is determined as the most effective factor. However, it does not significantly contribute to self-sufficiency in agricultural production, with an average rank of 6.07, being the least influential factor among the factors affecting organic farming. Among the average ranks of the components of influential factors in organic farming (educational, economic, social-managerial indicators), the lowest ranking is the government's financial support for organic farmers (average rank of 3.13), making it the most influential. Whereas, the lack of suitable marketability with an average rank of 2.67 is the least influential factor among the factors affecting organic farming. Furthermore, the results show that holding promotional and educational classes has a positive and significant impact on the acceptance of organic cultivation, as following the recommendations of promoters and having the necessary education can increase production and reduce costs.