Modeling correlated ordinal response data is usually more complex than the case of continuous and binary responses. Existing literature lacks an appropriate approach to modeling such data. For small sample sizes, however) these models lose their appeal since their inferences arc based OIl large samples. In this work, the Bayesian analysis of an asymmetric bivariate ordinal latent variable model has been developed. The latent response variable has been chosen to follow the generalized bivariate Gumble distribution. Using some specific priors and MCMC algorithms the regression parameters were estimated. As an application, a data set concerning Diabetic Retinopathy in 116 patients have been analyzed. This data set includes the disease status of each eye for patients as an ordinal response and a number of explanatory variables some of which are common to both eyes and the rest are organ specific.

Background: Response variables in most medical and health-related research have an ordinal nature. Conventional modeling methods assume predictor variables to be independent, and consider a large number of samples (n) compared to the number of covariates (p). Therefore, it is not possible to use conventional models for high dimensional genetic data in which p > n. The present study compared the predictive performance of decision trees, ordinal forest, and L1 penalized continuation ratio regression. Materials and Methods: In the present study, three data sets were used. The B-cell data contained 12, 625 gene expression data related to 128 patients with four ordinal levels of response variables. The HCC data related to liver cancer included 1469 genes of 56 patients with three ordinal levels of response variables. The Heart data contained information of five variables in 294 patients undergoing angiography with five ordinal levels of response variables. The performance of the methods was compared based on the same training and test datasets using indicators such as accuracy, gamma, and kappa. Results: For two high-dimensional data sets, the ordinal forest model had a higher predictive ability while for the low-dimensional data set, the L1 penalized continuation ratio model had a better predictive performance. Conclusion: The selection of the best prediction model depends on the data set, and for each data, different methods should be considered to achieve the best model.

In real life, occurrences of a series of things are supposed to come in an order. Therefore, it is necessary to regard sequence as a crucial factor in managing different kinds of things in fuzzy environment. However, few related researches have been made to provide a reasonable solution to this demand. Therefore, how to measure degree of uncertainty of ordinal fuzzy sets is still an open issue. To address this issue, a novel ordinal fuzzy entropy is proposed in this paper taking orders of propositions into consideration in measuring level of uncertainty in fuzzy environment. Compared with previously proposed entropies, effects on degrees of fuzzy uncertainty brought by sequences of sequential propositions are embodied in values of measurement using proposed method in this article. Moreover, some numerical examples are offered to verify the correctness and validity of the proposed entropy.

This paper studies the symmetrical relation between the underground economy and taxes in Iran using the most appropriate method for measuring this relationship applying the error-correction model. According to the results directed taxes have much more effect on the underground economy in the long-run and the indirect taxes are the more effective in the short-run. Moreover the underground economy shows a symmetric response to the direct tax changes but not to the indirect tax changes. The symmetric reaction of the underground economy to the changes of direct tax in Iran implies that taxpayers show symmetrical tendency to tax evasion when direct tax increases and enter to the formal economy when the direct tax decreases.

In this paper, by using the notion of ordinal sum of equality algebras which is defined in [4], we investigate some related properties and different kinds of filters of it such as prime and maximal. In addition, by focusing on chain equality algebra, we define the concept of a cut of an equality algebra and use it to introduce a new ordinal sum of them. By defining a relation relative to a cut, we show that the family of classes is made a cone algebra. Finally, we prove that every chain equality algebra can be represented as an ordinal sum of chain cone algebras.

In this paper, the fuzzy subnexuses over a nexus N are de ned and the notions of prime fuzzy subnexuses and fractions induced by them are studied. Finally, it is shown that if S is a meet closed subset of the set Fsub(N), of fuzzy subnexuses of a nexus N, and h = ∧ S ∈ S, then the fractions S􀀀 1N and {h}􀀀 1N are isomorphic as meet-semilattices.