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 are based on 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.

Skew Normal distribution is important in analyzing non-normal data. The probability density function of skew Normal distribution contains integral function which tends researchers to some problems. Because of this problem, in this paper a simpler Bayesian approach using conditioning method is proposed to estimate the parameters of skew Normal distribution. Then the accuracy of this metrology is compared with ordinary Bayesian method in a simulation study.

In two level modeling, random effect and error's normality assumption is one of the basic assumptions. Violating this assumption leads to incorrect inference about coefficients of the model. In this paper, to resolve this problem, we use skew normal distribution instead of normal distribution for random and error components. Also, we show that ignoring positive (negative) skewness in the model causes overestimating (underestimating) in intercept estimation and underestimating (overestimating) in slope estimation by a simulation study. Finally, we use this model to study relationship between shift work and blood cholesterol.