This work presents a new method for LATENT variable MIXED MODELS with missing data and extends the regression methods to obtain factor scores, as well as, letting covariates affect the LATENT variable directly. Maximum likelihood and least square methods are used to estimate model parameters and factor scores. The new model is applied to gross motor development data and the results are compared with two-stage factor analysis and structural equation MODELS.

Spatial generalized linear MIXED MODELS are usually used for modeling non-Gaussian and discrete spatial responses. In these MODELS, spatial correlation of the data can be considered via LATENT variables. Estimation of the LATENT variables at the sampled locations, the model parameters and the prediction of the LATENT variables at un-sampled locations are of the most important interest in SGLMM. Often the normal assumption for LATENT variables is considered just for convenient in practice. Although this assumption simplifies the calculations, in practice, it is not necessarily true or possible to be tested. In this paper, a closed skew normal distribution is proposed for the spatial LATENT variables. This distribution includes the normal distribution and also remains closed under linear conditioning and marginalization. In these MODELS, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, for maximum likelihood estimation of the model parameters and predictions of LATENT variables, an approximate algorithm is introduced that is faster than the former method. The performance of the proposed model and algorithm are illustrated through a simulation study.

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.