In some applications, the response variable assumes values in the unit interval. The standard LINEAR regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symmetric and skewed families. In this paper, a beta generalized LINEAR MIXED model with spatial random effect is proposed emphasizing on small values of the spatial range parameter and small sample sizes. Then some MODELS with both fixed and varying precision parameter and different combinations of priors and sample sizes are discussed. Next, the Bayesian estimation of the model parameters is evaluated in an intensive simulation study. Selected priors improved the Bayesian estimation of the parameters, especially for small sample sizes and small values of range parameter. Finally, an application of the proposed model on data provided by Household Income and Expenditure Survey (HIES) of Tehran city is presented.

Semiparametric LINEAR MIXED measurement error MODELS are extensions of LINEAR MIXED measurement error MODELS to include a nonparametric function of some covariate. They have been found to be useful in both cross-sectional and longitudinal studies. In this paper first we propose a penalized corrected likelihood approach to estimate the parametric component in semiparametric LINEAR MIXED measurement error model and then using the case deletion and subject deletion analysis we survey the influence diagnostics in such MODELS. Finally, the performance of our influence diagnostics methods are illustrated through a simulated example and a real data set.

When discussing non-Gaussian spatially correlated variables, generalized LINEAR MIXED MODELS have enough flexibility for modeling various data types. However, the maximum likelihood methods are plagued with substantial calculations for large data sets, resulting in long waiting times for estimating the model parameters. To alleviate this drawback, composite likelihood functions obtained from the product of the likelihoods of subsets of observations are used. The current paper uses the pairwise likelihood method to study the parameter estimations of spatial generalized LINEAR MIXED MODELS. Then, we use the weighted pairwise and penalized likelihood functions to estimate the parameters of the mentioned MODELS. The accuracy of estimates based on these likelihood functions is evaluated and compared with full likelihood function-based estimation using simulation studies. Based on our results, the penalized likelihood function improved parameter estimation. Prediction using penalized likelihood functions is applied. Ultimately, pairwise and penalized pairwise likelihood methods are applied to analyze count real data sets.

In this study, the stochastic restricted and unrestricted two-parameter estimators of fixed and random effects are investigated in the LINEAR MIXED measurement error MODELS. For this purpose, the asymptotic properties and then the comparisons under the criterion of mean squared error matrix (MSEM) are derived. Furthermore, the proposed methods are used for estimating the biasing parameters. Finally, a real data analysis and a simulation study are provided to evaluate the performance of the proposed estimators.

In this paper, we introduce the weighted ridge estimators of fixed and random effects in stochastic restricted LINEAR MIXED measurement error MODELS when colLINEARity is present. The asymptotic properties of the resulting estimates are examined. The necessary and sufficient conditions, for the superiority of the weighted ridge estimators against the weighted estimator in order to select the ridge parameter based on the mean squared error matrix of estimators, are investigated. Finally, theoretical results are augmented with a simulation study and a numerical example.

This paper is concerned with the estimation problem in semiparametric LINEAR MIXED MODELS when some of the covariates are measured with errors. The authors proposed the corrected score function estimators for the parametric and non parametric components. The resulting estimators are shown to be consistent and asymptotically normal. An iterative algorithm is proposed for estimating the parameters. Asymptotic normality of the estimators is also derived. Finite sample performance of the proposed estimators is assessed by Monte Carlo simulation studies. We further illustrate the proposed procedures by an application.