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In parameter driven models, the main problem is likelihood approximation and also parameter estimation. One approach to this problem is to apply simpler likelihoods such as composite likelihood. In this paper, we first introduce the parameter driven models and composite likelihood and then define a new model selection criterion based on composite likelihood. Finally, we demonstrate composite likelihood's capabilities in inferences and accurate model selection in parameter driven models throughout a simulation study.

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In this paper parameters of spatial covariance functions have been estimated using block composite likelihood method. In this method, the block composite likelihood is constructed from the joint densities of paired spatial blocks. For this purpose, after differencing data, large data sets are splited into many smaller data sets. Then each separated blocks evaluated separately and finally combined through a simple summation. The advantage of this method is that there is no need to inverse and to find determination of high dimensional matrices. The simulation shows that the block composite likelihood estimates as well as the pair composite likelihood. Finally a real data is analysed.