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.

The nonparametric and semiparametric regression models have been improved extensively in the field of cross-sectional study and independent data, but their improvement in the field of longitudinal data is restricted to the recent years or decade. Since the common methods for correlated data have a much lower ability rather than for the independent data, we should use the models which consider the correlation among the data. The mixed and marginal models consider the correlation factor among the data, and so obtain a better fit for that. Furthermore, the semiparametric regression has more flexibility compared to the parametric and nonparametric regression. Consequently, based on the properties of the longitudinal data, the marginal longitudinal semiparametric regression with the penalized spline estimations, is a suitable choice for the analysis of the longitudinal data. In this article, the semiparametric regression with different coefficients which specifies the relationship between a response variable and an explanatory variable based on another explanatory variable is assessed. In addition, Bayesian inference on the nonparametric model for a simulated data and the marginal longitudinal semiparametric model for a real data have been done by standard software; and the results have good performance.

Introducing some efficient model selection criteria for mixed models is a substantial challenge; Its source is indeed fitting the model and computing the maximum likelihood estimates of the parameters. Data cloning is a new method to fit mixed models efficiently in a likelihood-based approach. This method has been popular recently and avoids the main problems of other likelihood-based methods in mixed models. A disadvantage of data cloning is its inability of computing the maximum of likelihood function of the model. This value is a key quantity in proposing and calculating information criteria. Therefore, it seems that we can not, directly, define an appropriate information criterion by data cloning approach. In this paper, this believe is broken and a criterion based on data cloning is introduced. The performance of the proposed model selection criterion is also evaluated by a simulation study.