A recursive algorithm on estimating the parameters in multilevel models subject to the measurement errors on the covariates - Golalizadeh, Mousa; Mahmoudnejad, Hashem (Journal of statistical computation and simulation, 2016)
Multilevel models are popular models for analysing data inheriting a hierarchical structure. They are used in diverse fields including social, medical, economical and biological sciences. These models encounter some problems in estimating the parameters, if there are measurement errors in either explanatory or response variables. A common approach to tackle this obstacle is to consider the pseudo variables and follow some simulation methods to estimate the parameters. We propose a new algorithm constituting the iterative and simulation extrapolation steps in turn. To evaluate the proposed algorithm, various simulation studies are also conducted. Moreover, we investigate the implementation of our method on a real data set concerning the cost and expenditure of the households in Tehran city in the year 2007.