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‎Latent class analysis (LCA) is a method of evaluating non sampling errors‎, ‎especially measurement error in categorical data‎. ‎Biemer (2011) introduced four latent class modeling approaches‎: ‎probability model parameterization‎, ‎log linear model‎, ‎modified path model‎, ‎and graphical model using path diagrams‎. ‎These models are interchangeable‎. ‎Latent class probability models express likelihood of cross-classification tables in term of conditional and marginal probabilities for each cell‎. ‎In this approach model parameters are estimated using EM algorithm‎. ‎To test latent class model chi-square statistic is used as a measure of goodness-of-fit‎. ‎In this paper we use LCA and data from a small-scale survey to estimate misclassification error (as a measurement error) of students who had at least a failing grade as well as misclassification error of students with average grades below 14‎.

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The ordinary linear regression model is $Y=Xbeta+varepsilon$ and the estimation of parameter $beta$ is: $hatbeta=(X'X)^{-1}X'Y$. However, when using this estimator in a practical way, certain problems may arise such as variable selection, collinearity, high dimensionality, dimension reduction, and measurement error, which makes it difficult to use the above estimator. In most of these cases, the main problem is the singularity of the matrix $X'X$. Many solutions have been proposed to solve them. In this article, while reviewing these problems, a set of common solutions as well as some special and advanced methods (which are less favored by someone, but still have the potential to solve these problems intelligently) to solve them.