Multilevel modeling

Computing the point estimates and standard errors with mixed models using matrices

  1. Estimating the OLS model using matrices As a starting point, just begin with using an OLS model and estimating the results using different matrices. The standard ordinary least squares model (OLS) can be written as: (y = XB + \varepsilon) where (X) is a design matrix, (B) is a column vector of coefficents, plus some random error (\varepsilon). Of interest is (B) which is obtained through: (B = (X'X)^{-1}(X'y)).