Nonparametric REML-like Estimation in Linear Mixed Models with Uncorrelated Homoscedastic Errors

Restricted Maximum Likelihood (REML) is the most recommended approach for fitting a Linear Mixed Model (LMM) nowadays. Yet, as ML, REML suffers drawback that it performs such by assuming normality both random effects and residual errors, dubious assumption many real data sets. Now, there have been several attempts at trying to justify use of likelihood equations outside Gaussian world, with varying degrees success. Recently, new methodology, code named 3S, was presented LMMs only added (to basic ones) errors are uncorrelated homoscedastic. Specifically, 3S-A1 variant designed then shown, LMMs, differ slightly from ML estimation. In this article, using same 3S framework, we develop another iterative nonparametric estimation 3S-A1.RE, kind just mentioned. However, show if LMM is, indeed, i.i.d. set estimating defining any 3S-A1.RE procedure equivalent equations, but while including nonnegativity constraints on all variance estimates, well positive semi-definiteness covariance matrices. numerical tests some simulated world clustered longitudinal sets, our methods proved be highly competitive when compared traditional in R statistical software.