R for Mixed models

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Computing power and software programs have made the analysis of mixed models more available.

If you have undertaken one statistical course you may be wondering “where can I get an introduction to the principles of mixed modeling ?”

As usual there are a few words and definitions you will need to get used to:

Fixed effects and Random effects

Nested or Crossed designs

R package for Linear Mixed Models Function within the package for linear mixed models Can the model cope with non constant variance ?
lme4 lmer function for fi tting linear mixed models.
lmer can accommodate crossed random effects.
nlme lme function for fi tting linear mixed models.
cannot have crossed random effects
You can model non-constant error variance, via the weights argument to lme.
RGxE  For fi tting linear mixed models. studying performance of quantitative traits under different environmental conditions. (for  balanced data).  recently published by Mahendra Dia, Todd C. Wehner, Consuelo Arellano in American J. of Plant Sciences, 2017, 8, 1672-1698  (http://www.scirp.org/journal/ajps)

Outputs and Questions we look for in the analysis output:

Fixed effects: we look at the coefficients overall and within a subject.

Random effects:   Are the variances of the random effects in the model are different from 0.

We have to become familiar with Analysis of Deviance, AIC, the Wald statistic and other model outputs.

These two figures explain in a simple visual way that we are looking at the different slopes and intercepts of groups, and sometimes there is a non constant variance within a group over time

From reference ( https://stats.stackexchange.com/questions/51186/what-would-be-an-illustrative-picture-for-linear-mixed-models)