This package provides a modification of the lmer() function from the lme4 package. It estimates a spherical correlation of random effects when interacting fixed factors with random samples. The method is explained in detail in The correlation structure of mixed effects models with crossed random effects in controlled experiments.
Currently lme4 has the possibiliy to estimate the spherical random effects using + (1|id:f). However the parametrization used in lme4 puts constraints on lower interaction parameters, such that the covariance estimated using + (1|id) + (1|id:f) may have the variance of (1|id) estimated at the boundary (or simply 0). gANOVA reparametrizes the covariance matrix in order to extend the range of parameters such that variance of lower interactions estimated at 0 happen less. Check the vignette for examples.
Technically, this new parametrization is simply transforming factors into orthonormal contrasts and imposing a unique variance parameter for all contrasts of the factors.
Currently, the notation in lmer() to estimate spherical covariance of random effect is using + (1|id) + (1|id:f) + (1|id:g) + (1|id:f:g). This notation can be used in gANOVA() for this new parametrization. However, gANOVA() also provides a simplification of the notatation, such that + (1|id) + (1|id:f) + (1|id:g) + (1|id:f:g) may be rewritten simply as + (1|id|f*g).
Note that the gANOVA() is a “hack” of lmer()and should be used carefully. For instance, the sampling units, here represented by id should always be written after the first vertical. If + (1|id:g) equivalent to + (1|g:id) in lmer(), it is NOT the case in gANOVA().
Installation
Make sure to install gANOVA with its full documentation:
devtools::install_github("jaromilfrossard/gANOVA", build_vignettes = TRUE)
To see the difference between the lme4 and the gANOVA parametrization of the spherical correlation structure check the vignette or run:
vignette("spherical-distribution-example", package = "gANOVA")
