Degrees of freedom

As far as it is possible, inferential tests are based on an automatic selection of the degrees of freedom for the t-tests and the F-tests.

• For the t-tests the module relies on the Satterthwaite approximation of degrees of freedom as it is implemented by the lmerTest package. Lmertest::summary() produces t-test DF and p-values in the majority of cases. When the model does not converge, or some problem with the model occurs, the DF cannot be estimated and thus the p-values are not reported in the parameter estimates table. A warning note is displayed in those cases. See details in lmerTest package.

• For the F-tests of the main model (“Fixed Effects ANOVA”), the module relies again on the Satterthwaite approximation of degrees of freedom as it is implemented by the lmerTest package. Lmertest::anova() has difficulties in calculating F-test DF and p-values when the model does not converge, there are problems with the model random variances, or when numerical independent variables appear in complex interactions. When the lmerTest::anova() does not produce the DF and p-values, the module switches to car::Anova(..,type=3, test="F") function of the R car package. car::Anova(..,type=3, test="F") implements the Kenward-Roger method for degrees of freedom. A warning note is displayed in those cases.

• For F-tests of simple effects, the car::Anova(..,type=3, test="F") is always used, thus the the Kenward-Roger method for degrees of freedom is employed. This is because the lmertest::anova() requires the factor contrast to be contr.sum(), which does not allow to estimate simple effects. car::Anova(..,type=3, test="F") has not such a limitations, so it works fine for the purpose.

Post Hocs

Post-hocs tests are performed as implemented in the emmeans package. In particular, the actual implementation is as follows (for any given model term selected by the user) :

      formula <- as.formula(paste('~', term))
      referenceGrid <- emmeans::emmeans(private$.model, formula)
      bonferroni <- summary(pairs(referenceGrid, adjust='bonferroni'))
      holm <- summary(pairs(referenceGrid, adjust='holm'))
      tukey<-summary(pairs(referenceGrid, adjust='tukey'))
      scheffe<-summary(pairs(referenceGrid, adjust='scheffe'))
      sidak<-summary(pairs(referenceGrid, adjust='sidak'))

      

Optimizer

Estimating a mixed model requires to minimize several quantities and to refine the numerical solution is several ways. These operations are based on an algorithm that optimize the minimization. Different algorithms are available in R package lme4 provides different algorithms, among which the bobyqa, the Nelder_Mead and the nloptwrap algorithm see lme4 vignettes. GAMLj automatically starts the estimation using the bobyqa algorithm. If the model does not converge, it move to Nelder_Mead, and, upon a new failure, tries nloptwrap. If none converges, the first estimation is provided and a warning is issued.