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 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'))In Mixed module only bonferroni and
holm methods are implemented yet, because I did not find
enough evidence in the literature in support of other methods.
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