ANOVAtype analysis of fixed effect parameters
Description
fixef.varComp
and anova.varComp
test for fixed effect contrasts, as well as providing standard errors, etc.
Usage
1 2 3 4 5 6 
Arguments
object,x 
An object of class 
Lmat,L 
A matrix specifying the linear combinations of fixed effect parameters to be tested for nullity. Each row is a linear combination. If the column names are nonnull, the columns will be reordered according to the column names of 
alpha 
The requested level of test. 
test 
A character scalar requesting the type of the tests to be performed. 
... 
For 
Value
For anova.varComp
, this is a data frame with the following columns:

F value
: The scaled Fstatistic; 
Scale
: The multiplicative factor in the scaled Fstatistic; 
numDF
: The numerator degrees of freedom; 
denDF
: The denominator degrees of freedom; 
Pr(>F)
: The pvalue.
When ...
is missing but L
is given, each row of L
matrix will have a corresponding row in the result, testing the nullity of linear contrasts specified by that row of L
. Additionally, an "Overall" row will be the last row, testing the nullity of linear contrasts of all rows of L
.
When ...
is not missing, L
will be ignored and the result will have the same number of rows as the number of varComp
objects given (including the first object
argument). The order of rows is such that the rank of the fixed effect design matrix is nondecreasing, i.e., smaller models first. The results will be the comparison between the current model vs. the model in the preceding row, except for the first row. For the first row, the model being compared is a null model. If the fixed effect design matrix for the model in first row includes the intercept in its column space, the null model includes only an intercept. If the intercept is not in the column space of the first model, the null model will contain no fixed effects.
When both ...
and L
are missing, anova.varComp
will test each fixed effect parameters together with a last "Overall" row. However, this last row will remove the intercept from the model, if there is one. See example below.
For fixef.varComp
, the result is an object with class varCompFixEf
. This is a named numeric vector, providing estimates of fixed effect contrasts specified by Lmat
. The name will be the row names of Lmat
. It has the anova
attribute, a numeric matrix with the following columns:

Std. Error
: the standard error of estimate. Iftest='KR'
, this is the adjusted standard error. Iftest='Satterthwaite'
, this is the plugin estimate. 
Lower
: the lower limit of the1alpha
confidence interval. 
Upper
: the upper limit of the1alpha
confidence interval. 
t value
: the scaled tstatistic testing nullity of this contrast. 
Scale
: a multiplicative factor in the scaled tstatistic. 
Df
: the degrees of freedom for the tstatistic. 
Pr(>t)
: the pvalue.
Additionally, the anova
attribute also has the Overall
attribute, which is a singlerow matrix with the same columns as the results of anova.varComp
, testing for the overall nullity of linear contrasts specified by Lmat
.
print.varCompFixEf
prints the result from fixef.varComp
and return the argument invisibly.
Warning
When neither
...
norL
is given foranova.varComp
, the current implementation will test each fixed effect parameter separately. This behavior might be changed in future releases.When
L
is not explicitly given, the current implementation will rely ongetOption("digits")
when trying to find theL
matrix that test the difference between adjacent models.
Author(s)
Long Qu
References
Michael G. Kenward and James H. Roger (1997) Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 53, 983–997
Waseem S. Alnosaier (2007) KenwardRoger Approximate F Test for Fixed Effects in Mixed Linear Models. Oregon State University Department of Statistics Ph.D. Thesis
Fai and Cornelius (1996) Approximate Ftests of multiple degree of freedom hypotheses in generalized least squares analyses of unbalanced splitplot experiments. Journal of Statistical Computation and Simulation 54, 363378
See Also
satterth.varComp
, KR.varComp
Examples
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