wald.asreml {asreml} | R Documentation |
Pseudo analysis of variance using incremental Wald statistics or conditional F-tests.
## S3 method for class 'asreml' wald(object, Ftest = formula("~NULL"), denDF = c("none", "default", "numeric", "algebraic"), ssType = c("incremental", "conditional"), kenadj = c("none", "expected", "observed"), ...)
object |
An |
Ftest |
A one sided formula of the form |
denDF |
Compute approximate denominator degrees of freedom: can be
|
ssType |
Can be |
kenadj |
Can be |
... |
Arguments to |
wald.asreml()
produces two styles of analysis of variance
table depending on the settings of denDF
and
ssType
. If denDF = "none"
and ssType =
"incremental"
(the defaults), a pseudo analysis of variance table
is returned based on incremental sums of squares with rows
corresponding to each of the fixed terms in the object, plus an
additional row for the residual. The model sum of squares is
partitioned into its fixed term components, and the sum of squares
for each term listed in the table of Wald statistics is adjusted
for the terms listed in the rows above. The denominator degrees of
freedom are not computed and consequently Wald tests are provided.
If either denDF
or ssType
are not set at their
default values, a data frame is returned that will include columns
for the approximate denominator degrees of freedom and incremental
and conditional F statistics depending on the combination of
options chosen. update.asreml
is called to complete the
calculations.
The principle used in determining the conditional tests is that a term cannot be adjusted for another term which encompasses it explicitly (for example, A:C cannot be adjusted for A:B:C) or implicitly (for example, REGION cannot be adjusted for LOCATION when locations are nested in regions although coded independently). See the vignette for further information.
The numerator degrees of freedom for each term is determinaed as the number of non-singular equations involved in the term. However, the calculation of the denominator df is in general not trivial and is computationally expensive. Numerical derivatives require an extra evaluation of the mixed model equations for every variance parameter while algebraic derivatives require a large dense matrix, potentially of order the number of equations plus the number of observations. The calculations are supressed by default.
A list with class wald
with the following components:
An anova
object if denDF="none"
and
ssType = "incremental"
, or a data frame otherwise.
If denDF
is not "none"
, a
matrix of approximate stratum variances, degrees of freedom and
component coefficients is returned for simple variance component
models.
Kenward MG, Roger JH (1997). “The Precision of Fixed Effects Estimates from Restricted Maximum Likelihood.” Biometrics, 53, 983-997.