Description
wald.asreml: Pseudo analysis of variance using incremental Wald statistics or conditional F-tests.
Usage
## 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"), ...)
Arguments
object |
An asreml object. |
Ftest |
A one sided formula of the form ~ test-term | background-terms specifying a conditional Wald test of the contribution of test-term conditional on those listed in background-terms, and the those in the random and sparse model formulae. |
denDF |
Compute approximate denominator degrees of freedom: can be “none” (the default) to suppress the computations, “numeric” for numerical methods, “algebraic” for algebraic methods or “default” to automatically choose numeric or algebraic computations depending on problem size. The denominator degrees of freedom are calculated according to Kenward and Roger (1997) for fixed terms in the dense part of the model. |
ssType |
Can be “incremental” for incremental sum of squares (the default) or “conditional” for F-tests that respect both structural and intrinsic marginality. |
kenadj |
Can be “none” (the default) to compute Wald statistics using an unadjusted variance matrix for the fixed effects, “expected” to adjust for expected information, or “observed” to adjust for observed information. |
... |
Arguments to asreml can be passed through update.asreml if ssType is not “incremental“. |
Details
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.
Value
| A list with class wald with the following components: | |
| wald | An anova object if denDF="none" and ssType = "incremental", or a data frame otherwise. |
| stratumVariances | If denDF is not “none“, a matrix of approximate stratum variances, degrees of freedom and component coefficients is returned for simple variance component models. |
References
Kenward MG and Roger JH (1997). “The Precision of Fixed Effects Estimates from Restricted Maximum Likelihood.” Biometrics, 53, pp. 983-997