wald.asreml {asreml} | R Documentation

## Wald test constructor for asreml objects.

### Description

Pseudo analysis of variance using incremental Wald statistics or conditional F-tests.

### Usage

    ## S3 method for class 'asreml'
    wald(object, ..., incr = FALSE)

### Arguments

`object` | An `asreml` object.
`incr` | If `TRUE` (the default is `FALSE`) only incremental Wald tests are returned irrespective of the `asreml` argument `ssType`.

### Details

`wald.asreml()` produces two styles of analysis of variance table depending on the settings of `denDF` and `ssType` on the `asreml` function call. 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, Roger JH (1997). “The Precision of Fixed Effects Estimates from Restricted Maximum Likelihood.” Biometrics, 53, 983–997.

[Package asreml version 4.1.0.176 Index]