Exploration & description/ANOVA or REML?

By comparing the outputs from the previous two slides it can be seen that both the least squares analysis and the REML analysis without a random term obtain the same solutions (compare 'v.r.' and 'Wald/d.f.'). Just the format of the output is different. (Later we list the REML parameter estimates and associated standard errors; as will be seen these are the same as those from the least squares analysis.)

GenStat calculates values known as Wald statistics instead of F-values for a mixed model. The Wald test investigates the same hypotheses as the F test in the least squares analysis of variance – i.e. null hypothesis of no effect - but unlike the F-statistic, which follows an F-distribution, the Wald statistic follow a Chi-square distribution, but only approximately. 

Significance levels tend to be a little lower for the Wald test than for the F test when random terms are included, and this will, by and large, always be the case unless the sample size, as here, is comparatively large.

 
***** REML Variance Components Analysis *****

Response Variate : WEANWT

*** Approximate stratum variances ***
                                      Effective d.f.
*units*            4.933         688.00

*** Wald tests for fixed effects ***

Fixed term

Wald statistic

d.f.

Wald/d.f.

Chi-sq prob

* Sequentially adding terms to fixed model

YEAR

244.93

   5

48.99

<0.001

SEX

11.35

   1

11.35

<0.001

AGEWEAN

69.78

   1

69.78

<0.001

DL

30.72

   1

30.72

<0.001

DQ

55.91

   1

55.91

<0.001

RAM_BRD

9.10

   1

9.10

0.003

EWE_BRD

6.13

   1

6.13

0.013

Table of content  Back     next