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.
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*****
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
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d.f.
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Wald/d.f.
|
Chi-sq prob
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* Sequentially adding terms to
fixed model
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YEAR
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244.93
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5
|
48.99
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<0.001
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SEX
|
11.35
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1
|
11.35
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<0.001
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AGEWEAN
|
69.78
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1
|
69.78
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<0.001
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DL
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30.72
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1
|
30.72
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<0.001
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DQ
|
55.91
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1
|
55.91
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<0.001
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RAM_BRD
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9.10
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1
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9.10
|
0.003
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EWE_BRD
|
6.13
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1
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6.13
|
0.013
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