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< GenStat ~ WALD test in GLMM
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| Nick.Nicholls |
 Posted: Tue Feb 14, 2012 4:51 am |
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Running GLMM analyses across three response variables (assuming Poisson errors and using a log link) I appear to be getting two different headings to the table of Wald tests for fixed effects.
Why do I sometimes get a heading reading "Wald tests for fixed effects" and sometimes get "Tests for fixed effects"?
Dr A.O. Nicholls
Honorary Fellow
CSIRO Ecosystem Sciences
GPO Box 1700
CANBERRA ACT 2601
Telephone: (02) 6246 4132 (Tuesdays and Thursdays)
(02) 6236 8888 (Home)
Fax: (02) 6246 4094
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| Sue Welham |
| Posted: Wed Feb 15, 2012 8:45 am |
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This depends on whether adjustments are made to the Wald tests or not.
Heading "Wald tests for fixed effects" means that these are standard
Wald tests; heading "Tests for fixed effects" means that an adjustment
has been made to give approximate F-tests. The adjustment process
sometimes fails, and if failure is detected then the output reverts to
Wald tests, which may explain why you are getting a mixture of outputs.
Hope this helps,
Sue
Dr Sue Welham
VSN International Ltd
Software for Bioscientists
5 The Waterhouse, Waterhouse Street, Hemel Hempstead, HP1 1ES
Tel: +44 (0)1442 450 236, Fax: +44 (0)870 121 5653, Web: www.vsni.co.uk
Registered in England & Wales, company number: 4027977.
Registered office: 5 The Waterhouse, Waterhouse Street, Hemel Hempstead
HP1 1ES (England).
-----Original Message-----
From: GENSTAT-Request [mailto:GENSTAT@jiscmail.ac.uk] On Behalf Of
Nick.Nicholls@CSIRO.AU
Sent: 14 February 2012 04:51
To: GENSTAT@JISCMAIL.AC.UK
Subject: WALD test in GLMM
Running GLMM analyses across three response variables (assuming Poisson
errors and using a log link) I appear to be getting two different
headings to the table of Wald tests for fixed effects.
Why do I sometimes get a heading reading "Wald tests for fixed effects"
and sometimes get "Tests for fixed effects"?
Dr A.O. Nicholls
Honorary Fellow
CSIRO Ecosystem Sciences
GPO Box 1700
CANBERRA ACT 2601
Telephone: (02) 6246 4132 (Tuesdays and Thursdays)
(02) 6236 8888 (Home)
Fax: (02) 6246 4094
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| Nick.Nicholls |
| Posted: Wed Feb 15, 2012 10:36 pm |
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Sue,
Thank you for your reply. I admit that it does not initially make sense. So, firstly, is this feature documented somewhere? Secondly, if one asks for Wald tests and the heading indicates that standard Wald tests have been performed, why is an adjustment made that leads to presumably non standard Wald tests?
You then indicate that if the adjustment fails the tests revert to Wald tests, so does this imply that if the heading is of the form "Tests for fixed effects" the test of more appropriate or more reliable?
Dr A.O. Nicholls
Honorary Fellow
CSIRO Ecosystem Sciences
GPO Box 1700
CANBERRA ACT 2601
Telephone: (02) 6246 4132 (Tuesdays and Thursdays)
(02) 6236 8888 (Home)
Fax: (02) 6246 4094
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| Sue Welham |
| Posted: Thu Feb 16, 2012 7:50 am |
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Dear Nick,
Having looked at the documentation for the REML command, I agree that
the description is perhaps not as clear as it could be, and most of the
explanation about this is associated with the FMETHOD option, as
follows:
"The FMETHOD option controls whether to accompany the Wald tests for
fixed effects with approximate F statistics and corresponding numbers of
residual degrees of freedom. The computations, using the method devised
by Kenward & Roger (1997), can be time consuming with large or
complicated models. So, with the default setting FMETHOD=automatic,
GenStat assesses the model itself and decides automatically whether to
do the computations and which method to use. The other settings allow
you to control what to do yourself:
none = no F statistics are produced;
algebraic = F statistics are calculated using algebraic derivatives
(which may involve large matrix calculations);
numerical = F statistics are calculated using numerical derivatives
(which require an extra evaluation of the mixed model equations for
every variance parameter)"
To summarise the situation in the linear mixed model: Wald statistics
for fixed terms are an asymptotic test, and the asymptotic distribution
does not allow for the fact that the variance parameters are unknown. A
better approximation is usually achieved by the use of the approximate F
statistic and denominator df (Kenward & Roger, 1997 - full ref in help).
So, unless you explicitly turn it off using the FMETHOD option, REML
will calculate the F-statistic and approximate ddf. Occasionally this
fails - sometimes due to workspace issues (which can be addressed using
the WORKSPACE option of REML), sometimes due to a difficult combination
of parameter values and occasionally for no apparent reason. When
failure is detected (or seriously suspected) the output reverts to the
unadjusted Wald tests.
In GLMMs, the situation is slightly less straight-forward, but use of
the same procedures appears to be generally accepted.
Regards,
Sue
Dr Sue Welham
VSN International Ltd
Software for Bioscientists
5 The Waterhouse, Waterhouse Street, Hemel Hempstead, HP1 1ES
Tel: +44 (0)1442 450 236, Fax: +44 (0)870 121 5653, Web: www.vsni.co.uk
Registered in England & Wales, company number: 4027977.
Registered office: 5 The Waterhouse, Waterhouse Street, Hemel Hempstead
HP1 1ES (England).
-----Original Message-----
From: GENSTAT-Request [mailto:GENSTAT@jiscmail.ac.uk] On Behalf Of
Nick.Nicholls@CSIRO.AU
Sent: 15 February 2012 22:36
To: GENSTAT@JISCMAIL.AC.UK
Subject: Re: WALD test in GLMM
Sue,
Thank you for your reply. I admit that it does not initially make
sense. So, firstly, is this feature documented somewhere? Secondly, if
one asks for Wald tests and the heading indicates that standard Wald
tests have been performed, why is an adjustment made that leads to
presumably non standard Wald tests?
You then indicate that if the adjustment fails the tests revert to Wald
tests, so does this imply that if the heading is of the form "Tests for
fixed effects" the test of more appropriate or more reliable?
Dr A.O. Nicholls
Honorary Fellow
CSIRO Ecosystem Sciences
GPO Box 1700
CANBERRA ACT 2601
Telephone: (02) 6246 4132 (Tuesdays and Thursdays)
(02) 6236 8888 (Home)
Fax: (02) 6246 4094
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