A concrete type I/III Sum of square problem

classic Classic list List threaded Threaded
12 messages Options
Reply | Threaded
Open this post in threaded view
|

A concrete type I/III Sum of square problem

wphantom-2
Hi R-help members,

I have read a lot in the Archive about the "Type I" vs "Type III" sum
of square. I think I have read confusing post so
I want to have a clear idea of the problem.

Here is an example.
I have 3 groups of subjects of unequal sample size (G1 (n=7), G2
(n=7), G3 (n=4)).
for Each subject I have 4 measures corresponding to  the crossing of
2 factor  (A & B) of two levels each.

my dependant variable is X.

After reading a lot of tutorials on R I have tried the
summary(aov(X~GROUP*A*B+Error(SUJECT/(A*B) )

This results are with "type I SS".

What's wrong with these results ? Should I use type III SS and, if so
how to enter my design in Anova (car package, I still have not the
J.  Fox's book) ?
I have clearly not understood the difference between type I & III
(with the limits of each approach).  A link to a good tutorial on
this topic will help me a lot.



Sylvain CLEMENT
"Neuropsychology & Auditory Cognition Team"
Lille, FRANCE

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Prof Brian Ripley
More to the point, you are confusing multistratum AOV with single-stratuam
AOV.  For a good tutorial, see MASS4 (bibliographic information in the R
FAQ).  For unbalanced data we suggest you use lme() instead.

On Tue, 14 Feb 2006, WPhantom wrote:

> Hi R-help members,
>
> I have read a lot in the Archive about the "Type I" vs "Type III" sum
> of square. I think I have read confusing post so
> I want to have a clear idea of the problem.
>
> Here is an example.
> I have 3 groups of subjects of unequal sample size (G1 (n=7), G2
> (n=7), G3 (n=4)).
> for Each subject I have 4 measures corresponding to  the crossing of
> 2 factor  (A & B) of two levels each.
>
> my dependant variable is X.
>
> After reading a lot of tutorials on R I have tried the
> summary(aov(X~GROUP*A*B+Error(SUJECT/(A*B) )
>
> This results are with "type I SS".
>
> What's wrong with these results ? Should I use type III SS and, if so
> how to enter my design in Anova (car package, I still have not the
> J.  Fox's book) ?
> I have clearly not understood the difference between type I & III
> (with the limits of each approach).  A link to a good tutorial on
> this topic will help me a lot.
>
>
>
> Sylvain CLEMENT
> "Neuropsychology & Auditory Cognition Team"
> Lille, FRANCE

--
Brian D. Ripley,                  [hidden email]
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

wphantom-2
Thanks Brian for the reference.
  I just discover that it is available in our
library so I going to take it & read it soon.
Actually, I don't even know the difference
between a multistratum vs a single-stratum AOV. A
quick search on google returned me the R materials so that I imagine
that these concepts are quite specific to R.

I will read the book first before asking for more informations.

Thanks

Sylvain Clément

At 12:38 14/02/2006, you wrote:
>More to the point, you are confusing
>multistratum AOV with single-stratuam AOV.  For
>a good tutorial, see MASS4 (bibliographic
>information in the R FAQ).  For unbalanced data
>we suggest you use lme() instead.
>
>--
>Brian D. Ripley,                  [hidden email]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Peter Dalgaard
WPhantom <[hidden email]> writes:

> Thanks Brian for the reference.
>   I just discover that it is available in our
> library so I going to take it & read it soon.
> Actually, I don't even know the difference
> between a multistratum vs a single-stratum AOV. A
> quick search on google returned me the R materials so that I imagine
> that these concepts are quite specific to R.

You have to be careful not to confuse Google's view of the world with
Reality...

The concept of error strata is much older than R, and existed for
instance in Genstat, anno 1977 or so. However, Genstat seems to have
left little impression on the Internet.
 
> I will read the book first before asking for more informations.

The executive summary is that the concept of error strata relies
substantially on having a balanced design (at least for the random
effects), so that the analysis can be decomposed into analyses of
means, contrasts, and contrasts of means. For unbalanced designs, you
usually get meaningless analyses.


> Thanks
>
> Sylvain Clément
>
> At 12:38 14/02/2006, you wrote:
> >More to the point, you are confusing
> >multistratum AOV with single-stratuam AOV.  For
> >a good tutorial, see MASS4 (bibliographic
> >information in the R FAQ).  For unbalanced data
> >we suggest you use lme() instead.
> >
> >--
> >Brian D. Ripley,                  [hidden email]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>

--
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - ([hidden email])                  FAX: (+45) 35327907

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

John Maindonald
In reply to this post by wphantom-2
I have forwarded comments on these issues, in a separate message that  
is entitled:

"Strata and Degrees of freedom in anova and multi-level modeling"

John Maindonald             email: [hidden email]
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Mathematical Sciences Institute, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.


On 15 Feb 2006, at 10:00 PM, [hidden email] wrote:

> From: Peter Dalgaard <[hidden email]>
> Date: 15 February 2006 3:26:27 AM
> To: WPhantom <[hidden email]>
> Cc: [hidden email]
> Subject: Re: [R] A concrete type I/III Sum of square problem
>
>
> WPhantom <[hidden email]> writes:
>
>> Thanks Brian for the reference.
>>   I just discover that it is available in our
>> library so I going to take it & read it soon.
>> Actually, I don't even know the difference
>> between a multistratum vs a single-stratum AOV. A
>> quick search on google returned me the R materials so that I imagine
>> that these concepts are quite specific to R.
>
> You have to be careful not to confuse Google's view of the world with
> Reality...
>
> The concept of error strata is much older than R, and existed for
> instance in Genstat, anno 1977 or so. However, Genstat seems to have
> left little impression on the Internet.
>
>> I will read the book first before asking for more informations.
>
> The executive summary is that the concept of error strata relies
> substantially on having a balanced design (at least for the random
> effects), so that the analysis can be decomposed into analyses of
> means, contrasts, and contrasts of means. For unbalanced designs, you
> usually get meaningless analyses.
>
>
>> Thanks
>>
>> Sylvain Clément
>>
>> At 12:38 14/02/2006, you wrote:
>>> More to the point, you are confusing
>>> multistratum AOV with single-stratuam AOV.  For
>>> a good tutorial, see MASS4 (bibliographic
>>> information in the R FAQ).  For unbalanced data
>>> we suggest you use lme() instead.
>>>
>>> --
>>> Brian D. Ripley,                  [hidden email]
>>
>> ______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide! http://www.R-project.org/posting- 
>> guide.html
>>
>
> --
>    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>  (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45)  
> 35327918
> ~~~~~~~~~~ - ([hidden email])                  FAX: (+45)  
> 35327907

        [[alternative HTML version deleted]]


______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Gregor Gorjanc
In reply to this post by wphantom-2
> WPhantom <[hidden email]> writes:
>
>>> Thanks Brian for the reference.
>>>   I just discover that it is available in our
>>> library so I going to take it & read it soon.
>>> Actually, I don't even know the difference
>>> between a multistratum vs a single-stratum AOV. A
>>> quick search on google returned me the R materials so that I imagine
>>> that these concepts are quite specific to R.
>
> You have to be careful not to confuse Google's view of the world with
> Reality...
>
> The concept of error strata is much older than R, and existed for
> instance in Genstat, anno 1977 or so. However, Genstat seems to have
> left little impression on the Internet.
>  
>>> I will read the book first before asking for more informations.
>
> The executive summary is that the concept of error strata relies
> substantially on having a balanced design (at least for the random
> effects), so that the analysis can be decomposed into analyses of
> means, contrasts, and contrasts of means. For unbalanced designs, you
> usually get meaningless analyses.
>

Can you (prof. Dalgaard) please point us to relevant book with these
topics. I am very interested in it since my data are often unbalanced.

>>> Thanks
>>>
>>> Sylvain Cl?ment
>>>
>>> At 12:38 14/02/2006, you wrote:
>>
>>>> >More to the point, you are confusing
>>>> >multistratum AOV with single-stratuam AOV.  For
>>>> >a good tutorial, see MASS4 (bibliographic
>>>> >information in the R FAQ).  For unbalanced data
>>>> >we suggest you use lme() instead.

I do not have the whole book in my head as prof. Ripley probably does,
but I can not recall to read about this in MASS4. I am sure I am wrong
and would you (prof. Ripley) be please so kind and point us to relevant
chapters/pages.

Many thanks.

--
Lep pozdrav / With regards,
    Gregor Gorjanc

----------------------------------------------------------------------
University of Ljubljana     PhD student
Biotechnical Faculty
Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
Groblje 3                   mail: gregor.gorjanc <at> bfro.uni-lj.si

SI-1230 Domzale             tel: +386 (0)1 72 17 861
Slovenia, Europe            fax: +386 (0)1 72 17 888

----------------------------------------------------------------------
"One must learn by doing the thing; for though you think you know it,
 you have no certainty until you try." Sophocles ~ 450 B.C.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Peter Dalgaard
Gregor Gorjanc <[hidden email]> writes:

> > WPhantom <[hidden email]> writes:
> >
> >>> Thanks Brian for the reference.
> >>>   I just discover that it is available in our
> >>> library so I going to take it & read it soon.
> >>> Actually, I don't even know the difference
> >>> between a multistratum vs a single-stratum AOV. A
> >>> quick search on google returned me the R materials so that I imagine
> >>> that these concepts are quite specific to R.
> >
> > You have to be careful not to confuse Google's view of the world with
> > Reality...
> >
> > The concept of error strata is much older than R, and existed for
> > instance in Genstat, anno 1977 or so. However, Genstat seems to have
> > left little impression on the Internet.
> >  
> >>> I will read the book first before asking for more informations.
> >
> > The executive summary is that the concept of error strata relies
> > substantially on having a balanced design (at least for the random
> > effects), so that the analysis can be decomposed into analyses of
> > means, contrasts, and contrasts of means. For unbalanced designs, you
> > usually get meaningless analyses.
> >
>
> Can you (prof. Dalgaard) please point us to relevant book with these
> topics. I am very interested in it since my data are often unbalanced.

Hmm, the Danish tradition is highly based on lecture notes, so I don't
have a specific book for you. One possible starting point is

Tue Tjur (1984): Analysis of variance designs in orthogonal designs.
Int.Statist.Review 52, 33-81.

The thing to notice in relation to that paper is that the
decomposition (p.55) of the covariance matrix as sum(lambda_B Q_B^0)
is highly dependent on having an orthogonal design. Without the
orthogonality, it still defines a model, but typically one without a
sensible interpretation.

Look at a simple 1-way anova with three groups of equal size. The Q
matrices will be the projections P_X and I-P_X, where X is the design
matrix for the grouping factor, e.g.

> X <- model.matrix(~factor(rep(1:3,each=2)))
> X
  (Intercept) factor(rep(1:3, each = 2))2 factor(rep(1:3, each = 2))3
1           1                           0                           0
2           1                           0                           0
3           1                           1                           0
4           1                           1                           0
5           1                           0                           1
6           1                           0                           1
...

P_X can be found in the following semi-secret way:

> P <- stats:::proj.matrix(X)
> P
    1   2   3   4   5   6
1 0.5 0.5 0.0 0.0 0.0 0.0
2 0.5 0.5 0.0 0.0 0.0 0.0
3 0.0 0.0 0.5 0.5 0.0 0.0
4 0.0 0.0 0.5 0.5 0.0 0.0
5 0.0 0.0 0.0 0.0 0.5 0.5
6 0.0 0.0 0.0 0.0 0.5 0.5

Suppose we put a random component of 10 on P_X and 1 on (I-P_X).
We then get

> diag(6) - P + 10*P
    1   2   3   4   5   6
1 5.5 4.5 0.0 0.0 0.0 0.0
2 4.5 5.5 0.0 0.0 0.0 0.0
3 0.0 0.0 5.5 4.5 0.0 0.0
4 0.0 0.0 4.5 5.5 0.0 0.0
5 0.0 0.0 0.0 0.0 5.5 4.5
6 0.0 0.0 0.0 0.0 4.5 5.5

which is a perfectly sensible covariance for within-group correlated
data.

Now try the same stunt with unbalanced data:

> X <- model.matrix(~factor(rep(1:3,1:3))-1)
> P <- stats:::proj.matrix(X)
> diag(6) - P + 10*P
   1   2   3 4 5 6
1 10 0.0 0.0 0 0 0
2  0 5.5 4.5 0 0 0
3  0 4.5 5.5 0 0 0
4  0 0.0 0.0 4 3 3
5  0 0.0 0.0 3 4 3
6  0 0.0 0.0 3 3 4

I.e. we are de facto assuming that observations in the smaller group
have a larger variance than observations in the larger groups.



 

> >>> Thanks
> >>>
> >>> Sylvain Cl?ment
> >>>
> >>> At 12:38 14/02/2006, you wrote:
> >>
> >>>> >More to the point, you are confusing
> >>>> >multistratum AOV with single-stratuam AOV.  For
> >>>> >a good tutorial, see MASS4 (bibliographic
> >>>> >information in the R FAQ).  For unbalanced data
> >>>> >we suggest you use lme() instead.
>
> I do not have the whole book in my head as prof. Ripley probably does,
> but I can not recall to read about this in MASS4. I am sure I am wrong
> and would you (prof. Ripley) be please so kind and point us to relevant
> chapters/pages.
>
> Many thanks.
>
> --
> Lep pozdrav / With regards,
>     Gregor Gorjanc
>
> ----------------------------------------------------------------------
> University of Ljubljana     PhD student
> Biotechnical Faculty
> Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
> Groblje 3                   mail: gregor.gorjanc <at> bfro.uni-lj.si
>
> SI-1230 Domzale             tel: +386 (0)1 72 17 861
> Slovenia, Europe            fax: +386 (0)1 72 17 888
>
> ----------------------------------------------------------------------
> "One must learn by doing the thing; for though you think you know it,
>  you have no certainty until you try." Sophocles ~ 450 B.C.
> ----------------------------------------------------------------------
>

--
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - ([hidden email])                  FAX: (+45) 35327907

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Gregor Gorjanc
On 16 Feb 2006 11:55:47 +0100, Peter Dalgaard <[hidden email]> wrote:
> Gregor Gorjanc <[hidden email]> writes:
>
...
> > Can you (prof. Dalgaard) please point us to relevant book with these
> > topics. I am very interested in it since my data are often unbalanced.
>
> Hmm, the Danish tradition is highly based on lecture notes, so I don't
> have a specific book for you. One possible starting point is

If there are some good lecture notes around I would like to read them
even more ;)

> Tue Tjur (1984): Analysis of variance designs in orthogonal designs.
> Int.Statist.Review 52, 33-81.

Thank you very much for this reference and example code!

--
Lep pozdrav / With regards,
    Gregor Gorjanc

----------------------------------------------------------------------------------------------------
University of Ljubljana          PhD student
Biotechnical Faculty
Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
Groblje 3                            mail: gregor.gorjanc <at> bfro.uni-lj.si
SI-1230 Domzale                tel: +386 (0)1 72 17 861
Slovenia, Europe                 fax: +386 (0)1 72 17 888
----------------------------------------------------------------------------------------------------
"One must learn by doing the thing; for though you think you know it,
 you have no certainty until you try." Sophocles ~ 450 B.C.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Peter Dalgaard
Gregor GORJANC <[hidden email]> writes:

> On 16 Feb 2006 11:55:47 +0100, Peter Dalgaard <[hidden email]> wrote:
> > Gregor Gorjanc <[hidden email]> writes:
> >
> ...
> > > Can you (prof. Dalgaard) please point us to relevant book with these
> > > topics. I am very interested in it since my data are often unbalanced.
> >
> > Hmm, the Danish tradition is highly based on lecture notes, so I don't
> > have a specific book for you. One possible starting point is
>
> If there are some good lecture notes around I would like to read them
> even more ;)

You may find that there is a language barrier....
 
> > Tue Tjur (1984): Analysis of variance designs in orthogonal designs.
> > Int.Statist.Review 52, 33-81.
>
> Thank you very much for this reference and example code!

--
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - ([hidden email])                  FAX: (+45) 35327907

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Gregor Gorjanc
On 16 Feb 2006 13:30:31 +0100, Peter Dalgaard <[hidden email]> wrote:

> Gregor GORJANC <[hidden email]> writes:
>
> > On 16 Feb 2006 11:55:47 +0100, Peter Dalgaard <[hidden email]> wrote:
> > > Gregor Gorjanc <[hidden email]> writes:
> > >
> > ...
> > > > Can you (prof. Dalgaard) please point us to relevant book with these
> > > > topics. I am very interested in it since my data are often unbalanced.
> > >
> > > Hmm, the Danish tradition is highly based on lecture notes, so I don't
> > > have a specific book for you. One possible starting point is
> >
> > If there are some good lecture notes around I would like to read them
> > even more ;)
>
> You may find that there is a language barrier....

Oh, dear. I hoped for lecture notes written in universal language for
stats. i.e. R, you probably heard about it. Just joking. Thanks anyway.

--
Lep pozdrav / With regards,
    Gregor Gorjanc

----------------------------------------------------------------------------------------------------
University of Ljubljana          PhD student
Biotechnical Faculty
Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
Groblje 3                            mail: gregor.gorjanc <at> bfro.uni-lj.si
SI-1230 Domzale                tel: +386 (0)1 72 17 861
Slovenia, Europe                 fax: +386 (0)1 72 17 888
----------------------------------------------------------------------------------------------------
"One must learn by doing the thing; for though you think you know it,
 you have no certainty until you try." Sophocles ~ 450 B.C.

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Kjetil Halvorsen
Gregor GORJANC wrote:

> On 16 Feb 2006 13:30:31 +0100, Peter Dalgaard <[hidden email]> wrote:
>> Gregor GORJANC <[hidden email]> writes:
>>
>>> On 16 Feb 2006 11:55:47 +0100, Peter Dalgaard <[hidden email]> wrote:
>>>> Gregor Gorjanc <[hidden email]> writes:
>>>>
>>> ...
>>>>> Can you (prof. Dalgaard) please point us to relevant book with these
>>>>> topics. I am very interested in it since my data are often unbalanced.
>>>> Hmm, the Danish tradition is highly based on lecture notes, so I don't
>>>> have a specific book for you. One possible starting point is
>>> If there are some good lecture notes around I would like to read them
>>> even more ;)
>> You may find that there is a language barrier....
>
> Oh, dear. I hoped for lecture notes written in universal language for
> stats. i.e. R, you probably heard about it. Just joking. Thanks anyway.
>
> --

If that language behind the barrier is Danish, there must be at least a
few persons on the list who could benefit, so url's are welcome!
Would'nt hurt with some Danish lecture notes in my bookshelf, although
Piet Hein certainly have better grooks.

Kjetil

> Lep pozdrav / With regards,
>     Gregor Gorjanc
>
> ----------------------------------------------------------------------------------------------------
> University of Ljubljana          PhD student
> Biotechnical Faculty
> Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
> Groblje 3                            mail: gregor.gorjanc <at> bfro.uni-lj.si
> SI-1230 Domzale                tel: +386 (0)1 72 17 861
> Slovenia, Europe                 fax: +386 (0)1 72 17 888
> ----------------------------------------------------------------------------------------------------
> "One must learn by doing the thing; for though you think you know it,
>  you have no certainty until you try." Sophocles ~ 450 B.C.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
>

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: A concrete type I/III Sum of square problem

Peter Dalgaard
Kjetil Brinchmann Halvorsen <[hidden email]> writes:

> If that language behind the barrier is Danish, there must be at least a
> few persons on the list who could benefit, so url's are welcome!

URLs??? We're talking ca. 1980 here.... Try "yellowing leaflets in a
corner of my basement". Hand-written or sent to a secretary who was
juggling the golf-ball typehead on an IBM Selectric typewriter to get
mathematical symbols.

Actually, some were in English and published in the Springer Lecture
Notes series - one set by Martin Jacobsen on counting processes and
another by Søren Johansen on regression analysis topics. Some others
went on to become traditional textbooks (Asmussen, Lauritzen).

The tradition continues. I see that the current set of Stat 1 notes by
Ernst Hansen are for sale in Naturfagsbogladen for 365 DKK, so you
might be able to get them to send you a set.
 
> Would'nt hurt with some Danish lecture notes in my bookshelf, although
> Piet Hein certainly have better grooks.

"Problems worthy of attack
will prove their worth by fighting back"

--
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - ([hidden email])                  FAX: (+45) 35327907

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html