# [R-sig-ME] the equation of a mixed model fitted using nlme

Thierry Onkelinx thierry.onkelinx at inbo.be
Tue Mar 24 09:28:52 CET 2015

Dear Jos,

Please keep the mailing list in cc.

The markup for the equations can be used in LaTeX and Markdown. Here is a
Markdown tutorial: http://rmarkdown.rstudio.com/

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2015-03-23 17:27 GMT+01:00 jos matejus <matejus106 op googlemail.com>:

> Thanks you very much for your help Thierry.
>
> Just out of interest, what markup language are you using in your reply? Is
> there a software package to view this in?
>
> Cheers
> Jos
>
> On 19 March 2015 at 13:10, Thierry Onkelinx <thierry.onkelinx op inbo.be>
> wrote:
>
>> Dear Jos,
>>
>> Here is an attempt. Have a look at Pinheiro & Bates (2000) for examples.
>>
>> $c$ days - 7
>> $p1$ first order polynomial of days - 7
>> $p2$ second order polynomial of days - 7
>> $i$ family index
>> $j$ habitat index
>> $k$ treatment index
>> $l$ observation index
>>
>> $length_{ijkl} = \beta_0 + \beta_1 p1_{ijkl} + \beta_2 p2_{ijkl} + >> \beta_j + \beta_k + \beta_{1j} p1_{ijkl} + \beta_{2j} p2_{ijkl} + >> \beta_{1k} p1_{ijkl} + \beta_{2k} p2_{ijkl} + \beta_{1jk} p1_{ijkl} + >> \beta_{2jk} p2_{ijkl} + b_{0i} + b_{1i} p1_{ijkl} + b_{2i} p2_{ijkl} + >> \epsilon_{ijkl}$
>>
>> $b_i = \left[{\\begin{array}{c} >> b_{0i} \\\\ >> b_{1i} \\\\ >> b_{1i} >> \\end{array} >> }\right] >> \sim N(0, \Psi)$
>>
>> $E[\epsilon_{ijkl}] = 0$
>> $Var(\epsilon_{ijkl}) = \sigma ^ 2 exp(2 \delta_{jk} c_{ijkl})$
>>
>> Best regards,
>>
>> ir. Thierry Onkelinx
>> Instituut voor natuur- en bosonderzoek / Research Institute for Nature
>> and Forest
>> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
>> Kliniekstraat 25
>> 1070 Anderlecht
>> Belgium
>>
>> To call in the statistician after the experiment is done may be no more
>> than asking him to perform a post-mortem examination: he may be able to say
>> what the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner
>> The combination of some data and an aching desire for an answer does not
>> ensure that a reasonable answer can be extracted from a given body of data.
>> ~ John Tukey
>>
>> 2015-03-18 10:50 GMT+01:00 jos matejus <matejus106 op googlemail.com>:
>>
>>> Dear R mixed modellers
>>>
>>> I am writing to the R mixed modelling community to request some help and
>>> advice regarding reporting a mixed model in a publication. I have
>>> recently
>>> received referees comments regarding a paper I submitted some time ago.
>>> The
>>> referee has requested that I write one of the models used to analyse my
>>> data 'statistically'. I think they mean that I should write out the
>>> equation, and while I don’t think this is unreasonable I am having
>>> trouble
>>> doing so. I know many of you have heard the excuse ‘I am not a
>>> statistician’ but I’m afraid that this applies in my case, but I have
>>> tried
>>> for a couple of days to figure this one out and harassed many colleagues
>>> but without success. Therefore I am hoping I can prevail on the kindness
>>> of
>>> the R mixed modelling community to help me with this problem.
>>>
>>> The code used for the model was
>>>
>>> vf1Exp<-  varExp(form=~I(days-7)|habitat*treat)
>>>
>>> final.model <- lme(length.sq~ poly(I(days-7),2)*treat*habitat,
>>> data=mydata,
>>> method="REML",random=~poly(I(days-7),2)|family, weights=vf1Exp)
>>>
>>> length.sq = square root transformed length of fish
>>>
>>> days = day following exposure (10, one day intervals starting from day 7
>>> after exposure)
>>>
>>> treat = two level treatment factor
>>>
>>> habitat = two level habitat factor
>>>
>>> family = 19 level factor
>>>
>>>
>>>
>>> I have 10 fish per treatment combination (treat*habitat) at each time
>>> point
>>> for each family.
>>>
>>>
>>>
>>> The second order polynomial term for day was included to account for non
>>> linear growth and the variance structure to account for an increase in
>>> variance over time that was different depending on the treatment
>>> combination. The 3-way interaction was significant.
>>>
>>> How should I represent this model as an equation?
>>>
>>> Thanks a million for your help.
>>>
>>> Jos
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-mixed-models op r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>>
>

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