[R-sig-ME] FW: Variogram / confint prediction in LMM / time prediction some questions from Switerland area

[Ben Bolker]

On 8/8/21 5:17 AM, mudryjm wrote:
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> Sent: Sunday, August 1, 2021 5:32 PM
> To: mudryjm <mudryjm using bluewin.ch>
> Subject: Re: Variogram / confint prediction in LMM / time prediction some questions from Switerland area
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> I regret that I am not able to answer your questions at this time.  It has been a couple of decades since I worked on the nlme package and I have not kept up with the literature.
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> I suggest that you send your questions to the R-SIG-Mixed-Models using R-project.org <mailto:R-SIG-Mixed-Models using R-project.org>  mailing list.  Some information about the list is available at https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
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> On Sun, Aug 1, 2021 at 9:25 AM mudryjm <mudryjm using bluewin.ch <mailto:mudryjm using bluewin.ch> > wrote:
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> Dear Mr Bates and Pinhero
> 
> Tks for your incredible packages in R I did my master in statistics (attached). I’m a big fan!
> 
> However I’m puzzled with several theoretical questions on some topic where I’m struggling; instead of luring for stat input I asks directly WIZARDS!:
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> Variograms (Cressie):P 52 PDF
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> I have done several variograms on my model residuals expecting flat line along (sill flat).However some patient are at sill some on the correlation path-slope.

   I'm not really sure what this means.  One very common issue is that 
if you simply specify residuals(fitted_model), you get "raw" 
(observed-fitted) residuals; if you want residuals that take the 
autocorrelation structure of the model into account, you need to specify 
type="normalized" (see ?nlme::residuals.lme)
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> Q:How to interpret? (Two class of patient with biophysical discerpancies?

   Hard to say without more detail.

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> Q:The smoother fitted in graph is the theoretical one (Theoretical variogram based on exp?spherical?)?? Or is it a simple smoother.

   Not sure what you're referring to.  Perhaps some attached images got 
lost (the mailing list strips some attachment types).

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> Q: Is it possible with variogram (within (patient and sampling error) cor + between from LMM variance) to forecast the best time for re-measure? > I.e in cholesterol study some authors demonstrated when intra- 
variability exceed between variability? So measuring on too short 
intervals has no value.But I don’t know how to proceed

   This doesn't seem to have an obvious answer, but measurements taken 
with a time interval large enough that the estimated autocorrelation 
would be small would provide more information (e.g. if the 
autocorrelation model gives you a scale parameter, autocorrelation 
levels would typically drop to 'small' levels at a time difference of 
2*scale or 3*scale - but exactly how far it would drop depends on the 
particular autocorrelation model used, and the 'best' time for 
remeasurement would depend on a whole lot of details of the particular 
study system; how expensive or inconvenient is it to take additional 
samples? An autocorrelated sample doesn't provide *no* information, it 
just provides less information than one taken at a (typically) longer 
time interval.

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> Or do you had a good reference.?
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> Fiiting confindance bands on XB+ZU:
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> Q.I try to get con band for predictings patients trajectories. As they is no close form (at least very complex) is the better way to bootstrap some model and fit a bootstrap confint on the 1000 Fitted values? Or do you have a smplier function?
> 

    Bootstrapping seems like a good approach.
    Since your data are autocorrelated, you might need block 
bootstrapping (or, if you trust the model reasonably well, parametric 
bootstrapping)

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> Q:If I should predict when time  will be  reached for a patient his Upper reference limit how do I have to proceed? (back reversing formula?)
> Page 54 :patients prediction
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> Tks for your help in an old retrained statistician


  Yes, you probably need to invert the formula.  You might end up 
needing to solve numerically (?uniroot)

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> NB Your contribution to staworld is fabulous and inspired me in my daily work since  a year!
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> :)
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> Veuillez recevoir mes sincères salutations ,
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> Sincerely,
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> Mudry Jean-Marie
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> 8 ch du Châno
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> 1802 CORSEAUX
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> Switzerland
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> +41.79.708.87.15
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> +41.21.921.10.18.
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-- 
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
Graduate chair, Mathematics & Statistics