[R-sig-ME] Fwd: Re: [R] how to write crossed and nested random effects in a model

[Ben Bolker]

 [forwarded to r-sig-mixed-models at r-project.org: it is much better to
keep these discussions on a public, archived list]

-------- Original Message --------
Subject: 	Re: [R] how to write crossed and nested random effects in a model
Date: 	Tue, 13 Mar 2012 17:25:39 -0700 (PDT)
From: 	withanage Niroshan perera <wnnkp at yahoo.com>
Reply-To: 	withanage Niroshan perera <wnnkp at yahoo.com>
To: 	Ben Bolker <bbolker at gmail.com>



Dear Professor,

Thanks lot for your valuable idea, Could you please let me know the your
explanation in a model. I guess that would be much more informative for
me to get it understood.

  [snip]

BMB>  Well, if you're a PhD student in mathematics & statistics you
BMB> be able to do some of this yourself -- there must be some expertise
BMB> in mixed models (although possibly not in mixed models in R)
BMB> at your institution in order for you to be working in this line
BMB> of research ...

BMB> I did, more or less, give you the model formula below.

Something like:
glmer (resp ~ pathology + (pathology|reader)+(pathology|patient/eye),
   family=binomial(link="probit"),data=mydata)

  I would *strongly* recommend that you work out how to simulate some
data with known variance components so that you can see whether you
are getting the right sorts of answers ...

Niroshan <wnnperer <at> ucalgary.ca> writes:

> I have a question based on my research. I am analyzing reader-based 
> diagnostic data set.  My study involves diabetic patients who were 
> evaluated for treatable diabetic retinopathy based on the presence
> or absence of two pathologies in their eyes.  Pathologies were 
> identified using the clinical examination (Gold standard method). In 
> addition it can be identified by taking digital images of patients’ 
> eyes and this method is cost effective. Finally two readers go over 
> the images independently and patients are diagnosed as either 
> positive or negative for the pathologies. My objective is,
> estimation the sensitivity and specificity of reader-based diagnostic
> method.

> I am going to fit multivariate probit model. But the problem has 
> complex correlation structure. We have three different correlation: 
> readers results  are correlated, patients left and right eyes are 
> correlated and pathologies are correlated since all based on the 
> retina in the eye.

 [snip]

> Also I think patients and readers are crossed each other since each 
> reader go over each patients’ images. And [snip] eyes are nested with
> patients and pathologies are nested with in the eye.  Is this crossed
> and nested interpretation true?  If then how can I include these
> effects as random terms to the model?
> 
> My response is readers ‘ diagnosed values. Per patient I have 8 
> values (2 pathologies, left and right eye and 2 readers) Explanatory
>  variables are actual disease status of each pathology for left and 
> right eyes.
> 


  I think that *in principle* (if you are using lme4, which is
probably the most convenient option for dealing with crossed REs) you
probably want

~ pathology + (pathology|reader)+(pathology|patient/eye)

  The fixed effect term says that pathologies may vary in their
overall frequency.  The first RE term says that different readers can
vary, in a pathology-specific way (if they just differed overall in
their sensitivity you would want (1|reader) instead); the second says
that there is variance among eyes (within patients) in all pathologies
(and that they may be correlated).

  A few cautions about this:

* I'm not sure I got it right

* You might want to forward this (along with my answer, so we're not
starting from scratch) to r-sig-mixed-models at r-project.org
<mailto:r-sig-mixed-models at r-project.org> , where
there is more expertise in mixed models.

* if you have the _same_ two readers for all of your patients (as
opposed to two different readers chosen at random out of a large,
possibly overlapping pool), then it isn't be practical to treat them
as a random effect, no matter how much sense it makes philosophically
-- use pathology*reader instead.

* You may need a moderately large amount of data to fit this model ...