[R-sig-ME] 3-level binomial model

[Iasonas Lamprianou]

Thank you all for your suggestions. My question, however, is how to compute the % of the variance at the level of the school and at the level of the pupils. In other words, does the concept of  intraclass correlation hold in my context? If yes, then how can this be computed for the pupils and the schools? Is the decomposistion below reasonable? 
Prof. Bates, maybe you could suggesting something using the lmer?

VPCschool = VARschool/(VARschool+VARpupil+3.29) and 
  VPCpupil = VARpupil/(VARschool+VARpupil+3.29)
 
Dr. Iasonas Lamprianou
Department of Education
The University of Manchester
Oxford Road, Manchester M13 9PL, UK
Tel. 0044 161 275 3485
iasonas.lamprianou at manchester.ac.uk



On 16/04/2008, at 12:11 PM, David Duffy wrote:

>> I computed the school-level and the pupil-level variance like that
>> (as described for 2-level models in MlWin manual): I assumed that
>> my dependent variable is based on a continuous unobserved variable
>> (perfectly valid according to my theoretical model). Therefore, eijk
>> follows a logistic distribution with variance pi2/3=3.29. So,
>
>> VPCschool=VARschool/(VARschool+3.29)= 0.17577/(0.17577+3.29)=6.4% and
>> VPCpupil=VPCpupil /(VPCpupil+3.29)=0.19977/(0.19977+3.29)=7.3%.
>
>> The reviewers of my paper are not sure if this is the best way to
>> do it. They may reject my paper and I worry because I have spent
>> 3months!!!! writing it. Any ideas to support my method or to use a
>> better one?
>
> Would an IRT model for seven "items" be more to their taste?  I  
> don't think the
> substantive conclusions would be much different.
>

Multi-level IRT is more appropriate, this allows for the nesting  
within schools. There is a package mlirt that fits these models in a  
Bayesian framework, but I haven't tried it. There are commercial  
programs which will fit these, Mplus is advertised to and Latent Gold  
with the Syntax module will, at least for a unidimensional latent  
variable.

What is more worrying is the assumption of a single latent variable to  
model the correlation between tests.

Ken



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