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

[Ken Beath]

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