Empirical histogram

[a.rob...@bifie.at]

Hi Phil,

I continued with investigating the possibilities of the arguments customTheta, customPriorFun and empiricalhist. Unfortunately, it seems that the empiricalhist can only be applied for unidimensional models. I think the flexibility of model estimation in mirt (in addition to extending customPriorFun with the argument Etable) could be quite larger if one would also allow the empiricalhist to be multidimensional. Do you think that such an option would be easy to include?

Kind regards,
Alexander

[Phil Chalmers]

Hi Alexander,

Possible, yes, and it's something I played around with when I first added the EH method. Practical? Far from it. You'll notice that when the EH approach is run the number of quadrature nodes is set to 199 and the convergence tolerance dropped to 3e-5. These are to a) adequately capture the shape of the distribution during estimation and b) account for the added uncertainty in approximating the latent distribution at the same time as the item parameters.

The increase in quadrature make multidimensional models very unlikely at this point. Since they grow exponentially a 2-dimensional model would contain 199^2 = 39601 nodes to obtain the same degree of accuracy....which is obscene. A more reasonable number might be around 60 or less since that's only 3600, but from my experience with under 100 nodes it's hard to get an idea of what the real shape looks like (the distribution is extremely blocky). This is why the method is currently limited to unidimensional models. It should be possible to use an empirical histogram in the bifactor model for the primary dimension though, but I haven't added that yet. Cheers.

Phil

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[a.rob...@bifie.at]

Hi Phil,

Maybe I disagree with your comment. I would think in applications with a fixed number of classes (say in latent class models, mixed IRT models or located latent class models). I would not use the histogram for approximating any complex continuous distribution. The point is that for such a user defined model one could use a limited grid of theta points in customTheta and estimates the distribution of it via the empiricalhist method.

I hope this makes the motivation (and direction) a bit clearer.

Alexander

[Phil Chalmers]

Hi Alexander,

I think I see where you are coming from now, but you'll have to pardon my ignorance since I haven't studied latent class models in any kind of depth, especially with regards to their connection to IRT estimation techniques (on the todo list, along with a laundry list of others). References are certainly welcome! 

That being said, you don't need to use the empiricalhist inputs if you are planning to supply your own customTheta and customPriorFun to generate those models. Instead, if you want the final prior estimate just use the global resolution operator <<- in the customPriorFun to obtain the estimates in your workspace and inspect those directly. These also shouldn't be limited to unidimensional models, but they will be if the empiricalhist trigger is set to TRUE (which I think is pretty safe for now). 

By the way, if you do manage to construct something latent class-like using these inputs would you mind posting it here/sending it to me directly? Would help me get a better idea of what exactly it is you are try to accomplish, and might be something worth including into the package at a later time. Cheers.

Phil

[a.rob...@bifie.at]

On Saturday, August 9, 2014 5:45:27 PM UTC+2, Phil Chalmers wrote:

Hi Alexander,

I think I see where you are coming from now, but you'll have to pardon my ignorance since I haven't studied latent class models in any kind of depth, especially with regards to their connection to IRT estimation techniques (on the todo list, along with a laundry list of others). References are certainly welcome! 

That being said, you don't need to use the empiricalhist inputs if you are planning to supply your own customTheta and customPriorFun to generate those models. Instead, if you want the final prior estimate just use the global resolution operator <<- in the customPriorFun to obtain the estimates in your workspace and inspect those directly. These also shouldn't be limited to unidimensional models, but they will be if the empiricalhist trigger is set to TRUE (which I think is pretty safe for now). 

I agree. This should work. It seems that the "Etable" argument in the customPriorFun works in the mirt dev version? Maybe it is better to use only the custom arguments.

Thank you,
Alexander