Recent posts to Kronecker product in JAGShttps://sourceforge.net/p/mcmc-jags/discussion/610037/thread/17ddb2ce/Recent posts to Kronecker product in JAGSenWed, 03 Oct 2012 17:22:16 -0000Kronecker product in JAGShttps://sourceforge.net/p/mcmc-jags/discussion/610037/thread/17ddb2ce/I have an example, now, including data. In any case, I appreciate your time to consider this and am more than happy to produce an example. I'd ask for a more guidance on the components that compose an example of value to you. For example, do you want me to .tex up a formulation for a specific inferential problem? Would you rather I conveyed something in pseudo-JAGS script? The example I have in my mind is my current project assessing the performance for teacher lesson delivery over mutliple classrooms of students, evaluation events and raters. The evaluation protocol includes multiple dimensions that compose lesson delivery performance, so it produces multivariate ordered responses. The evaluation events may be video-taped and later scored or scored "live". Our inferential task is to evaluate a whether these two different scoring modes express similar teacher-level correlations. So inside the GLM we define a set of multivariate teacher random effects as the mean of a latent continuous response (or the intrinsic traits of an ordered logit formulation). We have D scoring dimensions per mode and M = 2 modes. I define two covariance matrices, a D x D dimension covariance and an M x M mode covariance. The teacher effects are defined over now M*D = 2*D dimensions for each of T teachers with covariance composed as the kronecker product of the dimension and mode covariances. These lower dimensional precision matrices would receive wishart priors and the teacher random effects a multivariate Gaussian. An alternative formulation that avoids the need to hand-compose a kronecker product is to employ the matrix variate normal. (Dawid-1981). Lastly, an alternative to this formulation that would be very valuable for me would be to place the inverse wishart prior on the dimension covariance matrix with a sparse, factor analytic contruction. In particular, S = LL' + Theta, where L would be restricted to lower triangular (which I do now in JAGS through a trick) and the elements would receive N(0,1) priors. Then the woodbury matrix identity could be used to reduce the dimension for computing the inverse of S, the dimension covariance.tds151Wed, 03 Oct 2012 17:22:16 -0000https://sourceforge.net16162e436133a18f39be8d40147d13a5ed11bac1Kronecker product in JAGShttps://sourceforge.net/p/mcmc-jags/discussion/610037/thread/17ddb2ce/I see the problem now. It is not just a question of defining a new function but getting the conjugate Wishart sampler to recognize it and do the appropriate calculations. This is a little more work but is probably worth doing.
If you want me to work on this you need to send me a simple example.Martyn PlummerMon, 03 Sep 2012 08:32:50 -0000https://sourceforge.net073faee5dbb121acd7b6e183d8eed2db3a27c83b