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LCMCMCA simple Latent class model.This is a very simple latent class model used for MCMC learning exercises in the tutorial and book. PurposeThis is a small example that was developed for Chapter 9 of Bayesian Networks in Educational Assessment. As the proficiency variable has two levels, it is a latent class? model. The example is fairly small as its purpose is to illustrate the Markov chain Monte Carlo (MCMC?) algorithm. This example also illustrates the label swapping? problem. Although the intention is that the value 1 represents mastery? of the skill and 0 represents nonmastery, swapping the meanings of 0 and 1 produces a new model with an identical likelihood. In order to ensure that the algorithm converges to the desired state, either prior constraints must be placed on the parameter, or some additional steps are required after model fitting to untangle the dependencies. Proficiency ModelsThe proficiency model consists of a single latent variable, theta, which has two possible states: 0 (nonmastery) and 1 (mastery?). The prior probability distribution for this variable is a mildlyinformative Beta?(3,3) distribution, which has a mean of .5. Task ModelsWe posit two tasks: a simple dichotomouslyscored task, and a partial credit task. Again, as this mostly a Bayes net calculation exercise, the task models are not fully developed. Evidence ModelsThere are two evidence models, one for the dichotomouslyscored tasks (with a twolevel observable?) and one for the partial credit task (with a threelevel observable). Evidence model for the dichotomouslyscored tasks"
Evidence model for 3level partial credit tasks"
In both cases, the conditional probability tables are given a hyperDirichlet? distribution. Assembly ModelA complete form of the assessment consists of two dichotomouslyscored tasks and one partial credit task. Note that there is a second task data description file for creating a second parallel form. Data SetsThe data can be found at http://pluto.coe.fsu.edu/BNinEA/lcmcmc/ (tarball) The subfolder initialOut contains the output of a MCMC run. ReferencesChapter 9 of Bayesian Networks in Educational Assessment. 