Probabilistic models with more than one latent variable are designed to report profiles of skills or cognitive attributes. Testing programs want to offer additional information beyond what a single test score can prov...
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We derive two convergence results for a sequential alternating maximization procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that th...
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We derive two convergence results for a sequential alternating maximization procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that the sequence attains the same deviation properties as shown for the profile M-estimator by Andresen and Spokoiny (2013), that means a finite sample Wilks and Fisher theorem. Further under slightly stronger smoothness constraints on the random functional we can show nearly linear convergence to the global maximizer if the starting point for the procedure is well chosen.
The precision of item parameter estimates can be increased by taking advantage of dependencies between the latent proficiency variable and auxiliary examinee variables such as age, courses taken, and years of schoolin...
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The precision of item parameter estimates can be increased by taking advantage of dependencies between the latent proficiency variable and auxiliary examinee variables such as age, courses taken, and years of schooling. Gains roughly equivalent to two to six additional item responses can be expected in typical educational and psychological applications. empirical Bayes computational procedures are presented, and illustrated with data from the Profile of American Youth survey.
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