Stochastic Learning Paths — Estimation and Simulation
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The focus of this paper is a stochastic theory (due to Falmagne, in press) capable of describing in detail the progress of students learning a particular field. This theory provides explicit predictions for the joint probabilities of observing, at times t 1 < t 2 < … < t n , the successive response patterns R 1, R 2,…, R n . The main concern of this paper is the feasibility of parameter estimation. The difficulties are that the number of parameters is large (the data to be explained are rich and intricate), and also that no closed form or approximation is currently available for a particular form of an “n-dimensional” beta integral playing a central role in the predictions. It is nevertheless shown, through simulated data, that very accurate estimates of the parameters can be obtained in exemplary, representative cases. The estimation procedure uses a combination of standard approximations and numerical integration. These results indicate that the model is applicable in realistic situations.
KeywordsLearning Rate Knowledge Structure Latent Trait Stochastic Theory Learning Path
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