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Stochastic Learning Paths — Estimation and Simulation

  • J.-Cl. Falmagne
  • K. Lakshminarayan
Chapter
Part of the Recent Research in Psychology book series (PSYCHOLOGY)

Abstract

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.

Keywords

Learning Rate Knowledge Structure Latent Trait Stochastic Theory Learning Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • J.-Cl. Falmagne
    • 1
  • K. Lakshminarayan
    • 1
  1. 1.University of CaliforniaIrvineUSA

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