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Estimating Parameters of Periodic Assessment Models PAA

Author(s):
Almond, Russell G.
Publication Year:
2011
Report Number:
RM-11-06
Source:
ETS Research Memorandum
Document Type:
Report
Page Count:
36
Subject/Key Words:
Periodic Accountability Assessments (PAA), Markov Decision Processes, Growth Models, Panel Data, Particle Filter, EM Algorithm, Vertical Scaling

Abstract

Periodic assessments involve a series of assessments intended to measure a complex of related competencies given to the same collection of individuals at several time points. This report models the periodic assessment with a partially observed Markov decision process (POMDP) model that is a general case of the hidden Markov model or state-space model. The model relates a series of observable variables to a series of latent variables, which are assumed to be changing over time, and a series of background variables. The relationship between the observed and latent variables at each time point is governed by a matrix that reflects the design of the assessment. It is assumed that latent variables change according to a Markov model that is governed by a series of instructional activities. This report describes a method for combining the particle filter and stochastic expectation maximization algorithms for estimating the parameters of periodic assessment models in the general case. As of the time of writing, the algorithm has not been implemented or tested. With certain restrictions, the POMDP framework corresponds to other better known models. This report notes some of the special cases. It also notes that almost all models for periodic assessments face an identifiability issue that is related to the problem of vertical scaling.

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