k-Cube Thurstonian IRT Models

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Description

Create, Simulate, Fit, Solve k-Cube Thurstonian IRT Models.

Details

Package: kcirt
Type: Package
Version: 0.6.0
Date: 2014-04-22
License: GPL (>= 2)

Use kcirt.model to define a k-Cube Thurstonian IRT model. The function kcirt.sim generates a random realization. The function kcirt.fitEE uses an expectation-expectation volley to approximately locate mu and Lambda and predict the states, Eta. The function kcirt.fitMSS makes use of metaheuristic stochastic search to further refine the predictions/estimates.

The system of interest is defined as

y_i* = Δ μ + Δ Λ S η_i + Δ ε_i

y = 1, if y* > 0

y = 0, otherwise

Y = (y_1, y_2, ..., y_N)

where

y_i is the (column) response vector for observation i.

Δ is the Delta matrix.

μ is the column vector of item means (aka, 'utilities').

Λ is the hyperparameter matrix (aka, 'loadings').

S is the Slot matrix.

η_i is the row vector of latent states (aka, 'constructs', or 'scales') for observation i.

ε_i ~ N[0, Σ_s] is a column vector of system shocks for observation i.

Author(s)

Dave Zes, Jimmy Lewis, Dana Landis @ Korn/Ferry International

<zesdave@gmail.com>

References

Brown, A., & Maydeu-Olivares, A. (2012, November 12). How IRT Can Solve Problems of Ipsative Data in Forced-Choice Questionnaires. Psychological Methods. Advance online publication. doi: 10.1037/a0030641