Description Usage Arguments Details Value References
Kullback-Leibler divergence based on the EAP and ML estimates of ability under the posterior distribution of theta. Computes the numerical integral of the expectation of KL under the posterior distribution.
1 2 3 4 | get_posterior_expected_kl_information(estimate, model, answers, administered,
available, number_dimensions, estimator, alpha, beta, guessing, prior_form,
prior_parameters, number_itemsteps_per_item,
eap_estimation_procedure = "riemannsum")
|
estimate |
Vector containing current theta estimate, with covariance matrix as an attribute. |
model |
One of |
answers |
Vector with answers to administered items. |
administered |
vector with indices of administered items. |
available |
Vector with indices of available items. |
number_dimensions |
Number of dimensions of theta. |
estimator |
Type of estimator to be used, one of |
alpha |
Matrix of alpha parameters, one column per dimension, one row per item. Row names should contain the item keys. Note that so called within-dimensional models still use an alpha matrix, they simply have only one non-zero loading per item. |
beta |
Matrix of beta parameters, one column per item step, one row per item. Row names should contain the item keys.
Note that |
guessing |
Matrix with one column of guessing parameters per item. Row names should contain the item keys. Optionally used in 3PLM model, ignored for all others. |
prior_form |
String indicating the form of the prior; one of |
prior_parameters |
List containing mu and Sigma of the normal prior: |
number_itemsteps_per_item |
Vector containing the number of non missing cells per row of the beta matrix. |
eap_estimation_procedure |
String indicating the estimation procedure if estimator is expected aposteriori and prior form is normal. One of |
Note that even with a simplified grid, the number of quadrature points which have to be calculated for each available item, at each step in the CAT is taken to the power Q. Use of KL information is likely to be slow in 3+ dimensional tests.
Vector with PEKL information for each yet available item. Kullback Leibler Divergence for given items and pairs of thetas x posterior density. returns vector containing information for each yet available item
Chang, H.-H, & Ying, Z. (1996). A Global Information Approach to Computerized Adaptive Testing. Applied Psychological Measurement, 20(3), 213 - 229. doi: 10.1177/014662169602000303.
Mulder, J., & van der Linden, W. J. (2010). Multidimentional Adaptive testing with Kullback-Leibler information item selection. In W. J. van der Linden & C. A. W. Glas (Eds.), Elements of adaptive testing (pp. 77 - 101). New York: Springer.
Wang, C., Chang, H.-H., & Boughton, K. A. (2010). Kullback-Leibler Information and Its Applications in Multi-Dimensional Adaptive Testing. Psychometrika, 76(1), 13 - 39. doi:10.1007/s11336-010-9186-0.
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