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Direct linkFalk, Carl F.; Cai, Li – Grantee Submission, 2016
We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…
Descriptors: Item Response Theory, Guessing (Tests), Mathematics Tests, Simulation
Falk, Carl F.; Cai, Li – Journal of Educational Measurement, 2016
We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood-based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…
Descriptors: Item Response Theory, Guessing (Tests), Mathematics Tests, Simulation
Falk, Carl F.; Cai, Li – National Center for Research on Evaluation, Standards, and Student Testing (CRESST), 2015
We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…
Descriptors: Guessing (Tests), Item Response Theory, Mathematics Instruction, Mathematics Tests
Tian, Wei; Cai, Li; Thissen, David; Xin, Tao – Educational and Psychological Measurement, 2013
In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…
Descriptors: Item Response Theory, Computation, Matrices, Statistical Inference
