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Falk, 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
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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
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Kim, G. D.; Engelhardt, J. – International Journal of Mathematical Education in Science and Technology, 2007
A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…
Descriptors: Numbers, Number Concepts, Mathematical Formulas, Problem Solving
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Ceulemans, Eva; Van Mechelen, Iven – Psychometrika, 2005
Several hierarchical classes models can be considered for the modeling of three-way three-mode binary data, including the INDCLAS model (Leenen, Van Mechelen, De Boeck, and Rosenberg, 1999), the Tucker3-HICLAS model (Ceulemans,VanMechelen, and Leenen, 2003), the Tucker2-HICLAS model (Ceulemans and Van Mechelen, 2004), and the Tucker1-HICLAS model…
Descriptors: Test Items, Models, Vertical Organization, Emotional Response