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Random Item Response Data Generation Using a Limited-Information Approach: Applications to Assessing Model

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Summary
This summary is machine-generated.

Fitting propensity analysis in item response theory (IRT) is now feasible using a novel limited-information (LI) approach. The Sequential Importance Sampling algorithm to Quickly and Uniformly Obtain Contingency tables (SISQUOC) enables efficient, random data generation for complexity evaluation.

Keywords:
fitting propensityitem response theorylimited-information methodsmodel complexitysequential importance sampling

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Educational Measurement

Background:

  • Fitting propensity (FP) analysis quantifies model complexity in item response theory (IRT).
  • Traditional full-information approaches face computational challenges in sampling response patterns.
  • Limited-information (LI) methods offer a viable alternative for IRT model evaluation.

Purpose of the Study:

  • To develop an efficient algorithm for sampling item response patterns in IRT.
  • To enable the evaluation of fitting propensity (FP) using a limited-information (LI) approach.
  • To compare the configural complexity of different IRT models.

Main Methods:

  • Developed the Sequential Importance Sampling algorithm to Quickly and Uniformly Obtain Contingency tables (SISQUOC).
  • Employed a limited-information (LI) approach, generating data from lower-order margins.
  • Utilized an iterative proportional fitting procedure to reconstruct joint probabilities for FP evaluation.

Main Results:

  • The SISQUOC algorithm effectively generates large, uniformly random datasets for IRT.
  • The LI approach simplifies data generation for both dichotomous and polytomous items.
  • Analysis of graded response and generalized partial credit models indicates similar configural complexity.

Conclusions:

  • The proposed LI approach and SISQUOC algorithm overcome computational barriers in IRT FP analysis.
  • This method facilitates robust model complexity assessment in item response theory.
  • The study provides insights into the configural complexity of common IRT models.