Empirical Histograms in Item Response Theory With Ordinal Data

Carol M. Woods
Washington University in St. Louis

The purpose of this research is to describe, test, and illustrate a new implementation of
the empirical histogram (EH) method for ordinal items. The EH method involves the
estimation of item response model parameters simultaneously with the approximation
of the distribution of the random latent variable (θ) as a histogram. Software for the EH
method with ordinal items (having more than two response options) has not been
readily available in the past but was created for the present research. Simulation results
suggest that with larger (but not smaller) numbers of quadrature points, graded-model
item parameter estimates from the EH method are highly accurate when the θ distribution
is either normal or skewed. Results for expected a posteriori scores depend on the
magnitude of θ.

Keywords: item response theory; IRT; nonnormality; empirical histogram; expectation
Maximation; EM; marginal maximum likelihood; MML


这是一篇使用经验直方图估计受测者潜在特质分布IRT方法的文献。同样也是一种可以处理受测者潜在特质非正态分布的方法。