Estimation of reliability coefficients using the test information function and its modifications

The reliability coefficient and the standard error ofmeasurement in classical test theory are not propertiesof a specific test, but are attributed to both a specifictest and a specific trait distribution. In latent trait models,or item response theory, the test information function(TIF) provides more precise local measures ofaccuracy in trait estimation than are available from thereliability coefficient. The reliability coefficient is stillwidely used, however, and is popular because of itssimplicity. Thus, it is worthwhile to relate it to the TIF.In this paper, the reliability coefficient is predictedfrom the TIF, or two modified TIF formulas, and a specifictrait distribution. Examples demonstrate the variabilityof the reliability coefficient across different traitdistributions, and the results are compared with empiricalreliability coefficients. Practical suggestions aregiven as to how to make better use of the reliabilitycoefficient. Index terms: adaptive testing, bias, classicaltest theory, item information function, latent traitmodels, maximum likelihood estimation, reliability coefficient,standard error of measurement, test informationfunction, trait estimation.