Using the normal-ogive model, Thomson (1919) estimated the Fechner-Müller-Urban thresholds using a method that is remarkably similar to the maximum-likelihood procedure introduced by Fisher in 1925, one of the procedures that is currently in use in the estimation of an examinee’s ability. In the testing context, Richardson (1936) and Ferguson (1942) used the normal-ogive model for scaling difficulties of dichotomously scored items. Lawley (1943, 1944) was the first to formally employ the normal-ogive model to directly model binary item response data, using the maximum-likelihood procedure to estimate threshold and discrimination parameters under the assumption that the observed test score serves as a measure of the ability of the examinee; this procedure, as pointed out by Finney (1944), was already widely known in toxicology as probit regression. Tucker (1946) used the term “item curve” repeatedly to indicate the relationship between item response and ability and in doing so anticipated the current term “item characteristic curve.” These early attempts at modeling binary response data culminated in the work of Lord (1952,

CONTENTS

11.1 Introduction ........................................................................................................................ 167 11.2 Presentation of the Model ................................................................................................. 170 11.3 Parameter Estimation ........................................................................................................ 177

11.3.1 Asymptotic Distribution of Estimators .............................................................. 178 11.4 Goodness of Fit ................................................................................................................... 182 11.5 Empirical Example ............................................................................................................. 183 11.6 Conclusion .......................................................................................................................... 184 References ..................................................................................................................................... 185

1953, 1980) who, unlike the early researchers, treated ability as a latent trait to be estimated and in doing so, laid the foundation for item response theory (IRT).