ABSTRACT
The normal probability density function is central to statistical modeling in the natural, social, and physical sciences. The cumulative normal distribution function, or the normal ogive, is thus a natural choice for modeling probabilities (Albert, Volume Two,Chapter 1). Gustav Fechner may have been the first to use the normal ogive in the mid-1860s to model stimulus intensity (Bock, 1997). Interest in normal-ogive models for analyzing binary response data was sparked in the early twentieth century byKarl Pearson’s (1900) work using the univariate and bivariate normal-ogive models for estimating the biserial and tetrachoric correlations, respectively. In fact, Pearson’s tetrachoric series, as we shall see later, continues to play an important role in the analysis of multidimensional binary item responses.
