The Numerical Solution of a Set of Conditional Estimation Equations

Abstract

Summary In this paper we discuss the numerical solution of a set of conditional likelihood equations essential for the statistical analysis of psychological questionnaires. The model underlying this type of statistical analysis is described in detail and the conditional maximum-likelihood method that is used for estimating item parameters is discussed in relation to the chosen model. The conditional likelihood equations contain a generalized version of the elementary symmetric functions. The main problem in solving the estimation equations consists in finding a rapid recursive way to compute these functions. Such a procedure is described in the paper. In the final section of the paper the developed method is illustrated by a numerical example.