AN EQUIPERCENTILE VERSION OF THE LEVINE LINEAR OBSERVED‐SCORE EQUATING FUNCTION USING THE METHODS OF KERNEL EQUATING

Abstract

ABSTRACTIn the nonequivalent groups with anchor test (NEAT) design, there are several ways to use the information provided by the anchor in the equating process. One of the NEAT‐design equating methods is the linear observed‐score Levine method (Kolen & Brennan, 2004). It is based on a classical test theory model of the true scores on the test forms to be equated and on the anchor test (Levine, 1955). The Levine linear method does not yet have an equipercentile analogue, and no version of kernel equating (KE), introduced in von Davier, Holland, and Thayer (2004b), approximates the Levine linear method. Nevertheless, the Levine observed‐score equating method is often computed in practical applications for comparison purposes because it is sometimes more accurate than other linear equating methods (Petersen, Marco, & Stewart, 1982). In situations when a linear equating function is not satisfactory, an equipercentile version of the Levine function may be desirable. This paper proposes a general method for constructing hybrid equating functions that combine linear and nonlinear equating functions in a systematic way that preserves the symmetry required of equating functions (Dorans & Holland, 2000). The general method is then applied to combine the linear Levine observed‐score equating function with a nonlinear equipercentile equating function derived using the poststratification equating (PSE) assumptions within the KE framework. An easily computed approximation to the resulting PSE‐Levine equipercentile equating function is illustrated on data from a special study and compared to the results from the traditional equating functions. The special data set includes a criterion equating function, and the closeness of the PSE‐Levine function to this criterion indicates that such hybrid equating functions may be useful in practice.