The Continuized Log-Linear Method: An Alternative to the Kernel Method of Continuization in Test Equating

Von Davier, Holland, and Thayer (2004) laid out a five-step framework of test equating that can be applied to various data collection designs and equating methods. In the continuization step, they presented an adjusted Gaussian kernel method that preserves the first two moments. This article proposes an alternative continuization method that directly uses the log-linear function from the smoothing step. This alternative method has the advantages of being simple and direct and producing smoother continuous distributions. When the number of score points is large, it can better preserve the moments. Two real test examples are provided to demonstrate these properties and to compare equating functions based on different methods. The standard error of equating for this method is derived.