An Alternative Continuization Method to the Kernel Method in von Davier, Holland and Thayer’s (2004) Test Equating Framework

von Davier, Holland and Thayer (2004) laid out a five-step framework of test equating which can be applied to various data collection designs and equating methods. In the continuization step, they present an adjusted Gaussian kernel method which preserves the first two moments. This paper proposes an alternative continuization method which 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 provide comparisons of equating functions based on different methods. The standard error of equating for this method is derived.