Simplicity Above Elegance: Another Look at the Asymptotically Correct Standardization of Snijders

Person-fit statistics are widely used to detect aberrant response patterns in educational and psychological measurement. Snijders suggested an asymptotically correct standardization for a broad class of such statistics. This paper presents an alternative derivation of this standardization. The derivation yields several advantages including a simpler formula and simpler description of several person-fit statistics including the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> statistic and a theoretical explanation of simulation findings reported by Snijders and van Krimpen-Stoop and Meijer, among others.