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A New Statistic to Assess Fitness of Cubic‐Spline Postsmoothing
Author(s) -
Kim Hyung Jin,
Brennan Robert L.,
Lee WonChan
Publication year - 2019
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/jedm.12244
Subject(s) - smoothing spline , smoothing , statistic , smoothness , mathematics , statistics , spline (mechanical) , standard deviation , thin plate spline , akaike information criterion , spline interpolation , engineering , mathematical analysis , structural engineering , bilinear interpolation
In equating, smoothing techniques are frequently used to diminish sampling error. There are typically two types of smoothing: presmoothing and postsmoothing. For polynomial log‐linear presmoothing, an optimum smoothing degree can be determined statistically based on the Akaike information criterion or Chi‐square difference criterion. For cubic‐spline postsmoothing, visual inspection has been an important tool in choosing such optimum degrees in operational settings. This study introduces a new statistic for assessing the fitness of the cubic‐spline postsmoothing method, which accommodates three conditions: (1) one standard error band, (2) deviation from unsmoothed equivalents, and (3) smoothness. A principal advantage of the new statistic proposed in this study is that an optimum degree of smoothing can be selected automatically by giving consistent amount of attention to deviation and smoothness across multiple equatings, whereas visual inspection may not be consistent.