Robust Mokken Scale Analysis by Means of the Forward Search Algorithm for Outlier Detection

Abstract

Exploratory Mokken scale analysis (MSA) is a popular method for identifying scales from larger sets of items. As with any statistical method, in MSA the presence of outliers in the data may result in biased results and wrong conclusions. The forward search algorithm is a robust diagnostic method for outlier detection, which we adapt here to identify outliers in MSA. This adaptation involves choices with respect to the algorithm's objective function, selection of items from samples without outliers, and scalability criteria to be used in the forward search algorithm. The application of the adapted forward search algorithm for MSA is demonstrated using real data. Recommendations are given for its use in practical scale analysis.

Discordancy Tests for Outlier Detection in Multi-Item Questionnaires

“…Analysis of J -way contingency tables has to deal with many empty cells for realistic sample size (Kotze & Hawkins, 1984, discuss the J = 2 case). Zijlstra, Van der Ark, and Sijtsma (2011b) adapted Atkinson and Riani’s (2000) forward search to J item scores in the context of Mokken scale analysis. Person-fit methods (Meijer & Sijtsma, 2001; also, see Emons, 2009; Goegebeur, De Boeck, & Molenberghs, 2010) assess the fit of item response theory models to an individual’s J item scores but such methods are ignored here for several reasons.…”

Distribution of Variables by Method of Outlier Detection

“…Despite these advantages, D 2 is sensitive to outliers because it is based on the sample covariance matrix, S , which is itself sensitive to outliers (Wilcox, 2005 ). In addition, D 2 assumes that the data are continuous and not categorical so that when data are ordinal, for example, it may be inappropriate for outlier detection (Zijlstra et al, 2007 ). Given these problems, researchers have developed alternatives to multivariate outlier detection that are more robust and more flexible than D 2 .…”