This project presents a novel application of bootstrapping to the results from multidimensional scaling (MDS) analysis. To illustrate this, it uses a data set on the psychology of food rejection. Forty-one subjects answered a battery of thirteen questions - known as a Food Rejection Index (FRI) - about each of nineteen items that are generally rejected. Subjects made their answers on visual analogue scales, the data from which were transformed using an arcsine root transformation. A dissimilarity matrix for the items was constructed for each subject. The dissimilarity index used was based on the correlation between items over the transformed FRI data. MDS was applied to a matrix produced by averaging over all the subjects' dissimilarity matrices.
The new bootstrap procedure involves refitting one item at a time in the MDS output, conditional on the other items being held constant. For each item, bootstrap samples were drawn randomly from the forty-one subjects' dissimilarity matrices with replacement. A new, averaged dissimilarity matrix was constructed for each bootstrap sample and the item of concern refitted into the original solution, the fitting constrained on the other items remaining fixed. This produces a point scatter. An alpha percent confidence region was constructed by fitting a two-dimensional kernel density estimate to the point scatter and drawing an isocontour that excludes alpha percent of the points. Properties of the method were investigated.
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