A general statistical framework for assessing categorical clustering in free recall.

Abstract

A graph-theoretic paradigm is used to generalize the common measures of categorical clustering in free recall based on the number of observed repetitions. Two graphs are defined: Graph G, which characterizes the a priori structure of the item set defined by a researcher; and Graph R, which characterizes a subject's protocol. Two indices of clustering, denoted by T and fi, are obtained by evaluating the sum of the pair-wise products of the weights on the corresponding edges of the two graphs. The r statistic is a direct generalization of the commonly used clustering indices and reduces to the number of repetitions whenever G represents a standard categorical decomposition of a stimulus list. The fi statistic, on the other hand, extracts more information from the protocol graph, R, than does r and incorporates a distance measure based on the number of intervening items in a subject's recall sequence.

A neighbourhood level mortality classification of England and Wales, 2006–2009

“…To inform this decision, a selection of statistics were used to choose the number of clusters that best represents the data. These included the 'C-index' (Hubert & Levin 1976) and Davies & Bouldin (1979) 'Validity Index' which both examine the similarity of clusters. These measures have both been shown to be effective at determining the correct number of clusters (Milligan & Cooper 1985).…”

Inflammatory endotypes of chronic rhinosinusitis based on cluster analysis of biomarkers

“…Next, clusters were calculated using the partitioning around medoids method, of which outcomes with the number of clusters ranging from 2 to 15 clusters were generated. The optimal number of clusters was based on the elbow (maximum change) of the scree plot of the mean silhouette width, Baker-Hubert Gamma statistic 18 , and Hubert-Levin C index 19 . Additionally, the optimal number of clusters was assessed using Jaccard stability after bootstrap resampling 20 and visual inspection of the clusplot after multidimensional scaling 20 .…”

Smoking Behavior: A Cross-Sectional Study to Assess the Dimensionality of the Brief Wisconsin Inventory of Smoking Dependence Motives and Identify Different Typologies Among Young Daily Smokers

“…Concerning the hierarchical method, different solutions were chosen based on the decrease in the explained error sum of squares (ESS) as suggested by Bergman. 46 In the latter nonhierarchical method, four indices were used to evaluate the optimal number of clusters: the C-index, 47 the G(+), 48 the Gamma, 49 and the Point-biserial correlation. 50 The minimum value of the former two indices and maximum of the latter two indices suggest the optimal number of clusters to be retained, hence the best cluster solution.…”