Fuzzy c-means clustering is a useful method for capturing group-level heterogeneity of objects. This method estimates cluster centroids and fuzzy memberships simultaneously. A potential limitation of fuzzy c-means is that it may fail to detect clusters of different sizes. To address this difficulty, we propose an extension of FCM, called hierarchically structured FCM, which can detect clusters of different sizes as well as provide additional information on nested structures of clusters. Unlike extant hierarchical extensions of FCM that execute FCM at each level of hierarchy separately in a sequential manner, the proposed method estimates cluster centroids and fuzzy memberships in different levels simultaneously by minimizing a single objective function. The optimal number of clusters and sub-clusters is determined by examining cluster validity measures. The usefulness of the proposed method is illustrated by analyzing two synthetic data and real image data.
Assuming specific values for item hyperparameters, Bayesian nonhierarchical modeling for unidimensional IRT models suffers from problems in that it relies on the availability of appropriate prior information for the three-parameter model or for small datasets. These problems can be resolved by specifying priors in a hierarchical fashion so that the item hyperparameters are unknown and have their own prior distributions. This study investigated the performance of such hierarchical modeling by comparing it with the nonhierarchical approach using Monte Carlo simulations. Their results provided empirical evidence for the advantage of using hierarchical priors in modeling unidimensional item response data when appropriate prior information is not readily available and when datasets are not sufficiently large.
This study aims to confirm Japanese food selection criteria and to identify gender-based differences in criteria. In the first part, 464 male and female students responded to a questionnaire about food choices. Factor analysis identified five factors: mood, safety, convenience, weight control, and price. To verify the reliability of these factors, 720 additional participants completed the same questionnaire. Confirmatory factor analysis confirmed the reliability of the factors. Furthermore, results of multiple-group analysis indicate that there are significant gender-based differences in food selection criteria. Females in their twenties attached more importance to safety and weight control than their male counterparts, while females in their forties considered mood, safety, weight control, and convenience more important than their male counterparts did.
Data sets in the social and behavioral sciences are often small or heavy-tailed. Previous studies have demonstrated that small samples or leptokurtic distributions adversely affect the performance of Cronbach’s coefficient alpha. To address these concerns, we propose an alternative estimator of reliability based on L-comoments. The empirical results of this study demonstrate that when sample sizes are small and distributions are heavy-tailed that the proposed coefficient L-alpha has substantial advantages over the conventional Cronbach estimator of reliability in terms of relative bias and relative standard error.
A Bayesian factor analysis procedure is proposed for obtaining a simple loading matrix based on prior information in which the loading matrix approximates a sparse target matrix including zero elements. A feature of this procedure is that the target matrix is unknown and estimated; the number and locations of zero elements are not specified. We derive the estimation of the full conditional distributions of parameters using Gibbs sampling. A simulation study and real data examples demonstrate that the proposed procedure can provide simpler loading matrices than existing rotation methods.
A familiar problem with respect to the analysis of network data (in which relations between objects can be described by links between the vertices of a graph) is the discovery of so-called community structures, i.e., the detection of subgraphs of closely connected vertices with comparatively few links joining vertices of different subgraphs. For this task modularity is a popular goodness-of-fit-index. While undirected graphs restrict considerations to basically symmetric relations, more realistic situations can be described by directed graphs. In this paper we consider shortest walk lengths between all pairs of vertices as dissimilarities instead of just using the adjacency information given by the directed edges of the graphs, which enables us to suggest a new approach in which the application of asymmetric clustering is a main step. This enrichment of the underlying adjacency matrix to a walk-length based dissimilarity matrix together with asymmetric hierarchical clustering are the keys of our proposed approach to community structure discovery in directed graphs. We use example graphs from the literature with known modularity values and apply computer-generated directed benchmark graphs for the evaluations. The findings show that our approach compares favourably with results available from the literature.