An EM algorithm for the block mixture model.

Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the Classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the EM algorithm for the block mixture model cannot be made directly; difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized EM algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.

A method for shortening instruments using the Rasch model. Validation on a hand functional measure.

BACKGROUND: Many measurement instruments, particularly measures of hand functional ability, frequently comprise a large number of items. Reduced versions of these instruments can facilitate their use. This work proposes a new method for shortening an instrument. METHODS: The method proposed was based on a scale of item difficulty calculated using the Rasch model. It was applied on a hand functional measure comprising 67 tests. The sample included 194 patients with hand lesions. The shortened instrument obtained was compared with those provided by classic methods used in the literature, with item random choice, and with shortened versions proposed by four independent experts, two rehabilitation physicians and two occupational therapists, who are clinicians familiar with the tool. All the statistical analyses were carried out on a random sub-group of two-thirds of the sample. A cross validation was then carried out on the remaining third. RESULTS: The reduction obtained had score non significantly different from that of the original instrument. In addition, the intra-class correlation coefficient and the Cronbach alpha coefficient were high. Among the different degrees of reduction investigated, the 12-item version seemed to be appropriate. Our method appeared to provide better results in terms of discriminant validity and internal validity than the choices of the four experts. The reductions produced were also better than those obtained by classic methods based on principal component analysis and multiple linear regression, as well as those obtained by random choices of items. CONCLUSION: The method presented is pertinent and useful. The reduction obtained appeared to be better than the choices of experts and the reductions provided by classic methods. The method could be used in other fields.

[Unidimensionality of a functional measure for patient with an injured upper limb]. / Unidimensionnalité d'une mesure fonctionnelle pour des malades ayant une lésion du membre supérieur.

The construction of an instrument including a number of tests requires an analysis of its structure and its unidimensionality (which allows calculation of global score), and the determination of the difficulty level of various tests. This study examined a tool including 67 tests designed to evaluate the functional ability of patients with an injured upper limb. The patients seen in a rehabilitation centre during 12 months (173 subjects) were evaluated by the occupational therapists familiar with the tool. The statistical analyses were made using the principal component analysis method (PCAM), the Cronbach's coefficient and the Rasch model. The PCAM showed 3 principal factors which explained 44%, 10% and 4% of the total variance respectively in the case of patients with injured dominant limb. The predominance of the first axis and the high ratio of first by second eigenvalues suggested the unidimensionality of the tool. The Cronbach's value of 0.97 attested the good congruence of the items. The results obtained with the Rasch model seemed to be consistent with the hypothesis of the unidimensionality of the tool. This analysis also provided the difficulty scale of various tests. Similar results were obtained in patients with injured non dominant limb or with all the sample. The methods used provide complementary results.