Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance andWilliams’ formula which enables the implementation of the algorithm in a recursive way. The authors thank A. Arenas for discussion and helpful comments. This work was partially supported by DGES of the Spanish Government Project No. FIS2006–13321–C02–02 and by a grant of Universitat Rovira i Virgili.     

Effects of vitamin B12 on plasma melatonin rhythm in humans: increased light sensitivity phase-advances the circadian clock?

Vitamin B12 (methylcobalamin) was administered orally (3 mg/day) to 9 healthy subjects for 4 weeks. Nocturnal melatonin levels after exposure to bright light (ca. 2500 lx) were determined, as well as the levels of plasma melatonin over 24 h. The timing of sleep was also recorded. Vitamin B12 was given blind to the subjects and crossed over with placebo. We found that the 24-h melatonin rhythm was significantly phase-advanced (1.1 h) in the vitamin B12 trial as compared with that in the placebo trial. In addition, the 24-h mean of plasma melatonin level was much lower in the vitamin B12 trial than with the placebo. Furthermore, the nocturnal melatonin levels during bright light exposure were significantly lower in the vitamin B12 trial than with the placebo. On the other hand, vitamin B12 did not affect the timing of sleep. These findings raise the possibility that vitamin B12 phase-advances the human circadian rhythm by increasing the light sensitivity of the circadian clock.     

Estimation and testing of time-varying coefficient regression models in the presence of linear restrictions

A linear regression model with random walk coefficients is extended to allow for linear restrictions between the coefficients to be satisfied at each point in time. Estimation in this model is shown to be no more involved than estimation in the standard model. It is also demonstrated how, after a slight modification to the testing problem, classical test procedures may be applied to the problem of testing for such restrictions. The performance of the Lagrange Multiplier test for a variety of different restrictions is then investigated via simulation. An empirical application involving testing for homogeneity in a random walk coefficient version of the AIDS model is given.     

Seasonality in human sleep.

The timing of sleep and sleep EEG parameters in 10 healthy male subjects were investigated in four seasons under controlled conditions. The phase of nocturnal sleep was delayed about one and a half hours in winter as compared to that in summer. The duration of stage 4 sleep decreased and REM sleep increased significantly in winter compared with summer. The seasonality in the timing of sleep can be explained by photoperiodic time cues, but the changes in sleep EEG parameters are difficult to explain in terms of photoperiod.