Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completely absent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involved parts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method is introduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that the theoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approach has reasonable properties from a compositional point of view. In particular, it is “natural” in the sense that it recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in the same paper a substitution method for missing values on compositional data sets is introduced

PhD Students’ Research Group Networks: a Qualitative Approach

This article examines the networks within the research groups where Spanish PhD students are pursuing their doctorate. Capó et al. (2007) used quantitative data to predict PhD students’ publishing performance from their background, attitudes, supervisors’ performance and research group networks. Variables related to the research group network had a negligible explanatory power on student performance once the remaining variables had been accounted for. In this article, a qualitative follow up of the same students is carried out using extreme case sampling and indepth interviews. The qualitative research shows networking as important for students. Out of the 115 aspects that students mention in the interviews as relevant to publishing in the qualitative research, 92 have to do with their supervisors, their research group or their network as a whole. Similarly, out of the 50 hindrances mentioned, 20 have to do with the networks or relations. The most commonly mentioned network-related topics are research group members pushing PhD students to publish, meeting researchers outside the research group, existence of other PhD students in the group, help with the PhD from group members, supervisor’s interest in the thesis, the possibility of discussing with experts on the PhD’s topic and frequent contact with the supervisor and research group members. Some of these characteristics were not, however, measured in the conventional quantitative social network survey