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

Student self-assessment a feedback seeking strategy through competence evaluation

There is a body of literature that suggests that student self-assessment is a main goal in higher education (Boud et al., 1995; Tan, 2008); moreover new forms of work organization require a high level of skills and competences. The efforts to deal with competence gaps could be developed at many levels, such as employers, educational institutions, individuals and public agents. Employers could put into practice competence development programs to moderate these gaps. Educational institutions can restructure the curriculum to support students in attaining the competences that are essential in the labour market. Individuals themselves may deploy their resources (time and money) in general or specific competence training. Further, government agencies could fund competence promotion programs. Such challenges for education drive change in learning curricula and method, to properly include the competences required for developing global workers who can move beyond basic competence, to enhanced flexibility and adaptability. In performance assessment methods, there is a shift from the traditional exam-based assessments to more innovative task assessment, which considers performance in multiple different tasks carry out by students. ICTs make it technologically feasible to carry out a complete and complex selfassessment of competences, which provides immediate results to students or other recipients. In the case of students, the evaluation of competences is relevant as developing competences is part - if not all - of the objectives of education. Therefore, it is an important element of the quality of educational organizations (e.g., universities), and of their organizational success. Further, educational organizations may put special emphasis on some differentiating competences, which can be a means of positioning and differentiation from competitors. Competence assessment is an instrument to make students conscious of their strengths and weaknesses, leading to higher motivation to develop their own learning career