Kriging coordinates: what does that mean?

Kriging is an interpolation technique whose optimality criteria are based on normality assumptions either for observed or for transformed data. This is the case of normal, lognormal and multigaussian kriging. When kriging is applied to transformed scores, optimality of obtained estimators becomes a cumbersome concept: back-transformed optimal interpolations in transformed scores are not optimal in the original sample space, and vice-versa. This lack of compatible criteria of optimality induces a variety of problems in both point and block estimates. For instance, lognormal kriging, widely used to interpolate positive variables, has no straightforward way to build consistent and optimal confidence intervals for estimates. These problems are ultimately linked to the assumed space structure of the data support: for instance, positive values, when modelled with lognormal distributions, are assumed to be embedded in the whole real space, with the usual real space structure and Lebesgue measure

When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’t includes below detection limits and/or zero values, and since most of the geological data responds to lognormal distributions, these “zero data” represent a mathematical challenge for the interpretation. We need to start by recognizing that there are zero values in geology. For example the amount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-exists with nepheline. Another common essential zero is a North azimuth, however we can always change that zero for the value of 360°. These are known as “Essential zeros”, but what can we do with “Rounded zeros” that are the result of below the detection limit of the equipment? Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimes we need to differentiate between a sodic and a potassic alteration. Pre-classification into groups requires a good knowledge of the distribution of the data and the geochemical characteristics of the groups which is not always available. Considering the zero values equal to the limit of detection of the used equipment will generate spurious distributions, especially in ternary diagrams. Same situation will occur if we replace the zero values by a small amount using non-parametric or parametric techniques (imputation). The method that we are proposing takes into consideration the well known relationships between some elements. For example, in copper porphyry deposits, there is always a good direct correlation between the copper values and the molybdenum ones, but while copper will always be above the limit of detection, many of the molybdenum values will be “rounded zeros”. So, we will take the lower quartile of the real molybdenum values and establish a regression equation with copper, and then we will estimate the “rounded” zero values of molybdenum by their corresponding copper values. The method could be applied to any type of data, provided we establish first their correlation dependency. One of the main advantages of this method is that we do not obtain a fixed value for the “rounded zeros”, but one that depends on the value of the other variable. Key words: compositional data analysis, treatment of zeros, essential zeros, rounded zeros, correlation dependency

Networks of PhD Students and Academic Performance: A Comparison across Countries

In this article we compare regression models obtained to predict PhD students’ academic performance in the universities of Girona (Spain) and Slovenia. Explanatory variables are characteristics of PhD student’s research group understood as an egocentered social network, background and attitudinal characteristics of the PhD students and some characteristics of the supervisors. Academic performance was measured by the weighted number of publications. Two web questionnaires were designed, one for PhD students and one for their supervisors and other research group members. Most of the variables were easily comparable across universities due to the careful translation procedure and pre-tests. When direct comparison was not possible we created comparable indicators. We used a regression model in which the country was introduced as a dummy coded variable including all possible interaction effects. The optimal transformations of the main and interaction variables are discussed. Some differences between Slovenian and Girona universities emerge. Some variables like supervisor’s performance and motivation for autonomy prior to starting the PhD have the same positive effect on the PhD student’s performance in both countries. On the other hand, variables like too close supervision by the supervisor and having children have a negative influence in both countries. However, we find differences between countries when we observe the motivation for research prior to starting the PhD which increases performance in Slovenia but not in Girona. As regards network variables, frequency of supervisor advice increases performance in Slovenia and decreases it in Girona. The negative effect in Girona could be explained by the fact that additional contacts of the PhD student with his/her supervisor might indicate a higher workload in addition to or instead of a better advice about the dissertation. The number of external student’s advice relationships and social support mean contact intensity are not significant in Girona, but they have a negative effect in Slovenia. We might explain the negative effect of external advice relationships in Slovenia by saying that a lot of external advice may actually result from a lack of the more relevant internal advice