Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.

Performance assessment and league tables. Comparing like with like

We formulate performance assessment as a problem of causal analysis and outline an approach based on the missing data principle for its solution. It is particularly relevant in the context of so-called league tables for educational, health-care and other public-service institutions. The proposed solution avoids comparisons of institutions that have substantially different clientele (intake).

An adaptation of correspondence analysis for square tables

The application of correspondence analysis to square asymmetrictables is often unsuccessful because of the strong role played by thediagonal entries of the matrix, obscuring the data off the diagonal. A simplemodification of the centering of the matrix, coupled with the correspondingchange in row and column masses and row and column metrics, allows the tableto be decomposed into symmetric and skew--symmetric components, which canthen be analyzed separately. The symmetric and skew--symmetric analyses canbe performed using a simple correspondence analysis program if the data areset up in a special block format.

Historical contingency affects signaling strategies and competitive abilities in evolving populations of simulated robots.

One of the key innovations during the evolution of life on earth has been the emergence of efficient communication systems, yet little is known about the causes and consequences of the great diversity within and between species. By conducting experimental evolution in 20 independently evolving populations of cooperatively foraging simulated robots, we found that historical contingency in the occurrence order of novel phenotypic traits resulted in the emergence of two distinct communication strategies. The more complex foraging strategy was less efficient than the simpler strategy. However, when the 20 populations were placed in competition with each other, the populations with the more complex strategy outperformed the populations with the less complex strategy. These results demonstrate a tradeoff between communication efficiency and robustness and suggest that stochastic events have important effects on signal evolution and the outcome of competition between distinct populations.

Correspondence analysis of two transition tables

The case of two transition tables is considered, that is two squareasymmetric matrices of frequencies where the rows and columns of thematrices are the same objects observed at three different timepoints. Different ways of visualizing the tables, either separatelyor jointly, are examined. We generalize an existing idea where asquare matrix is descomposed into symmetric and skew-symmetric partsto two matrices, leading to a decomposition into four components: (1)average symmetric, (2) average skew-symmetric, (3) symmetricdifference from average, and (4) skew-symmetric difference fromaverage. The method is illustrated with an artificial example and anexample using real data from a study of changing values over threegenerations.

Tying up the loose ends in simple correspondence analysis

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

New reference tables and user-friendly Internet application for predicted heart weights.

BACKGROUND: Knowledge of normal heart weight ranges is important information for pathologists. Comparing the measured heart weight to reference values is one of the key elements used to determine if the heart is pathological, as heart weight increases in many cardiac pathologies. The current reference tables are old and in need of an update. AIMS: The purposes of this study are to establish new reference tables for normal heart weights in the local population and to determine the best predictive factor for normal heart weight. We also aim to provide technical support to calculate the predictive normal heart weight. METHODS: The reference values are based on retrospective analysis of adult Caucasian autopsy cases without any obvious pathology that were collected at the University Centre of Legal Medicine in Lausanne from 2007 to 2011. We selected 288 cases. The mean age was 39.2 years. There were 118 men and 170 women. Regression analyses were performed to assess the relationship of heart weight to body weight, body height, body mass index (BMI) and body surface area (BSA). RESULTS: The heart weight increased along with an increase in all the parameters studied. The mean heart weight was greater in men than in women at a similar body weight. BSA was determined to be the best predictor for normal heart weight. New reference tables for predicted heart weights are presented as a web application that enable the comparison of heart weights observed at autopsy with the reference values. CONCLUSIONS: The reference tables for heart weight and other organs should be systematically updated and adapted for the local population. Web access and smartphone applications for the predicted heart weight represent important investigational tools.