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We describe an implementation of simple, multiple and joint correspondence analysis in R. The resulting package comprises two parts, one for simple correspondence analysis and one for multiple and joint correspondence analysis. Within each part, functions for computation, summaries and visualization in two and three dimensions are provided, including options to display supplementary points and perform subset analyses. Special emphasis has been put on the visualization functions that offer features such as different scaling options for biplots and three-dimensional maps using the rgl package. Graphical options include shading and sizing plot symbols for the points according to their contributions to the map and masses respectively.

Within the limitations of this study, the results suggest that male resource defense could be a strategy benefitting both sexes if male reproductive skew was low and many males benefited from increased female fertility.

SUMMARYWe describe the development of a Web-based rainfall atlas for southern Africa, a decision support system for the management of water resources. The rainfall atlas, which is accessible online at the URI http://134.76.173.220/ rainfall/index.html, was constructed in a number of phases over some 20 years. In the first phase, a 16 parameter model was developed, validated for representative sites, and then fitted to daily rainfall data from 2550 sites. Eight years later the estimates of the model parameters were updated, extended to 5070 sites, and interpolated on a grid of 1 minute of a degree of latitude and longitude over the entire region of southern Africa, namely South Africa, Lesotho and Swaziland. The method of kriging with external drift was used for the interpolation. The interpolated estimates were used to generate long artificial daily rainfall sequences at a spatial resolution of 1 minute of degree square. The sequences were used to compute rainfall-related statistics, such as percentiles of annual and monthly rainfall distributions, probabilities associated with droughts, and additional measures relating to the timing and intensity of rainfall. The final phase, information transfer, was the construction of the Atlas website, which offers online access to a wide range of rainfall-related statistics and some 5000 maps. To facilitate the computation of statistics that are not available in the database, the Atlas enables users to generate, and then import, artificial sequences online, for any grid point in southern Africa. These sequences are designed to mirror the properties of real rainfall records (seasonality, serial dependence, distributional properties, etc.) at the required grid point and can be used to compute quantities of interest empirically.

The generalization of simple correspondence analysis, for two categorical variables, to multiple correspondence analysis where they may be three or more variables, is not straighforward, both from a mathematical and computational point of view. In this paper we detail the exact computational steps involved in performing a multiple correspondence analysis, including the special aspects of adjusting the principal inertias to correct the percentages of inertia, supplementary points and subset analysis. Furthermore, we give the algorithm for joint correspondence analysis where the cross-tabulations of all unique pairs of variables are analysed jointly. The code in the R language for every step of the computations is given, as well as the results of each computation.