Multivariate Analysis of Ecological Data ......| .... Biplots in Practice

This page contains the videos are used in Multivariate Analysis of Ecological Data and Biplots in Practice.

# Multivariate Analysis of Ecological Data

• Chapter 13: Video 13.1
In this video we see the three-dimensional scatterplot of the samples and species of the "Barents fish" data set - see Exhibit 13.4 of the book.

# Biplots in Practice

• Chapter 1: Video 1.1
This video shows the scatterplot of the trivariate data from Exhibit 1.1, rotating the scatterplot around the vertical dimension ("Purchasing power").

• Chapter 1: Video 1.2
This video shows the same trivariate data from Exhibit 1.1, rotating the scatterplot in a “diagonal” direction until the country points are as spread out as possible., where the video pauses. This shows that the points must lie approximately in a plane and this viewpoint is looking at that plane.

• Chapter 2: Video 2.1
In this video we see the three-dimensional scatterplot of species d versus pollution (y) and depth (x) and the regression plane defined by the model d = 6.135-1.388y+0.148x [see equation (2.1) and the schematic version on the left of Exhibit 2.2].

• Chapter 2: Video 2.2
In this video we see the same three-dimensional scatterplot of species d versus pollution (y) and depth (x) , but with all variables standardized (mean 0, variance 1). The regression plane in these standardized variables is now d* = -0.446y*+0.347x*. [see schematic version on the right of Exhibit 2.2]. The plane can de uniquely defined by the white arrow pointing up the plane in the direction of steepest ascent, called a biplot axis or biplot direction. Lines in white are drawn at right angles to this direction according to units of standard deviation in the response variable d above and below the mean, as predicted by the regression model. On the x-y plane there is a shadow of the plane as well as the direction of the biplot arrow in red and the parallel lines in red which are now the corresponding contour lines of the plane. These contours can be seen in Exhibit 2.3, illustrating how the projections of the points on the biplot direction onto these contours are just the regression plane estimates.

• Chapter 5: Video 5.1
If you play this video you will hear Michael Greenacre's musical rendition of the singular value decomposition (SVD), which is the basis of all the dimension-reducing methods presented in this book. The song was recorded by Gurdeep Stephens (voice) and Lisa Olive (piano) on 21 June 2011 in Victoria, BC, Canada, with animations and commentary added by Michael in Barcelona. It was presented for the first time in Michael's invited talk "Biplot Videos" at the 9th Tartu Conference on Multivariate Analysis, 28 June 2011, in Estonia.