Multi-variate data

Multi-variate data has one or more independent variables and more than one dependent ones. Think, for instance, of weight-at-time for females and males. The concept that predictions for the various data are coupled by sharing parameters is key to DEB theory as well as to multi-variate data.

Uni-, bi- and tri-variate variables have one, two or three independent variables. More independent variables can be included via auxiliary data.

Since AmP deals with an arbitrary number of data sets, and a collection of uni-variate data sets can have the same independent variable and presented in a grouped plot, there is no need, other than convenience, to deal with multi-variate data with several dependent variables explicitly. To present a set of uni-variate data in a grouped plot, they all must have the same units and labels. To produce a grouped plot, the metaData as defined in a mydata-file needs to have field metaData.grp.sets and, optionally, fields metaData.grp.title and metaData.grp.subtitle. A title becomes part of the produced png-file, a subtitle not and is only shown in the modal-presentation of the plot (i.e. after clicking on it). An example of a grouped plot is given in the dog-entry. Bi- and tri-variate data sets do not need a grouped-plot definition; it is not possible to combine such data sets with other data sets in a grouped plot.

An example of multi-variate can be found with the Doliolid: Dolioletta gegenbauri. The excerpt of the code below show how the multi-variate is set within the mydata file:

	  % food density - ingestion rate
	data.XJX = [ ... % phytoplankton conc. (mug C/l), ingestion rate (mug C/d)
	20	3.059  7.620 10.471
	60	6.328 15.259 30.081
	160 7.753 25.995 69.321
	390	4.171 12.533 38.757];
	units.XJX = {'mug C/l', 'mug C/d'};     label.XJX = {'phytoplankton conc.', 'ingestion rate'};  
	treat.XJX = {2, [5; 15; 35]}; units.treat.XJX = 'mug C'; label.treat.XJX = 'zooid C weight';
	temp.XJX = C2K(20); units.temp.XJX = 'K'; label.temp.XJX = 'temperature';
	bibkey.XJX = 'GibsPaff2000';
	subtitle.XJX = 'ingestion rate';
	comment.XJX = 'Data for gonozooid';

If a data-matrix has 3 columns, i.e. 1 independent variable and 2 dependent ones, and if the units as well as the label for that data set is a cell-string of length 3, a plot is created with 2 different y-axes. The first element of treat must then be 0 or 1, not 2, and no legend is produced. All that relates to the left yaxis is plotted in red, to the right in blue. An example of a plot with two different y-axes is given in the entries Vipera_aspis and, Sialia_mexicana (first element of treat is 1).

Yet it can be handy to specify a multi-variate data set as a matrix where the first column is treated as the independent variable and the others are dependent ones. The specification in AmP follows the rules of those for bi-variate data, where the first element of auxData.treat is 0 or 1. See further under bi-variate data.