DCIRCULAR procedure

Plots circular data (P.W. Goedhart & R.W. Payne).


Options

PLOT = strings
Information to be plotted (counts, kerneldensity, lines, mean, rose); default coun, mean, rose

TITLE = text
Title for the graph; default * i.e. none

SEGMENT = scalar
Width of sectors (in degrees) into which to group an ANGLES variates before plotting; default 20

MSEGMENT = scalar
Defines the centre (in degrees) of the sectors; default 0

BANDWIDTH = scalar
Bandwidth to use for the kernel density estimate; if this is unset, the value h0 suggested by Fisher (1993, page 26) is used

NGRID = scalar
Defines the number of grid points for the kernel density estimate; default 180

WINDOW = scalar
Window for the graph; default 3

SCREEN = string
Whether to clear screen before displaying the graph (keep, clear); default clea


Parameters

ANGLES = factors or variates
Directional observations to be plotted

GRID = variates
Saves the grid (in degrees) on which the kernel density is estimated

DENSITY = variates
Saves the kernel density estimate

SAVEBANDWIDTH = scalar
Saves the calculated bandwidth h0 when BANDWIDTH is unset


Description

DCIRCULAR plots data values that consist of directional observations recorded as angles between 0 and 360 degrees. The data values are supplied by the ANGLES parameter, in either a variate or a factor. With a variate, the observations are grouped for plotting into sectors of width specified (in degrees) by the SEGMENT option, with centres defined by the MSEGMENT option. The sectors are centred at MSEGMENT, MSEGMENT+SEGMENT, MSEGMENT+2*SEGMENT, and so on. The default value for SEGMENT and MSEGMENT is 20 and 0 respectively. If ANGLES is set to a factor, its levels define the midpoints of the sectors and these must be in clockwise order.

   The graph contains a circle with marks at every 10 degrees, and labels at 0, 90, 180 and 270 degrees. The representations of the observations are determined by the settings supplied for the PLOT option as follows

    counts
plots counts of the number of observations in each sector.

    kerneldensity
plots estimates of the probability distribution of the data, using a quartic kernel function with bandwidth specified by the BANDWIDTH option. If BANDWIDTH is unset, a default is calculated based on the estimated concentration of the data (this is the value h0 suggested by Fisher, 1993, page 26). The kernel is calculated on a grid of values with number of values defined by the NGRID option.

    lines
plots lines in each direction with lengths proportional to the number of observations in that direction.

    mean
plots the mean vector (see Fisher 1993, page 31).

    rose
plots a "rose" diagram in which the observations in each sector are represented as a triangle with apex at the centre of the circle and area proportional to the number of observations there.

By default PLOT=counts,mean,rose.

   The options TITLE, WINDOW and SCREEN allow you to define a title for the plot, specify which window to use, and indicate whether or not to clear the screen beforehand. Parameters GRID, DENSITY and SAVEBANDWIDTH can be used to save the grid (in degrees), kernel estimate and bandwidth h0. The latter is saved only when BANDWIDTH is unset.

 

Options: PLOT, TITLE, SEGMENT, MSEGMENT, BANDWIDTH, NGRID, WINDOW, SCREEN.

Parameters: ANGLES, GRID, DENSITY, SAVEBANDWIDTH.


Method

DCIRCULAR uses GenStat's standard graphics and calculation commands. The underlying methodology is described by Fisher (1993).


Action with RESTRICT

If ANGLES is restricted, only the unrestricted units are plotted.


Reference

Fisher, N.I. (1993). Statistical Analysis of Circular Data. Cambridge University Press, Cambridge.