Plots a correlation matrix (A.I. Glaser).

### Options

`PLOT` = string tokens |
Type of plot (`together` , `separate` ); default `sepa` |
---|---|

`SHOW` = string tokens |
What features to include on the plots (`axes` , `diagonal` ); default `axes` |

`NCOLOURS` = scalar |
Number of distinct colour to use from 0 to -1 or 1; default 20 |

`COLOURS` = text or variate |
Text or variate with three values, defining the colours to use for correlations of -1, 0 and 1; default `*` chooses the colours automatically |

`WEIGHTS` = variate |
Provides weights for the units of the variates; default `*` assumes that they all have weight one |

### Parameters

`PVARIATES` = pointers or symmetric matrices |
Pointer to either the first (P-) set or the only set of variates to be correlated, or symmetric matrix containing the correlations themselves |
---|---|

`QVARIATES` = pointers |
Pointer to the second (Q-) set of variates to be correlated |

`PROWS` = scalars |
Specifies the number of rows corresponding the first (P-) set of variates in a correlation matrix supplied by `PVARIATES` , when this contains two sets |

`TITLE` = text |
Title for the plot |

### Description

`DCORRELATION`

provides a graphical representation of a correlation matrix, which can show the correlation within a dataset, as well as the correlation within and between two different datasets. Each element of the correlation matrix is represented by a shaded rectangle indicating the value at that location, using a different colour or shading density. This type of display is often used before a canonical correlation analysis to see if there are any significant correlations within and between the datasets to be analysed; see the `CANCORRELATION`

procedure for details.

The `PVARIATES`

parameter can supply a symmetric matrix containing correlations that have already been calculated (e.g. using the `FCORRELATION`

procedure). If the matrix involves two sets of variates (as in a canonical correlation analysis), you should arrange for them to be specified in set order i.e. all the first set, and then all the second set. You should then specify the number of variates in the first set using the `PROWS`

parameter.

Alternatively, you can set `PVARIATES`

to a pointer containing the variates themselves. You can then use the `QVARIATES`

parameter to supply a pointer with a second set of variates.

The `WEIGHTS`

option can provide a variate of weights for the units of the variates; by default these are all assumed to have weight one.

The `PLOT`

option selects the type of plot, with settings:

`together` |
to plot the correlation matrix as one symmetric matrix, with a dashed black line to show the boundaries between two datasets (if supplied), and |
---|---|

`separate` |
to plot the correlation matrix in three separate components with the within dataset correlations at the top of the window, and the between-dataset correlations underneath. When there are more variates in the second (Q-) set than the first (P-) set, the separate plot will display the transpose of the between-dataset correlations. |

The default is `PLOT=separate`

, unless there is only one set of variates when it defaults to ‘together’.

The `SHOW`

option controls whether some features are included on the plots:

`axes` |
includes axes, and |
---|---|

`diagonal` |
includes the diagonal of the correlation matrix. |

The default is `SHOW=axes`

.

There is also a key containing a strip of colours showing how the colours in the plot represent the different correlations. The `NCOLOURS`

option specifies the number of distinct colours to use as the correlations decrease from 0 to -1 or increase from 0 to 1. This can vary from 2 upwards, with a default of 20. The `COLOURS`

option allows you to control the range of colours that are used. It should be set to a text or variate with three values: the first value defines the colour to use for correlations of -1, the second value gives the colour for correlations of 0, and the third gives the colour for correlations of 1. (See `PEN`

for details of how colours are defined.) The default colours, if `COLOURS`

is unset, range from dark blue for values close to -1 to dark red for values close to 1.

The `TITLE`

parameter supplies a main title for each plot.

Options: `PLOT`

, `SHOW`

, `NCOLOURS`

, `COLOURS`

, `WEIGHTS`

.

Parameters: `PVARIATES`

, `QVARIATES`

, `PROWS`

, `TITLE`

.

### Method

The plots in `DCORRELATION`

are produced using `DBITMAP`

.

### See also

Directive: `CORRELATE`

.

Procedures: `FCORRELATION`

, `PARTIALCORRELATIONS`

, `PRCORRELATION`

.

Commands for: Graphics, Multivariate and cluster analysis.

### Example

CAPTION 'DCORRELATION example',\ 'Data from Table 3.7 of Digby & Kempton (1987).';\ STYLE=meta,plain TEXT [VALUES='1d','3a','3d','4a','4d','7a','7d','8a','8d','9a','9d',\ '10a','10d','11/1a','11/1d','11/2a','11/2d','14a','14d','16a','16d',\ '17a','17d','18d'] Plot POINTER [VALUES=N,Nstar,P,K,Lime] Treats & [VALUES=Axis_1,Axis_2,Axis_3,Axis_4] Species VARIATE [NVALUES=Plot] Treats[],Species[] READ Treats[] 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 1 0 1 2 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 2 0 1 1 1 2 0 1 1 0 2 0 1 0 1 2 0 1 0 0 3 0 1 1 1 3 0 1 1 0 3 0 1 1 1 3 0 1 1 0 0 2 1 1 1 0 2 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 2 0 0 1 0 : READ Species[] 354 177 -173 85 211 -406 2 -170 299 -294 -11 -46 191 11 246 209 331 226 -262 28 -333 -145 -212 36 200 -149 -11 -6 136 -347 -7 -100 162 -302 29 -194 -416 59 -27 19 281 257 -130 -154 9 -28 166 182 333 228 -251 33 -386 111 86 -92 52 242 52 -349 -387 98 42 -50 36 252 72 -346 -391 -127 -170 196 -419 30 -137 118 -333 -143 -171 149 -254 -89 -121 12 102 -388 11 -140 135 -260 -68 -60 331 238 -245 38 : CALCULATE Species[] = Species[] / 100 DCORRELATION [PLOT=separate, together] PVARIATES=Treats; QVARIATES=Species PRINT Plot,Treats[],Species[]; FIELDWIDTH=7; DECIMALS=(0)6,(2)4 MATRIX [ROWS=Plot; COLUMNS=4] Specs_Sc,Treat_Sc CANCORRELATION [PRINT=correlations,pcoeff,qcoeff,pscores,qscores]\ Treats; Species; PSCORES=Treat_Sc; QSCORES=Specs_Sc PRINT Specs_Sc