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# PCORELATE directive

Relates the observed values on a set of variates or factors to the results of a principal coordinates analysis.

### Options

`COORDINATES` = matrix Points in reduced space; no default i.e. this option must be specified Number of latent roots for printed output; default `*` requests them all to be printed

### Parameters

`DATA` = variates or factors The data variables Test type, defining how each variable is treated in the calculation of the similarity between each unit (`simplematching`, `jaccard`, `russellrao`, `dice`, `antidice`, `sneathsokal`, `rogerstanimoto`, `cityblock`, `manhattan`, `ecological`, `euclidean`, `pythagorean`, `minkowski`, `divergence`, `canberra`, `braycurtis`, `soergel`); default `*` ignores that variable Range of possible values of each variable; if omitted, the observed range is taken

### Description

One way of interpreting the principal coordinates obtained from a similarity matrix by `PCO` is by relating them to the original data variables. For each coordinate and each data variable, an F-statistic can be computed as if the variable and the coordinate vector were independent. This is not the case but, although the exact distribution of these pseudo F-values is not known, they do serve to rank the variables in order of importance of their contribution to the coordinate vector.

The `DATA` parameter lists the variables (variates or factors) that are to be related to the `PCO` results and the `TEST` parameter indicates their “type” as in the `FSIMILARITY` directive. The `RANGE` parameter contains a list of scalars, one for each variable in the `DATA` list, allowing you to standardize quantitative variates.

Qualitative variables (variates or factors with `TEST` settings `simplematching - rogerstanimoto`) are treated as grouping factors, and the mean coordinate for each group is calculated. Only 10 groups are catered for; group levels above 10 are combined. The pseudo F-statistic gives the between-group to within-group variance ratio. Missing values are excluded.

Quantitative variables (i.e. variates with other settings) are grouped on a scale of 0-10 (where zero signifies a value up to 0.05 of the range), and mean coordinates for each group are calculated. The printed pseudo F statistic is for a linear regression of the principal coordinate on the ungrouped data variate, after standardizing the data variate to have unit range; the regression coefficient is also printed.

The `COORDINATES` option must be present and must be a matrix. This represents the units in reduced space. Usually the coordinates will be from a principal coordinates analysis. The number of rows of the matrix must match the number of units present in the variables, taking account of any restriction.

The output from `PCORELATE` can be extensive. You may not be interested in relating the variables to the higher dimensions of the principal coordinates analysis even though you may have saved these in the coordinate matrix. The `NROOTS` option can request that results for only some of the dimensions are printed. If `NROOTS` is not specified, `PCORELATE` prints information for all the saved dimensions: that is, for the number of columns of the coordinates matrix.

(Note: this directive was originally called `RELATE`.)

Options: `COORDINATES`, `NROOTS`.

Parameters: `DATA`, `TEST`, `RANGE`.

Directives: `PCO`, `FSIMILARITY`, `ADDPOINTS`.

Commands for: Multivariate and cluster analysis.

### Example

```" Examples 2:6.10.3 "
UNITS [NVALUES=16]
VARIATE Engcc,Ncyl,Tankl,Weight,Length,Width,Height,Wbase,Tspeed,Stst,\
Carb,Drive,Vct[1...3]
POINTER Cd; VALUES=!P(Engcc,Ncyl,Tankl,Weight,Length,\
Width,Height,Wbase,Tspeed,Stst)
1490  4  50  966 414 161 133 245 177 10.9  1  2
1409  4  50  845 399 162 139 242 174 10.2  1  2
2492  6  49 1160 433 163 140 251 210  8.2  1  1
3185  8  87 1430 458 179 126 265 249  7.4  2  1
4942 12 120 1506 449 198 113 255 291  5.8  2  1
1995  4  70 1180 450 176 143 266 209  7.8  2  2
965  4  35  761 338 149 146 216 134 16.8  1  2
1585  4  55  970 426 165 141 244 180 10.0  1  2
1714  4  55  980 426 165 141 245 150 18.9  3  2
999  4  42  720 364 155 143 236 145 16.2  1  2
1498  4  48  912 397 157 118 220 171 11.0  1  1
5167 12 120 1446 414 200 107 245 286  4.9  1  1
1585  4  45 1000 389 162 138 247 195  8.2  1  2
1995  4  70 1150 459 175 143 266 224  7.6  2  2
1049  4  47  790 339 151 143 216 179 11.8  1  2
1995  4  45 1050 414 162 125 228 190  9.0  2  1 :
TEXT [VALUES=Estate,'Arna1.5','Alfa2.5',Mondialqc,\
X19,Contach,Delta,Thema,Y10,Spider] Carname
FACTOR [Carname; LEVELS=16] Fcar; VALUES=!(1...16)
SYMMETRICMATRIX [ROWS=Carname] Carsim
" Form similarity matrix between cars."
FSIMILARITY [SIMILARITY=Carsim; PRINT=*] #Cd,Carb,Drive;\
TEST=4(cityblock),4(Euclidean),2(cityblock),2(simplematch)
" Produce output from ordination of Carsim and
relate matrix of coordinates to the original variates "
LRV [ROWS=Carname; COLUMNS=6] Carpco; VECTORS=Carvec
PCO [PRINT=roots] Carsim; LRV=Carpco
PCORELATE [COORDINATES=Carvec; NROOTS=3] Weight,Carb;\
TEST=cityblock,simplematch
```
Updated on June 19, 2019