Home / Monte Carlo / Model Building / Correlations / Correlations Options
Correlations Options¶
Every control in the Correlations dialog. There is one page and no tabs.
The window has two halves. On the left, the list of correlations already in the workbook and the checklist of marked inputs. On the right, the editor for whichever correlation is selected.
Defined correlations in this workbook¶
One row per stored correlation. There is no "new correlation" row; Add Correlation is the way to make one.
A row reads the correlation's own name. A correlation stored before names existed reads its family
and its members instead, as in Gaussian: Thickness, Width.
With no correlation in the workbook the list shows:
No correlations defined.
Click "Add Correlation" to create one.
The whole editor is disabled while that is true, and again after the last correlation is deleted.
Add Correlation¶
Opens an empty editor on a correlation that is not in the list yet, with a name filled in for you
(Correlation 1, Correlation 2 and onward). It is unsaved from the moment it is pressed.
Delete Correlation¶
Removes the selected correlation. You are asked first:
Delete "name"? This cannot be undone.
The row that took its place is then selected. When the list is left empty, nothing is selected and the editor greys.
Why the list and these two buttons go quiet¶
While the editor holds unsaved work, the list, Add Correlation and Delete Correlation are all greyed, and a semibold line under the grid says why:
Unsaved changes. Press Save correlation to keep them.
Clicking a row to look at it never traps you. The lock arrives on the first change you make, not on the click.
Inputs in this correlation¶
One tickable row per marked input, in sheet tab order and then by row and column. Each row shows the input's name and its cell address.
A row is greyed for one of three reasons:
| Why | What the row says |
|---|---|
| the input is already in another correlation | inthat correlation's name |
| ten inputs are already ticked | nothing on the row; the cap sentence appears instead |
| the input is a member of this correlation but is no longer a marked input | no longer a marked input |
At ten ticked inputs:
A correlation holds at most 10 inputs.
Two ticks are needed before the correlation can be saved:
A correlation holds at least two inputs.
A member that is no longer marked blocks the save until you untick it:
An input in this correlation is no longer a marked input. Untick it first.
The order of the checklist is the order of everything else. The matrix rows and columns, the Reflected boxes and the stored member list all follow it. A correlation stored in another order is shown in checklist order, and each typed matrix value stays with the pair of cells it was typed for, so ticking and unticking never move a number onto a different pair.
Name¶
Required. Save correlation is greyed while it is empty:
A correlation needs a name.
At most 60 characters. The box stops at the cap.
A correlation name is at most 60 characters.
Names must be distinct, ignoring case:
A correlation called "name" already exists.
Description¶
Optional and uncapped in length. A two-line box that accepts line breaks and scrolls when what you type will not fit. Your own note about the correlation; nothing in the software reads it.
Family¶
A dropdown of four, in this order: Gaussian, Student-t, Clayton, Gumbel. A one-line description of the selected family sits beside it, and a thin rule separates the row from whatever follows it.
Changing the family hides some controls and shows others. It clears nothing. Switch from Gaussian to Clayton and back and your matrix is still there.
Which controls each family shows:
| Family | Degrees of freedom | Theta | Reflected | Matrix |
|---|---|---|---|---|
| Gaussian | yes | |||
| Student-t | yes | yes | ||
| Clayton | yes | yes | ||
| Gumbel | yes | yes |
Degrees of freedom¶
Student-t only. Default 5. A whole number of 1 or more.
Fewer degrees of freedom make jointly extreme values more likely. A large value makes the family behave much like the Gaussian.
Degrees of freedom is not a whole number.
Correlation group 1: Degrees of freedom must be a whole number of at least 1 (got 0).
Theta¶
Clayton and Gumbel only. One number covering the whole group, with its rule stated beside the box.
Clayton:
Theta is a finite number above 0. A larger theta ties the inputs more tightly; as theta nears 0 they become independent.
Gumbel:
Theta is a finite number of 1 or more. 1 is independence; a larger theta ties the inputs more tightly.
Refusals:
Theta is not a number.
Correlation group 1: Clayton theta must be greater than zero.
Correlation group 1: Gumbel theta must be a finite number of at least 1 (1 means no correlation).
A Gumbel theta of exactly 1 is accepted and means no dependence at all. The run then takes the independent path.
Reflected¶
Clayton and Gumbel only. The label carries its own description:
Reflected reverses the direction of an input's relationship.
Under it, one check box per ticked input, named for that input. Ticking one turns that input's relationship the other way: with Clayton, whose dependence is strongest at low values, reflecting one input of a pair makes its high values the ones that occur with the other's low values.
Reflected settings are written to the workbook only when at least one box is ticked, so a correlation with nothing reflected is stored exactly as one written before the setting existed.
The correlation matrix¶
Gaussian and Student-t only. The heading names what the grid holds:
Rank correlation matrix (Spearman)
Every number in this grid is a Spearman rank correlation. There is no control that changes the scale, and a Pearson product-moment correlation is not entered anywhere in this dialog. See Math Details.
One row and one column per ticked input, in checklist order. The diagonal is fixed at 1 and
cannot be typed in. A pair you have never typed reads 0. Typing a cell above the diagonal fills its
mirror below it, so each pair is entered once.
Each box selects its whole contents when it takes the focus, whether you tab into it or click into it, so typing replaces the value rather than appending to it. A click inside a box that already holds the focus is left alone, so a value can still be edited in the middle.
Refusals on Save correlation:
The matrix entry for Name and Name is not a number.
Correlation group 1: The correlation between inputs 1 and 2 must be a number between -1 and 1.
Correlation group 1: The correlations are mathematically inconsistent in that the matrix is not positive semi-definite.
The last of those may be followed by the nearest valid matrix offer, described below.
Read from Excel range¶
Opens Excel's range picker and reads a block of cells into the grid. The block must be square, with one row and one column per input in the correlation.
Only the upper half is taken. The lower half is read too, and a disagreement refuses the whole read rather than quietly discarding one of the two values:
The selected range is 3 by 4; it must be 3 by 3, one row and one column per input in the correlation.
The cell for Name with itself is value; every cell on the diagonal is 1.
Cells for Name and Name disagree: value above the diagonal and value below it.
A diagonal cell that is not 1 refuses the read as well, because the grid's diagonal is fixed at 1 and a sheet saying otherwise disagrees with what would be saved.
Cancelling the pick changes nothing.
The nearest valid matrix offer¶
When a matrix family's entries are mathematically inconsistent and a repair exists, the refusal sentence is followed by a blank line and then:
Quantum XL can replace these entries with the nearest correlation matrix that is mathematically consistent. The replacement values are placed in the grid for you to review before saving.
Two buttons:
| Button | What it does |
|---|---|
| Use the nearest valid correlations | puts the repaired numbers in the grid at full precision. Nothing is saved |
| Keep my entries | leaves the grid exactly as it was. This is the plain refusal |
After accepting, the line under the grid changes to:
The nearest valid correlations have been placed in the grid. Press Save correlation to keep them.
That line stands only while the accepted numbers are still in the grid unchanged. Edit any of them and it goes back to the ordinary unsaved-changes line.
The offer is never made twice on the same numbers. Press Save correlation on the accepted numbers and they are saved.
A theta family has no matrix to repair, so the offer never appears for Clayton or Gumbel.
Save correlation¶
Writes the correlation in the editor to the workbook, creating it or replacing it. It is greyed whenever the correlation cannot be saved, and also when nothing has changed, because pressing it would write what the workbook already holds.
After a save, the saved row is selected again and nothing you typed is cleared.
Discard changes¶
Throws away the unsaved work. Live exactly when there is something to throw away. You are asked first:
Discard the changes to "name"?
Discard the changes to this correlation?
The second form appears only when the name box has been cleared. Discarding a correlation added with Add Correlation and never saved returns you to the row that was selected before you pressed it.
The footer¶
| Button | What it does |
|---|---|
| Help | opens this tool's help |
| Done | closes the dialog |
There is no Cancel button, because every write has already happened at the moment its button was pressed, so there would be nothing for a Cancel to take back. Done only releases the window, and the Escape key does the same thing Done does.
Done, Escape and the window's own close box all ask about unsaved work before letting go:
Save "name" before closing?
Save this correlation before closing?
Answering yes runs the same save the button runs, refusals included.