From "Nick Cox" To Subject RE: st: Graphing Quadratic Interactions Date Tue, 16 Dec 2008 15:17:06 -0000

```No, we can't erase that.

Ronan has a good point, which I doubt is controversial anywhere, that
just because you have 3 variables doesn't meet that you are best off
with 3-D graphics.

In particular if you have 3-D scatter, meaning a point cloud or swarm,
3-D graphics are not necessarily going to help you much. If you have 3
categorical variables, the same is likely to apply.

But plenty of us have data that define surfaces, often quite smooth
ones, and for that use any 2-D projections or summaries don't capture
the whole thing well. And if your data don't define a surface, your
model predictions often will.

Nick
n.j.cox@durham.ac.uk

Martin Weiss

" This is not true, and all of the good high-dimensional charts I can
think
of use only two dimensions to display the data."

So we can erase this perennial grievance ("When will Stata be able to
draw
3-D graphs"?) from future "wishes & grumbles"...

Ronan Conroy

On 16 Noll 2008, at 12:42, Nick Cox wrote:

> It wasn't very clear what she wants.  My guess was that she wants a
> plot
> of predicted response in terms of X4 and X5, adjusting for X1 ...
> X3. As
> mentioned on this list very frequently, Stata isn't serious at 3-D
> graphics that might meet this need, whether contour plots or
> perspective
> views.

What are often called 3D graphics are a small, and very poor, subset
of the ways in which higher dimensional data can be displayed on a
flat surface.

Their immediate drawback is that of point of view. They represent a
two-dimensional view of a three-dimensional object. Thus, the point of
view must be carefully chosen if it is not to result in some
interesting features being obscured, and there is no guarantee that
any single view will show you all the features of your data.

However, it is possible to display data in many dimensions on a flat
surface, and we do this all the time. Use of -by- and -over- to
display different groups in the same chart increases the number of
dimensions while keeping all the data visible at once.

. sysuse auto
. stripplot mpg, by(foreign) over(rep78) bar

This shows domestic and foreign cars as two graphs within the chart,
allowing us to see a third dimension easily.

You can, with a little ingenuity, increase the number of dimensions by
using what Tufte calls 'small multiples' - a tiled arrangement of
smaller graphs which follows a logical order.

My own contribution to the field was making a chart that displayed
age, sex, smoking, cholesterol, blood pressure and cardiovascular risk
on a flat surface. The resulting chart is also technically a table,
since it displays risk numerically as well as using a traffic-light
colour system. You can see the thing in various places on the net,
including Chance News

http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_13.
03.h
tml#item10

I mention this because people assume that you need "3D" to show more
than two dimensions. This is not true, and all of the good high-
dimensional charts I can think of use only two dimensions to display
the data.

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```