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Re: st: logarithmic scales


From   Roger Newson <roger.newson@kcl.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: logarithmic scales
Date   Thu, 27 Nov 2003 18:21:17 +0000

At 16:04 27/11/03 +0000, Nick Cox wrote:
Here's a small issue which is utterly elementary, but it may
provide a moment's bemusement, and I'd welcome any comments.

When drawing graphs with one or both axes on a logarithmic scale,
Stata by default tries to provide "nice" labels, just as usual.

I'm writing a graphics program for a kind of plot in which one
axis will _always_ show a logarithmic scale, yet I find that
Stata's default for labels often gives me what is both a very
sensible and a very poor answer. The fault is possibly as much
mine as Stata's, as I may be quirky in what I most often want.
Also, despite years of acquaintance, Stata can't know what I
want unless I tell it.

.
.
.
Any views on this, including reports on tribal attitudes or
customs?
I too have had a similar experience to Nick's, while writing my own -smileplot- package (downloadable from SSC). My personal custom is to use my own -explist- package (downloadable from SSC and modelled broadly on Nick Cox's -listutil- suite) to define an exponentially spaced list of numbers, with a logarithmic base defined by the -base()- option and a scale defined by the -scale()- option. -explist- takes, as input, a list of numbers x_1, ... , x_n, and creates, as output, a list of numbers y_1, ... , y_n, derived exponentially from the input list, so that, for each i,

y_i = scale*base^x_i

Therefore, if I want a scale that starts at 0.75 and has a tick at each doubling, then I might type


. explist 0(1)10, scale(0.75) base(2)

. retu list

macros:
r(explist) : ".75 1.5 3 6 12 24 48 96 192 384 768"


If I want the scale to be a bit busier, then I might use multiple -explist- lists with the same -base()- option and different -scale()- options, and concatenate them in the -xlabel()- option of -graph twoway- as follows:


. sysuse auto, clear
(1978 Automobile Data)

. explist 0(1)2, base(2) scale(1000) global(g1)

. explist 0(1)2, base(2) scale(1500) global(g2)

. scatter length weight, xscale(log) yscale(log) xlab($g1 $g2)

and the X-axis labels will be -xlab(1000 1500 2000 3000 4000 6000)-.

This leaves the question of choosing the base, scale and input list for -explist-. In the case of -smileplot-, the Y-axis variable is a P-value, so I set the logarithmic scale to start from one and to end at ceil(-log(pmin)/log(base)), where -pmin- is the smallest P-value. The increments are chosen, by default, to keep the number of labels to no nore than 25 (which was the largest number allowed by Stata 7). In the general case, it is probably a good idea to use the -ceil()- function on the maximum log (to the chosen base) and the -floor()- function on the minimum log (to the same chosen base) to define the top and bottom of the scale, and to choose the scale(s) and input list to optimise the number of tick marks or labels by some criterion.

Roger


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk
Website: http://www.kcl-phs.org.uk/rogernewson

Opinions expressed are those of the author, not the institution.

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