Ordinal variables

[Wish Tre]

Hi, I have two ordinal variables. The first takes values from a 3-point scale, the second from a 4-point scale. What is the best way to visualize their relationship?

I have tried:

histogram var1, by(var2, col(1)) discrete frequency

but the graph doesn't seem like a good way to analyze the relationship. Can I plot the mean for one variable over the other?

[William Lisowski]

I personally appreciate the spineplot command contributed to SSC by Nick Cox who however I think favors other graphical commands he has developed.

ssc describe spineplot
ssc install spineplot

Here are two examples of spinelplot.

. sysuse auto, clear
(1978 automobile data)

. spineplot foreign rep78

. spineplot rep78 foreign

[Nick Cox]

Thanks to William Lisowski for the mention of spineplot --which isbest cited as published through the Stata Journal

SJ-16-2 gr0031_1 . . . . . . . . . . . . . . . Software update for spineplot
(help spineplot if installed) . . . . . . . . . . . . . . . N. J. Cox
Q2/16 SJ 16(2):521--522
x-axis labels have been improved; references added to help file

SJ-8-1 gr0031 . . . . . . . . . . . Speaking Stata: Spineplots and their kin
(help spineplot if installed) . . . . . . . . . . . . . . . N. J. Cox
Q1/08 SJ 8(1):105--121
discusses spineplots (mosaic plots), a type of bar chart for
showing frequencies, proportions, or percentages of cross-
classified categorical variables

On occasion spineplot can be exactly right for showing structure in a two-way contingency table, although it is best to put the outcome or response variable -- if there is one -- on the y axis and to arrange a graded series of colours. My thinking is that repair record is possibly a response to (is influenced by) being foreign but not conversely.

My reservations about spineplot are partly technical and partly a matter of taste. It can be hard work seeing structure if

1. There are cells with zero or small frequencies.

2. There are problems showing text labels legibly or agreeably. See examples at https://medium.com/the-stata-guide/s...s-49caa27c5554

Beyond that. mosaic plots (including much more complicated variants for three-way tables and higher) have been promoted energetically by some authors with examples that seem to me often very confusing to try to understand.
The principle that all the information is encoded in the plot is admirable but does not stop some results being hard to fathom.

I tend to recommend

R1. tabplot from the Stata Journal

R2. floatplot from SSC

The command names are search terms for mentions of either command on Statalist: tabplot often and floatplot only a few times.

R3. quantile or (empirical) (cumulative) distribution function plots, as supported by qplot and distplot (both Stata Journal) using cumulative probabilities in the form

proportion less than this PLUS (1/2) proportion equal to this (sometimes called ridits (*), although I find the term mid-distribution function more transparent).

This idea was floated in 2004 in Section 5 of https://journals.sagepub.com/doi/pdf...867X0400400209 and here it is again for the data mentioned.

sysuse auto

set scheme s1color 

* SJ 
qplot rep78, over(foreign) midpoint recast(connected) name(O1, replace) legend(ring(0) col(1) order(2 1) pos(5))

* ssc install mylabels 
mylabels .02 .1(.2).9 .98, myscale(logit(@)) local(pla)

qplot rep78, over(foreign) midpoint recast(connected) trscale(logit(@)) xla(`pla') ///
legend(ring(0) col(1) order(2 1) pos(5)) xtitle(mi0-distribution function (logit scale)) name(O2, replace) 

graph combine O1 O2

The order R1 R2 R3 here is roughly in terms of what is easiest to explain to sceptical supervisors and readers and what works reasonably well most of the time.

On R3 the idea starts with

* if the predictor has an influence, the quantile traces will differ

* if we can find simple structure, that is a bonus: if extreme responses are rarer than intermediate responses, the quantile traces will be straightened by something like a logit scale.

I draw short of saying: run ologit and think of a good way to plot the results.

(*) Irwin Bross introduced ridits with a tongue in cheek explanation of what the word meant that I found hard to follow but seemed to convince people who quoted it. Decades later he admitted that all along he was naming them for his wife Rida. (This is a true story.)

[Nick Cox]

See also a 2021 presentation at https://www.stata.com/meeting/uk21/slides/UK21_Cox.zip

[Wish Tre]

Thank you, Nick and William.