ridit calculate and hypothesis tests

[Chen Samulsion]

Dear Stata users,

I read some literature on ridit analysis. A short skeleton about it is:

The name 'ridit' was used by Irwin Bross (1958) in his article 'How to Use Ridit Analysis' (Biometrics). And in Joseph Fleiss' book 'Statistical Methods for Rates and Proportions' (1981,p150-57), there's a section §9.4 titled ridit analysis. RIDIT stands for ‘Relative to an Identified Distribution’ or ‘relative to an identified distribution integral transformation’.
Ridits provide a method for replacing the categories of an ordinal variable by scores between 0 and 1. The score for each category is the percentile rank of an item in the reference population and is equal to the number of items in all lower categories plus one-half the number of items in the subject category, all divided by the population size.
To perform RIDIT analysis, you first split the sample into two groups: a control group and a treatment group. From the control group data, you calculate ‘control ridits,’ based on the frequency response to each question. From the treatment group data, you calculate the mean ridit and the standard error. Then a z-score determines the statistical significance of the difference between the control group and the treatment group. (Croushore and Schmidt, 2010)

And I know that in Stata Nick Cox introduced an egen function ridit() to compute ridits, and Roger Newson wrote wridit to compute weighted ridits, both unfolded and folded.

My questions are:
1) Is ridit analysis used spread in addressing ordered categorical data such as Likert items and pain-rating scales?
2) How to perform hypothesis tests of ridit means comparison between control group and treatment groups in Stata? and
3) Concretely, how to use egen ridit() function or wridit command to perform ridit analysis? And as far as I know, both of the ridit() function and the wridit command could not do hypothesis test.

[George Ford]

there are examples in help wridit

[Nick Cox]

Much, much more can be said, but my headline is that what is here called ridit analysis is just a matter of using a scale that may be convenient for an ordered categorical variable as an ingredient of anything else that makes sense.

The term ridit was itself a private joke by Bross that got into print and evidently fooled many, judging by the number of authors who have recycled the wording as it meant something, and as if they too understood what it meant.

Bross later explained that he was honouring his wife Rida but thought that a short, punchy quasi-technical term would help push the idea. The timing was good -- statistical people were learning about probit, logit, and the like -- and the public relations thought was bang on.

(As in the famous commentary on Wagner's Ring operas, I am not making this up, you know.)

Consider any sets of cumulative probabilities, such as for rep78 in the auto data.

. sysuse auto, clear
(1978 automobile data)

. tab rep78

     Repair |
record 1978 |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |          2        2.90        2.90
          2 |          8       11.59       14.49
          3 |         30       43.48       57.97
          4 |         18       26.09       84.06
          5 |         11       15.94      100.00
------------+-----------------------------------
      Total |         69      100.00

Reporting 0.0290, 0.1449, 0.5797, 0.8406, 1.0000 as cumulative probabilities has the dual problem that 1 is vacuous -- all cumulative probability series end in 1 -- and more to the point 1 can't be pushed through many functions with finite result.

Reporting 0.0000, 0.0290, ... (probability < rather than probability <=) has a similar dual problem with 0.

Splitting the difference is what ridit does. Ridit is simply pr(<) + 1/2 pr(=) in a clumsy but I hope clear notation.

More recently, I've discovered that Dixon and Massey used the idea before Bross in their well-known introductory text. (That was a very good book which didn't survive its authors.) Perhaps no one expects innovation from introductory texts, or many authors thought the idea too trivial to make a fuss about. I wouldn't be at all surprised at yet earlier mentions.

Documentation can be found in qplot as updated in Stata Journal 24(4).

In short, ridit scale is just one way to report cumulative probabilities. Use it if it helps.

[Chen Samulsion]

Thank you very much Nick Cox. I posted this question because some people applied ridit analysis in quantitative empirical studies (Xia Chuanling, 2022). They said that there are two important problems often faced in quantitative empirical research: first, the lack of statistics and their statistical tests for descriptive statistics of ordinal variables; and second, the problem that scale analysis focuses only on measurement structure and not on measurement format. These two problems lead to biases in parameter interpretation and research findings. Using ridit analysis could in some degree eliminate these biases.
Here is an old thread posted by Paul Seed, addressing how to specify the identified distribution: https://www.stata.com/statalist/arch.../msg01210.html