Is Converting an Ordinal 'Linkert' Type Variable (0 to 10, from completely disgaree to completely agree) to a Fraction ( 0 to 1) Acceptable?

[Max Baard]

Dear Statalist users,

(I am running Stata17/MP)
I have looked across the internet (and Statalist) and I haven't been able to find a straight answer to my question.

I have multiple variables from a survey of approximately 3000 people in which they were asked questions on a scale of 0 to 10. 0 represents "Completely Disagree" and 10 represents "Completely Agree".
I know that I can use an ordinal probit or ordinal logit regression with each of these ordinal variables as the dependent variable. However, I want to try and keep the interpretation simple, which oprobit and ologit tend to make it difficult to convey. Additionally, when running the ordinal probit/logit models I find that some of my variables fail to pass the parallel lines assumption.

        
. ologit B5 female lowage loweduc lowincome

Iteration 0:   log likelihood = -6433.0606  
Iteration 1:   log likelihood = -6417.1843  
Iteration 2:   log likelihood = -6417.1752  
Iteration 3:   log likelihood = -6417.1752  

Ordered logistic regression        Number of obs =  3,002
        LR chi2(4)    =  31.77
        Prob > chi2   = 0.0000
Log likelihood = -6417.1752        Pseudo R2     = 0.0025

        
B5  Coefficient  Std. err.      z    P>z    [95% conf. interval]
        
female   -.1533167   .0678278    -2.26    0.024    -.2862567   -.0203768
lowage   -.1846502   .1240223    -1.49    0.137    -.4277295    .0584291
loweduc   -.2329156   .0690683    -3.37    0.001    -.3682871   -.0975442
lowincome   -.1648473   .0744144    -2.22    0.027    -.3106968   -.0189978
        
/cut1   -3.408178    .107404        -3.618686    -3.19767
/cut2   -3.209815   .1007814        -3.407343   -3.012287
/cut3    -2.78373   .0892951        -2.958745   -2.608714
/cut4   -2.357594   .0808882        -2.516132   -2.199056
/cut5   -1.955083   .0751846        -2.102442   -1.807724
/cut6   -.8541042    .066344        -.984136   -.7240723
/cut7    -.366501   .0645431        -.4930031   -.2399989
/cut8    .2682416   .0641922        .1424272     .394056
/cut9    1.140942   .0682417        1.007191    1.274693
/cut10    1.699653   .0746818        1.55328    1.846027

              
. brant, details

Estimated coefficients from binary logits

                        
Variable   y_gt_0     y_gt_1     y_gt_2    y_gt_3     y_gt_4    y_gt_5    y_gt_6    y_gt_7    y_gt_8    y_gt_9  
                        
female     0.212      0.184      0.118    0.033      0.021    -0.208    -0.203    -0.164    -0.143    -0.229  
1.12       1.06       0.81    0.27       0.20    -2.53    -2.60    -2.05    -1.50    -2.01  
lowage     0.326      0.390      0.203    0.082     -0.183    -0.324    -0.159    -0.173    -0.132    -0.056  
0.82       1.05       0.71    0.36      -1.00    -2.26    -1.12    -1.15    -0.73    -0.26  
loweduc    -0.426     -0.329     -0.439    -0.199     -0.090    -0.331    -0.287    -0.186    -0.206    -0.086  
-2.19      -1.85      -2.98    -1.60      -0.84    -4.04    -3.63    -2.26    -2.06    -0.72  
lowincome    -0.403     -0.389     -0.301    -0.330     -0.304    -0.186    -0.187    -0.234    0.043    0.289  
-2.04      -2.14      -1.98    -2.57      -2.72    -2.14    -2.22    -2.64    0.41    2.34  
_cons     3.317      3.078      2.724    2.256      1.823    0.952    0.429    -0.256    -1.214    -1.848  
18.33      18.77      19.63    19.49      18.41    12.41    5.99    -3.55    -14.20    -17.95  
                        
                        Legend: b/t

Brant test of parallel regression assumption

chi2     p>chi2      df

All       79.23      0.000      36

female       10.54      0.308       9
lowage        9.44      0.398       9
loweduc       24.82      0.003       9
lowincome       27.60      0.001       9

A significant test statistic provides evidence    that the parallel
regression assumption has been violated.

I have come across the use of fractional probit/logit regressions and I am wondering if it is acceptable to convert these 'Likert' type variables into fractions between 0 and 1 (by simply dividing by 10).

For example, B5 is the original variable (coded from 0 to 10) and B5_1 is the fraction of it. The other variables are: female is a binary variable for gender, lowage is a binary variable for age (1 for 18 to 24-year-olds and 0 for older), loweduc is binary (1 for primary education and 0 for more), lowincome is binary as well

* Example generated by -dataex-. For more info, type help dataex
clear
input double B5 float B5_1 byte(female lowage loweduc lowincome)
 3 .3 1 1 0 0
 8 .8 1 0 1 1
 7 .7 1 0 1 0
 5 .5 0 0 0 1
 5 .5 1 0 1 1
 5 .5 1 0 1 1
 1 .1 0 0 0 0
 4 .4 0 0 0 0
 4 .4 0 0 0 0
 2 .2 0 0 1 0
 6 .6 0 0 0 0
 8 .8 1 0 1 1
 5 .5 1 0 0 0
 5 .5 1 0 1 1
 3 .3 0 0 0 0
 6 .6 1 0 1 1
 5 .5 1 0 0 0
 5 .5 0 0 1 0
 3 .3 1 0 0 0
 0  0 0 0 1 0
 8 .8 0 0 0 1
 9 .9 1 0 1 1
 4 .4 0 0 1 1
 7 .7 0 0 1 0
 5 .5 1 0 0 0
 7 .7 0 0 1 1
 6 .6 1 0 1 1
10  1 1 0 1 1
 5 .5 1 0 1 1
 6 .6 1 0 1 1
end
label values female genderl
label def genderl 0 "Male", modify
label def genderl 1 "Female", modify

eststo: oprobit B5 female lowage loweduc lowincome, vce(robust)


eststo: fracreg probit B5_1 female lowage loweduc lowincome, vce(robust)

After all that, is this an appropriate transformation of this data and if so. Do you have any recommendations for what postestimation tests I should conduct?

Your assistance is much appreciated.

[Nick Cox]

There isn't a straight answer to this for good reasons. What is "acceptable" is not a constant, even within sub-sub-disciplines. The problem is not waffle or incompetence, although those can be found, but a range of judgments.

I've treated ordinal scores as if numeric whenever it seemed reasonable but not otherwise. That is a totally vacuous answer for anyone else: the point is that looking at the data to see how they behave, thinking about goals, and thinking about who is the readership are all key to a decision.

In almost any University some academics in some departments are firm that only certain analyses are defensible with ordinal data, while most of the rest of the academics engage in decisions based on some kind of weighted average of roughly ordinal grades originally based on personal judgment. (Often they have no alternative; it's a University ruling to work with a grade point average or some local equivalent.)

There are feedback loops that aren't always benign. In various Earth and environmental sciences I know something about, ordinal logit and probit models have been suggested from time to time but haven't really taken off. There is a high chance that a paper including them would be reviewed by people who are unfamiliar with or even hostile to them. (Unfamiliarity and hostility often go hand in hand.)

Conversely, in various pockets of social science they have become routine and there is repeated ritual display of lengthy tables of coefficients and P-values and stars of various kinds.