Pema,

If you are looking for a percentile, it is not directly related to the logit. You would have to check descriptives.

Remember that logit is the log of the odds. So if you exp you get the odds. Now odds/odds+1=probability.

for example logit of 0 would be 1 in odds, a probability of 0.5

Hi Diago,

Thanks for the response.

Descriptive statistics I got are:

Mean is 1.88

Std. Deviation is 1.22

Since these scores are generated using Rasch analysed person scores, i was wondering if I could present in percentage form. Relying on the insight provided by you, is it correct to interpret that a mean of 1.88 is same as 88% of survey participants endorsed a survey scale? or 88% of participants are more likely to endorse a survey scale?

Hello Perma,

Diago is correct; the (mean) logit is simply an indication of location on a scale that (in theory) goes to infinity in both directions. If the stimuli / items were scaled so that the mean was arbitrarily set at zero, then you may conclude that the average level of agreement / endorsement / correct or preferred response for the respondents was higher than the average level of the stimuli used to elicit responses. A person whose scale level was equal to 1.88 would be predicted to endorse / agree / answer correctly an item / stimulus at the "average" level of zero with a probability of .87.

exp(1.88) / [1 + exp(1.88)] = 6.55 / 7.55 = .87

You may, of course, discuss where one respondent is relative to others in a normative way, but that will depend on the specific distribution of scores in your data set. The usual benefit of item response or Rasch models is the ability to look simultaneously at scale position of stimuli and persons, as opposed to the limited (and item- and sample-dependent) normative perspective of classical test theory.

Good luck with your work!

Pema,

The average (person-measure) tells you that your scale is relatively "easy" for your sample. In other words, that, as an average, people has higher levels of attribute (ability) than required by items (difficulty). Instead of just comparing those statistics, I would recommend you to analyze Wright's map (ítem-person map). There you can qualify the average score of your sample in terms of item-content by looking for ítems with a difficulty (measure, beta) similar to 1.8 (person-measure average). Complement your analysis with relative position according to item hierarchy.

That might contribute to make your analyzes more informative.

See an example in: http://www.winsteps.com/winman/table1.htm

and in:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5132390/pdf/rm4.pdf (Figure 6)

Also read about targeting:

http://www.winsteps.com/a/winsteps-tutorial-2.pdf (pag. 11)

https://www.rasch.org/rmt/rmt211m.htm

Dear David and Diego,

Thank you very much for the insightful comments and links.

I have analysed the survey data using Winsteps 32.9.1 and got both item and case scores. The data also achieved construct validity (98 to 100%) and reliability & Separation (> .80 & >.5). The fit statistics are all within .70 to 1.3. Instruments validations are provided under three headings, namely, scale, fit statistics and threshold levels. I have discussed Item difficulty analysis for all the scales using the hierarchical graphs. Using the non-extreme case scores I have also run the MANOVA & Factorial MANOVA, and Regression tests on SPSS for all the scales. I was looking for descriptive stats to be presented in percentage form as it is usually done in classical test reports. Now I am convinced that it is different in approach.

I will now present my final report as suggested by you. Thanks for the wisdom. Researchgate.net is a wonderful platform to deepen one's understanding of a concept.

Winsteps gives you scoring tables (raw to logit and percentile) in menu Output Files -> Score File SCFILE=, in case that you want to append normative data. It gives yo e.e. if you want to provide confidence intervals.

I am glad we have been helpful!

Dear Pema,

Good to see you working on your next project. Hope this helps but feel free to disregard the suggestions.

The new Rasch scale that is created is just that, a scale. Thought experiment: Consider a temperature rating in Celsius, say 8 degrees C. Would we ask what is the percentage this represents? A more typical question might be, for those of us accustomed to the Fahrenheit scale, “but how cold is this, really?” The answer probably would come from a comparison to where 8 degrees falls with respect to something familiar, like freezing or boiling point of water, in Celsius.

Fortunately, with the Rasch approach, we have a way to answer what that average person ability score of 1.8 logits represents - the items! If we look at a Wright Map, it displays the (estimates for) item difficulties against the (estimates for) person abilities. Further, if we locate and review those items with difficulty levels that are near 1.8 logits, we have an indication of how difficult it is to obtain that 1.8 logit score. Thus, to help explain how difficult it is to obtain any score on the new scale, it is often easier to reveal what the items with difficulty levels near that score look like.

Warm regards, David

Dear David,

I absolutely agree with you. Rasch model is the key to solving the measurement problems.

I was a bit confused with the polytomous data obtained using a four-point Likert's rating scales (Strongly disagree, disagree, agree and strongly agree). I have looked at the Wright Map for person ability and item difficulty estimates. Based on this map and other output tables (Winsteps) I have also undertaken an item difficulty analysis. I wanted to emphasise the average case mean score to provide the level of participants' agreeability of a scale. I have reported the average case mean score of 1.88 logits as thus, the the survey respondents endorsed “Agree” and “Strongly Agree” more as opposed to “Disagree” and “Strongly Disagree” because the odds of a scale under analysis was predicted to agree or endorse 1.88 times greater at the average level of zero logits with probability of .87 (exp(1.88) / [1 + exp(1.88)] = 6.55 / 7.55 = .87). In other words, the average case score of 1.88 logits was greater than 0.00 logits.

I would appreciate your additional comments if my interpretations concerning the average case mean score of 1.88 logits are correct.

Remember, the 1.8 logit score is a measure of the degree of agreement because that is what your scale represents. Try this. Select an item and see what the logit scores are for each of the rating levels from Strongly Disagree to Strongly Agree. You might need to review to one of the tables or to the Wright Map. Where does 1.8 logit score fall with respect to the rating levels for that item? Is it closer to Agree or closer to Strongly Agree?

Then, instead of doing this for each item, take the average of the logit scores for each of the rating levels for all the items in the domain. This will give you an estimate of the domain-level cut-points for each of the rating levels (as opposed to the item-level cut points for each of the rating levels). Now ask where does 1.8 fall in comparison to these domain-level cut points. Is it closer to Agree or closer to Strongly Agree at the (domain-level)? The answer to this is one interpretation of the 1.8 logit score for that set of items that were used to compose the scale.

Hi David,

Thank you for your insightful suggestions and tutorial.

I have examined the output tables showing the category measures for all the category labels, Strongly disagree (1), Disagree(2), Agree (3) and Strongly agree (4) for 14 survey items. The logits scores are -2.62 for strongly disagree, -.89 for Disagree, .77 for Agree, and 2.82 for Strongly agree (Winsteps 3.92.1 output tables). Now I have the average case score of 1.88 logits. I have reviewed by placing all those categorical scores on a Wright map and tried to aligned 1.88 with those scores. This case score 1.88 seems to sit closer to 2.82 (Strongly agree). Thus, I conclude that the average performance of the survey participants is strong, indicating higher person ability/ agreeability/endorsability.

Could you kindly confirm if my interpretation is correct and if so, is this the way to ascertain the magnitude of case score on Rasch Model?

Thank you once again for your valuable comments and time.

Kind Regards.

Pema

Are those logit scores averaged over the rating levels for the 14 items? If so, they represent the domain estimate of the category level ratings and your interpretation is correct. The 1.88 logit score falls somewhere in between Agree (0.77 logits) and Strongly Agree (2.82 logits) but slightly closer to Strongly Agree. Because the domain estimate is high, this is an indication that it was easier for the respondents to agree with the items within this group, as noted by Diego above.

Yes David, those logit scores were the average scores of the 14 items. Thank you for the support.

Kind regards.

Two steps are listed: (1) Odds = exp (Logit); and (2) Probability = Odds / (1+Odds).