I have a data set with paygrades from 3 to 16. The difference between each pay grade was probably not exactly the same, but the differences are very unlikely to have been big. From a different dataset from the similar context there was around $6-$9 difference between one grade and the next. I don't have figures for what people were actually paid, and for this dataset I don't know exactly what each paygrade meant in money terms. Since this is historical data, there might not be any way to find out.
At first I used an ordinal regression with paygrade as an outcome variable, but it seems overly complex and hard for readers to interpret with the large number of intercepts, and I am wondering if I could treat them as a continuous variable and do a linear regression instead.
i wish this question would go away. ordinal is ordinal not continuous . here is what these guys say: https://www.google.com/search?source=hp&ei=iCdrX-jQAs7QtQawqamADQ&q=how+to+approximate+ordinal+with+continuois&oq=how+to+approximate+ordinal+with+continuois&gs_lcp=CgZwc3ktYWIQAzIHCCEQChCgATIHCCEQChCgATIHCCEQChCgAToOCC4QsQMQxwEQowIQkwI6CAguEMcBEKMCOgsILhCxAxDHARCjAjoICAAQsQMQgwE6BQgAELEDOgIIADoECAAQAzoFCAAQkgM6BAgAEAo6BggAEBYQHjoFCCEQoAE6BQghEKsCOggIIRAWEB0QHlDfFFiljANgopUDaAJwAHgAgAGGAYgB2x-SAQUzNC4xMJgBAKABAaoBB2d3cy13aXo&sclient=psy-ab&ved=0ahUKEwjotM7fjP_rAhVOaM0KHbBUCtAQ4dUDCAk&uact=5
Best D. Booth
David Eugene Booth the big majority of that discussion is people asking about Likert scales, which seem fundamentally different to the case I described above.
Don't you think that there are cases that are harder to categorize? (Student assignments marked as a %, with grade thresholds at specific points, for example).
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too bad ... your case is just the perfect example for ordinal regression from a latent variable with an clear intuitive meaning (the true money)
does showing the latent variable with its nice cut-off points and its clean linear modelling really make your audience faint from fear ? sigh ...
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then, why not go for linear regression ... but for "ease of exposition" purposes only ! :)
and i would first check the consistency of this (handwavy) linear regression with the (correct) ordinal regression : you might be surprised as David Eugene Booth warns.
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it is unfair to linear regeression to use it as some universal statistical comfort object , but i'd bet we've all done it !
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