[daniel klein]

Now I feel I need to clarify my earlier post. There is indeed no question about missing values being coded as such. There is also no question that the median would in any case be appropriate for the data at hand while the mean is not, from a (mathematical) statistical point of view. So Clyde's approach is the bullet-proof one in that sense, and probably the one to follow here.

I just wanted to point out, that we are usually not so interested in the mathematical correctness for the sake of mathematical correctness. We are using statistical models to interpret the data we have seen in the light of substantive theory. In doing so we make lots of assumptions and treating an ordinal Likert-type variable as interval is, in my opinion, not a very critical one. This is to say, while Clyde is clearly correct, it might be a little bit to hard to state that the mean is meaningless for ordinal data. In my (admittedly limited both, in quantity and in scientific discipline) experience, using the mean or median tends to give the same substantial answer in situations as the one described here. If they do not, this might have other reasons than the measurement of the variables. That is not to say, it is always and automatically appropriate to treat such variables as interval data, but I have the feeling the circumstances in which it would not be a reasonable assumption are the exception rather than the rule. Anyway, Clyde is also correct in pointing out that this is an empirical question.

As a last comment, given the (complex) research question outlined above, I guess treating this variable as ordinal or (quasi) interval data, is probably not the decision that matters most for the validity of the answer.

Best
Daniel

[Stephen Jenkins]

Daniel's remarks remind me of the debate among applied economists regarding modelling of life satisfaction outcomes -- recorded on a Likert scale, typically of 7 or 11 values. The categories are manifestly ordered. So, should one insist on using models such as oprobit or ologit for them, or will regress suffice? Among the economists who use these data a lot, most choose the latter and claim that it doesn't matter very much. In part, this is because they point out that often these LS outcomes are available as panel data, and they think it's important to use fixed effects models (think xtreg, fe). The article most often cited in this connection is:Ferrer-i-Carbonell, Ada and Frijters, Paul (2004) "How Important is Methodology for the estimates of the determinants of Happiness?", The Economic Journal 114 (497), 641-659, http://dx.doi.org/10.1111/j.1468-0297.2004.00235.x. As it happens, there are FE estimators coming along for ordered data, with Stata implementations too, see e.g. http://www.stata.com/meeting/uk11/ab.../UK11_Hole.pdf

[Marcos Almeida]

There is an interesting discussion on the matter (here, the link:http://www.theanalysisfactor.com/can...be-continuous/), appropriately entitled:

"Can the Likert Scale Data ever be Continuous?"

The author presents pros and cons, as well as sound references.

Best,

Marcos

[Nick Cox]

This has been contentious at least since Karl Pearson and George Udny Yule a century ago. Pearson's bias was that a latent continuous variable was trapped inside any ordinal measure yearning to be set free, although he didn't use such wording; Yule wanted categorical variables to be respected as such.

Even if you follow the line that medians not means are the best summaries for graded (e.g. Likert) data, you then face the problem that medians do a lousy job at summarising the difference between (say)

1,2,2,2,3,3,3

and

1,1,1,2,2,2,2

as the uncontentious result that 2 is the median in both examples leaves a lot of "information" in the data. Every education system I know about takes means even when there is emphasis that the raw data are judgement-based ordinal measures.

For one of many possible approaches, see iquantile on SSC and the thread that led it at http://www.stata.com/statalist/archi.../msg00652.html