Normalising a variable between 0 and 1

[Guest]

I am running a regression where my dependent variable is a 0-6 scale Likert item, and I am planning to run the regression via OLS before I compare the results to an ordered logit model. In my OLS model, I've normalized my dependent variable to be a scale between 0 and 1 (which will hopefully get around the issue that running OLS on Likert scale items will produce biased and inconsistent results). How do I interpret my regression output in this case? if I receive a coefficient of 0.04 for example, can I say that this is a 4% increase in the dependent variable for a unit increase in the independent variable?

[Joseph Coveney]

I've normalized my dependent variable to be a scale between 0 and 1 (which will hopefully get around the issue that running OLS on Likert scale items will produce biased and inconsistent results).

What makes you think that?

I don't have a reference handy, but recall reading somewhere that with upwards of seven ordered categories—and with 0 to 6, you seem to have that—you can often get away with treating the variable as interval scaled and fit a reasonably interpretable linear regression model to the unit-incremented values, using OLS or whatever.

[Nick Cox]

I fail to see how dividing by 6 can remove any bias or inconsistency.

Besides, the values 0 ... 6 should mean something to you and other people working with the same data, as would a prediction of 3.45 or whatever. It isn't going to be easier to think about a predicted value of 3.45/6 = 0.575.

[Guest]

Dear Nick,

Thank you for your reply, this makes sense to me, and my original plan was to do what Joseph recommends. Where my confusion comes from is that I have been told that:

"Typically, a scale made up of several 7-point Likert items is not appropriate for OLS. One issue is that the data are necessarily limited to the left (all people answer "1") and to the right (all people answer "7"). Another issue is that you are assuming that the responses can be summed to mean in a meaningful way. That is, you are assuming that an answer of "2" and an answer of "4" average out to an answer of "3". For most data, this is not true. In that case using OLS may give you biased and inconsistent results."

Could you comment on this and add to what Joseph said? Would running OLS on this type of data be reasonable?

[Joseph Coveney]

" . . .a scale made up of several 7-point Likert items . . ."

You have several such items? If so, then what does a factor analysis (see example below) tell you? If the factor loadings are all about the same, then you might be able get by with linear regression of their sumscore. You can get an idea of what passes for "all about the same" from inspection of the factor loadings in the example below.

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.

But, if you've already done the factor analysis, then you might as well go ahead and add a structural component to the measurement model (as illustrated above) in order to fit a regression model then and there.

Anyway, how to handle ordered-categorical responses has been a long-standing debate among those who use Likert scales and their individual items. You can get a flavor of the points to consider by Googling likert-scale sum-score and taking what you encounter as a second opinion to what you've been told.

[Nick Cox]

I would say that the advice quoted in #4 makes sense but puts the emphasis in the wrong place. It's not the fault of OLS if it doesn't know where the data come from or what their limits are. Similarly, saying that OLS provides a biased and inconsistent solution is puzzling as the whole point of the outcome being just ordered codes is that any kind of weighted average is at best arbitrary so no other estimator could find correct estimates of the parameters either because correct values aren't even defined in principle.