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I have a three point Likert scale question: 

How happy are you?
    1= low levels of happiness 
    2= medium levels 
    3= high levels

I want to do multiple linear regression on the variable. I am making the assumption that that it has the same difference between low and medium and medium and high. I want to treat it as a continuos dependent variable.

I know some people would see this as inappropriate, and there is the age old issue about whether to treat survey data as continuous.

  • But are there any further problems applicable to my dependent variable because it is only on a 3 point scale as opposed to 4 or 5?
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    $\begingroup$ Although explicitly not asked for, this question on when Likert scales should be treated as ordinal or interval scales may be of interest: stats.stackexchange.com/q/10/442 $\endgroup$
    – Henrik
    Commented Sep 27, 2011 at 11:37

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What I like to do in situations like this is run ordinal logistic, multinomial logistic and linear regression and compare results. I compare results by looking at predicted values from the different models. This is easy for multinomial vs. ordinal, because both yield probabilities. To compare with linear, I sometimes see what the highest probability response is from logistic, and how close it is to the predicted value from linear.

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    $\begingroup$ Thanks for this. I need to justify what i have done is right. So it is for my thesis, i cannot do more stats and do a small section on methodogy i.e. different ways of running the models produces the same/different answers. I dont have the word space! $\endgroup$
    – Laila
    Commented Sep 27, 2011 at 13:40
  • $\begingroup$ @Laila In the cases that I've seen, thesis appendices do not count towards the word count. Appendices are a good place to report supplementary analyses. $\endgroup$
    – Jeromy Anglim
    Commented Sep 28, 2011 at 0:41
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A bit on terms first. Your observable variable isn't continuous, it is descrete. Instead of "continuous" you should have better use word "scale" (or "metrical" or "interval"+"ratio"), as opposed to "ordinal". And you plan to treat the variable as scale rather than ordinal.

Formally logically you have the right to treat any Likert variable as scale variable if it has 3 or more levels. Unless you suspect that the intervals are psychometrically uneven. For example, in many countries they use 1 through 5 scale to assess performance at schools. This scale is not equiinterval because difference in knowledge appeares to be greater between 3 (satisfactory) and 4 (good) than between 4 and 5 (excellent). So, the school gauge is ordinal.

If you are right deciding to treat a Likert variable as metrical then the more it has levels the beter it is statistically. But if the variable is rather ordinal and has many levels it may be better to roughen it into less levels. One example is awful 10-point (1 to 10) scale frequently used in marketing to assess satisfaction. I usually recode it into 3-level "1 through 4", "5 through 8", "9 through 10".

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  • $\begingroup$ Hi @ttphns Have you got any links or further comments about why the 10 level scale is "awful" and why roughening it makes it better? $\endgroup$
    – Peter Flom
    Commented Sep 27, 2011 at 9:32
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    $\begingroup$ First, because it looks trivial it exaggerates focal effects on "magic" numbers 5, 7, 10 - you always encounter this 3-modality in the distribution. Second, looking at "intrapsychic scale" or usual respondent of satisfaction question, 9/10 almost indistinquishable, but stand apart from 5-7 or 5-8 range, and this is in turn apart from 1-3 or 1-4 range. Third, 10 points is just too much for a usual human differentiation capacity. 6 or 7 Likert scales are optimal for an adult, and 3 to 4, for a child. $\endgroup$
    – ttnphns
    Commented Sep 27, 2011 at 10:01
  • $\begingroup$ Interesting. Long ago in grad school, I did some work on alternate scorings of a depression inventory - either 4 point or essentially infinite point (we let the respondents check a spot on a line). Results were highly correlated, but the factor structure was different. I guess you could always check trimodality. Have you got any references for the stuff about intrapsychic scales or human differentiation capacity? Thanks $\endgroup$
    – Peter Flom
    Commented Sep 27, 2011 at 13:06
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    $\begingroup$ The idea that "happiness" occurs on a discrete scale is amusing. $\endgroup$
    – whuber ♦
    Commented Sep 27, 2011 at 14:11
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    $\begingroup$ @richie Yes, I'm familiar with some of the happiness studies. Most recently the best of them use a ten point scale but even that's not good enough because much of the scale is unused (typical results are $7 \pm 1$, for instance). Happiness, whatever it may be, quite obviously does not occur on a discrete scale, even though opinions about happiness must be measured discretely. Therein lies opportunity: namely, researchers need to elicit opinions on finer scales than heretofore used if they want to achieve reasonable power to make comparisons. $\endgroup$
    – whuber ♦
    Commented Sep 28, 2011 at 14:56
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The issue is not about "treating it as a continuous variable", but rather, as you point out, the assumption that 1v2 is the same as 2v3.

There's no real issue about the 3 categories (vs more). If there were just two categories, it would be equivalent to a 0/1 binary variable. All that would change (for different encodings) would be the scale of the coefficient.

A full model would contain two columns (say, indicators for medium and high). Using just the one column is perfectly reasonable but the assumption deserves to be checked.

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  • $\begingroup$ My answer is wrong, as I was thinking of it as the independent variable not the dependent variable. I guess I should delete it? Let's just say I'm answering a different question. $\endgroup$
    – Karl
    Commented Sep 27, 2011 at 14:54

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