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I would like to regress the influence of income, education, marital status etc. on life satisfaction. The data I use is from the SHARE survey – life satisfaction can take values of 1–10, most values are around 6–8.

OLS regression seems to be a poor choice to me, as it might produce predicted values outside the 1–10 interval.

My colleagues have suggested that I might take a look at truncated/censored analysis, such as tobit regression. However, I do not believe that I have data which is censored in the way tobit regression would assume, which would be the case if only part of the real spectrum of values can be observed.

Most researchers use ordered logistic regression. This seems valid to me, but 10 might be quite high number of possible outcomes for ologit (I have usually done it with fewer outcomes, though I am not sure if this is an issue at all), and I believe ologit does not assume the intervals between the categories to be of equal size (stated here), which I however believe is the case in my scenario (why would the difference between 3 and 4 be any different than between 7 and 8?)

I wonder if interval regression is what I need. I think it is, but I need proof :)

So, which statistic analysis would you recommend?

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I'd say ordinal logistic is a good choice, if you think your intervals are not equally spaced. I don't know of a reason that having 10 categories would be problematic. The problem would be if the proportional odds assumption is violated, but you can cross that bridge when and if you come to it.

In my experience, ordered logistic with a large number of categories often gives similar results to OLS regression. "Similar" in the sense of giving similar predicted values.

A very good reference on this is Agresti, Analysis of Ordinal Categorical Data with lots of details of all sorts of lesser-known models.

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  • $\begingroup$ Thanks for your answer. Would you regard life satisfaction score as featuring equally spaced intervals? $\endgroup$ – mzuba May 4 '12 at 10:18
  • $\begingroup$ Not exactly equal, but maybe about equal. If you want to let the data set the spacing, you could look at ridits. $\endgroup$ – Peter Flom May 4 '12 at 11:41
  • $\begingroup$ So if the intervals are spaced evenly, would you prefer interval regression over ordered logit? $\endgroup$ – mzuba May 9 '12 at 10:32
  • $\begingroup$ well, interval regression is simpler and easier to understand. If the intervals are evenly space, the two methods ought to give similar result. $\endgroup$ – Peter Flom May 9 '12 at 13:35
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To complement Peter Flom's answer:

  1. What might be a problem if when some of the categories (in your case, apparently, poor life satisfaction at the lower end) are sparsely populated. In this case, the corresponding threshold parameters will be poorly identified, and will carry huge standard errors. This may also cause convergence difficulties. If you have just a handful of observations in these lower values, you might want to consider collapsing them into say "3 or lower" category, just to improve convergence. (You should still state it in your paper/report, though.)
  2. I would say that Agresti is generally a biostats/SAS book, and a social science/Stata book is J Scott Long's Regression Models for Categorical and Limited Dependent Variables.
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  • $\begingroup$ Hi @stask Good addition to my comment. I have both Agresti and Long, and somehow never thought of either of them as related to particular software. But I think both books are very good. $\endgroup$ – Peter Flom May 4 '12 at 11:42
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I would consider logistic quantile regression for bounded outcome. If you're a Stata user, there's also a command (lqreg) for the estimation, prediction and graphical representation of a logistic quantile regression.

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