regression with binned (interval) data

[JJBDubois]

I often have to analyze data where the dependent,  independent, or both variables were recorded in bins (intervals), when they really should have been recorded as continuous. Most of the time, the intervals are not even equal, and the highest is unbounded.

For example price of an item= $0-20, $21-100, $101-500, $501-5000, $5001 and up.

Say that price is a function of weight of the item, which is measured exactly to the nearest gram. Maybe these are truffles...

What is the best way to salvage this situation, and build a regression model of price as a function of weight? Rick Wicklin has some posts that seem close to this, such as http://blogs.sas.com/content/iml/2013/04/17/quantile-regression-vs-binning.html , but I am unsure.

Looking forward to all suggestions!

[StatDave]

If you are mostly just interested in assessing how weight increases price, you might just consider price as ordinal and fit an ordinal logistic model such as in PROC LOGISTIC. This would avoid having to quantify the spacing of the response levels.

[JJBDubois]

Thank you. I never think of logistic regression. I won't be able to state something like this, though:  "every 1 gram increment in weight is associated with a $26.43 increase in price", as I would if the price data had been recorded exactly and I used linear regression.

Or am I not realising something?

[JJBDubois · Accepted solution]

Since the situation described can be viewed as a matter of interval censoring, UCLA's  Institute for Digital Research and Education statistics resources suggest using PROC LIFEREG. http://stats.idre.ucla.edu/sas/dae/interval-regression/

The original suggestion can be found on page 145-146 of one of that article's citations: Long, J. S. 1997. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, CA: Sage Publications.