interpretation of linear probability model

[Jonathan Marin]

Hello!

I am examining in an experiment the effect of an intervention on attendance at a hospital. I have a control group and a treatment group.

I regress a treatment dummy on attendance. The latter is a binary variable where 1=patient attended and 0= patient did not attend. So the following model is estimated: reg y treatment

Say the treatment effect is 0,04 and is significant. Can i interpret this as "the treatment group has a 4%-points higher attendance rate than the control group". Since it is just a difference in means estimator I would guess the treatment effect is just the percentage points difference in the share of patients attending. Am i correct?

Best regards

[Marcos Almeida]

If I understood your query correctly, being the DV binary, it is inappropriate to perform a linear regression. Instead, a logistic regression model is the correct option.

[Jonathan Marin]

Yes, but this is more just a question of interpretation. Not a question of which model is correct

[Brad Anderson]

That's correct. Though why not just do a 2 x 2 table and use a chi-square test? I don't see any other covariates. The LPM is technically not correct, though if the n is relatively large and the distribution of you dichotomous outcome is not badly skewed, the results of the LPM will be very close to a logit or probit model.

[Marcos Almeida]

In #1, the approach to the matter is as described in this text, where we can find the proposed interpretation as well as "a case" in favour of OLS under certain circunstances.

[Bruce Weaver]

If one wants the risk difference rather than the odds ratio, the approach described in the following article may be useful.

• https://www.ncbi.nlm.nih.gov/pubmed/18000021

HTH.

[Richard Williams]

See also this blog by Paul Allison:

https://statisticalhorizons.com/in-d...f-logit-part-2

The upshot is that combining logistic regression with the margins command gives you the best of both worlds. You get a model that is likely to be a more accurate description of the world than a linear regression model. It will always produce predicted probabilities within the allowable range, and its parameters will tend to be more stable over varying conditions. On the other hand, you can also get numerical estimates that are interpretable as probabilities. And you can see how those probability-based estimates vary under different conditions.