Interpretation of twoway fitted line with dummy variable

[Justin Davis]

Hello all,

Using Stata 13

I'm looking at the two-way quadratic fitted line between a dummy and continuous variable using the code:
twoway qfit Earningssurprise IO

See the image of the graph attached.

My question is the interpretation of the fitted values on the left.
My understanding is that the fitted values represent the estimated likelihood of the dummy variable taking the value of 1 when the continuous variable (IO) is a given value.

Is my interpretation correct?

Many many thanks in advance!

[Nick Cox]

Yes and no. The graph shows the value predicted for the outcome variable. The conditional mean of an indicator in {0, 1} is somewhere between 0 and 1 depending on one or more predictors: here you are fitting a quadratic in one predictor. It doesn't show a likelihood function. It does, if you like, show the probability of recording 1 rather than 0 for your outcome, although if that is of interest a logit regression is generally preferable.

Otherwise put, likelihood is often at elementary or lay level an informal synonym for probability, but likelihood has a separate technical meaning.

You may be expected to know all of this, and indeed more.

[Justin Davis]

Thank you for your thoughtful reply, that really helps clarify it for me!