Linear Probability Model Interpretation

[Jungran Lee]

Hi All!

I hope you are well.
I have been trying to use linear probability models, but I am not so sure I am doing correctly..

My regression results are here:

Measure	Coefficient	P-value	95% Confidence Interval
Unadjusted Estimates
Readmission to Hospital	-.0052133	.009	-.0091095, -.0013172
Discharge to Community	-.0074036	.005	-.0126198, -.0021873
ADL Decline	-.000303	.655	-.0016311, .0010251
Length of Stay	2.023417	<.001	1.562751, 2.484082
90-day Costs	978.885	<.001	737.5332, 1220.237
Adjusted Estimates
Readmission to Hospital	-.0067059	.309	-.019629, .0062172
Discharge to Community	.0193361	.016	.003642, .0350301
ADL Decline	-.0029406	.206	-.0074942, .0016131
Length of Stay	.2742938	.717	-1.210172, 1.75876
90-day Costs	-337.8859	.363	-1065.894, 390.1217

The first three outcomes are binary variables and the other two are continuous.

The key independent variable is 1= advanced practitioners (APs) and 0= physicians.


My interpretations for the adjusted estimates are:

Patients treated by APs are more likely to discharge to the community (1.93 percent point more; p-value 0.16; 95% CI 0.003642 to 0.0350301).
There were no significant differences in the other four outcomes.


Am I correct?

Any advice would be highly appreciated!

Thank you so much for your help in advance!!

[Jenny Williams]

That seems to be the correct interpretation of the specific point estimates.

However, perhaps you thought of this, but it's straightforward to run a "true" binary outcome model such as logistic or probit, followed by margins to generate the predicted probabilities.

See here for a discussion: https://www.stata.com/meeting/us20/s...20_Allison.pdf
And here: https://stats.idre.ucla.edu/stata/da...ic-regression/

webuse nhanes2, clear

/*linear probability model*/
regress diabetes i.black i.sex c.age

/*the first margins command gives you the predicted probalities of the outcome, for each exposure level*/
/*the second margins command gives you the difference in predicted probabilities across exposure levels*/
/*you can see that the difference in predicted probabilities from the margin command matches the coefficient from the regression model above*/
margins black, asobserved
margins, dydx(black) asobserved

/*now, run as a logistic model and calculate the difference in predicted probabilities*/
/*you can see that the estimates are different from the linear probability model*/
logistic diabetes i.black i.sex c.age
margins black, asobserved
margins, dydx(black) asobserved

/*you can also run as a probit model and calculate the difference in predicted probabilities*/
/*the results are similar to the logistic model*/
probit diabetes i.black i.sex c.age
margins black, asobserved
margins, dydx(black) asobserved

/*note you can also run the margins command setting the covariates at mean values*/
margins black, atmeans
margins, dydx(black) atmeans

[Jungran Lee]

Thank you so much for the explanations and resources!!