Dear Statalist

I have run a simple logistic regression using a child labour survey in an East African country.

I ran the number of households that reported begging against those households that were child headed.

The logistic regression showed that child headed households had an odds ratio of 2.51. The constant was 0.54.I interpret this as meaning that child headed households are 2.5 times more likely to beg that non-child headed households (although I am not sure if i need to subtract the constant?)

However the margins command shows the predicted probability of begging in a child-headed household is 0.57 while in a non-child headed household it is 0.35. The odds ratio and margins do not speak to each other as I understand. How can the odds of begging in a child headed household be 2.5 times greater using the odds ratio but the probability of begging in a child-headed household be far less at 1.6 times greater?

Apologies for the no doubt obvious question, but I am struggling to find any answers.




. logistic begging i.child_head

Logistic regression Number of obs = 1,288
LR chi2(1) = 3.95
Prob > chi2 = 0.0470
Log likelihood = -836.89941 Pseudo R2 = 0.0024

------------------------------------------------------------------------------
begging | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.child_head | 2.51981 1.180173 1.97 0.048 1.006238 6.310081
_cons | .545676 .032052 -10.31 0.000 .4863365 .6122557
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

.
end of do-file

. margin child_head

Adjusted predictions Number of obs = 1,288
Model VCE : OIM

Expression : Pr(begging), predict()

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
child_head |
0 | .3530339 .0134158 26.31 0.000 .3267393 .3793285
1 | .5789474 .113269 5.11 0.000 .3569443 .8009505
------------------------------------------------------------------------------