logistic regression standard errors

[Don Vicendese]

Hi All,

When I run the logit command I get the following result

outcome | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------------+----------------------------------------------------------------
indep_var | 3.147702 1.095392 2.87 0.004 1.000772 5.294632


When I run the same command with the or option I get the following output

outcome | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
--------------------------------+----------------------------------------------------------------
indep_var| 23.2825 25.50347 2.87 0.004 2.720382 199.2642


I understand how the confidence interval is calculated from the log scale results - for example -

exp(3.147702 + 1.96*1.095392) approx.= exp(5.294632) = 199.2642


How does the numerical scale Std Err of 25.50347 relate to the log scale Std Err of 1.095392 and how would it be used to calculate the confidence interval on the numerical scale?

Thanks in advance,

Don

[Richard Williams]

See https://www.stata.com/support/faqs/s...cs/delta-rule/

[Don Vicendese]

Thanks Richard.

Using the link you gave, I can see that, in my case Variance[exp(b)] = Variance(b)*exp(b) = 1.095392*23.2825 = 25.50347.

I don't quite understand how exp(b)*Variance(b) relates to the Taylor expansion for the variance

Variance[exp(b)] = Variance(b)*[exp'(b)]² , where exp' means the derivative, d(exp(b))/d(b).

I understand that the derivative of the exponential is itself so I don't understand why we multiply by exp(b) instead of [exp'(b)]² ?

Thanks again in advance,

Don

[Richard Williams]

Sorry, I can't help you. This is one of those things I take on blind faith.

[FernandoRios]

Hi Don
I think you are forgetting the following:
exp'(b)=exp(b)
and indeed:
Variance[exp(b)] = Variance(b)*[exp(b)]²
But what the "table" shows is the standard error (square root of the above expressions)
STDDev(exp(b))=STDDEV(b)*[exp(b)]

HTH

[Don Vicendese]

Of course! Thanks very much Fernando and thanks again Richard for taking the time to consider this.


Don