Interpretation of "/logs" in Stata17 output using mestreg

[Ben Lazrus]

Dear Stata users,

Can someone please kindly explain in simple terms what the "/logs" output refers to in the following code? I've looked in the mestreg help, streg help, this blog file https://www.stata.com/stata-news/new...-correlations/ and the "An introduction to survival analysis using stata" textbook and can't find an explanation anywhere.

use https://www.stata-press.com/data/r17/catheter
stset
mestreg age female || patient:, distribution(lognormal) time

Mixed-effects lognormal AFT regression Number of obs = 76
Group variable: patient Number of groups = 38

Obs per group:
min = 2
avg = 2.0
max = 2

Integration method: mvaghermite Integration pts. = 7

Wald chi2(2) = 14.13
Log likelihood = -328.70499 Prob > chi2 = 0.0009
------------------------------------------------------------------------------
_t | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
age | -.0060556 .0106775 -0.57 0.571 -.0269832 .014872
female | 1.334213 .3570964 3.74 0.000 .634317 2.034109
_cons | 3.480046 .5453814 6.38 0.000 2.411118 4.548973
-------------+----------------------------------------------------------------
/logs | .0359558 .1297168 -.2182844 .290196
-------------+----------------------------------------------------------------
patient |
var(_cons)| .322698 .2641533 .0648667 1.605354
------------------------------------------------------------------------------
LR test vs. lognormal model: chibar2(01) = 1.62 Prob >= chibar2 = 0.1017


If I calculate the exponent of the /logs output, i.e. exp(0.0359558) = 1.03667, is this the estimated residual variance between catheters?

Kind regards,
Ben

[Clyde Schechter]

The lognormal distribution has two parameters, a mean (of log t) and a standard deviation. The /logs parameter is the estimate of the log of that standard deviation. All of the distributions used in both -streg- and -mestreg-, except exponential, have some ancillary parameter of this nature, and their estimates are shown in the output in this way (which might be called something other than /logs, depending on what that parameter is.) Exponentiating it will give you something that is "like" the residual standard deviation, not variance, but is not actually quite that. To get a more specific feel, go to the PDF documentation on -streg- and scroll through that chapter to Table 1, where the parameterization of the various survival distributions is shown.