Hello, I am working with a large data set on families (1/2 million families). I am using melogit to estimate the association of several covariates with my outcome.
After running melogit, I run margins--for categorical covariate x, and continuous covariate z--and get the following results:
Note that for z = 5, the point estimates of the two groups are inside the confidence interval of the other.
However, when I test the last two margins against each other, I get:
I am aware of the discussion at https://www.statalist.org/forums/for...ns-overlapping, and elsewhere, that overlapping CI's do not mean that differences can not be statistically significant. However, I had thought, per Greenland et al. (2016), that when the point estimate of one group was inside the confidence interval of another group, that this meant that the two groups could not be different to a degree that was statistically significant.
Any thoughts on this would be very much appreciated.
Reference
Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European Journal of Epidemiology, 31(4), 337–350. https://doi.org/10.1007/s10654-016-0149-3
After running melogit, I run margins--for categorical covariate x, and continuous covariate z--and get the following results:
Code:
margins x, at(z = (33.1, 45.5, 55.4, 59.1, 66.3)) post
-----------------------------------------------------------------------------------
| Delta-method
| Margin std. err. z P>|z| [95% conf. interval]
------------------+----------------------------------------------------------------
_at#x |
1 0 | .205419 .0163226 12.58 0.000 .1734273 .2374108
1 1 | .276733 .0198932 13.91 0.000 .2377429 .315723
2 0 | .2836444 .0134719 21.05 0.000 .25724 .3100488
2 1 | .3489734 .014977 23.30 0.000 .319619 .3783279
3 0 | .3573103 .0164563 21.71 0.000 .3250566 .389564
3 1 | .412324 .0171394 24.06 0.000 .3787313 .4459166
4 0 | .3868972 .0192173 20.13 0.000 .349232 .4245624
4 1 | .4369036 .0196641 22.22 0.000 .3983627 .4754446
5 0 | .4467064 .0260632 17.14 0.000 .3956234 .4977894
5 1 | .4855433 .026031 18.65 0.000 .4345235 .5365632
-----------------------------------------------------------------------------------
However, when I test the last two margins against each other, I get:
Code:
test _b[5._at#0bn.x] == _b[5._at#1.x]
( 1) 5._at#0bn.x - 5._at#1.x = 0
chi2( 1) = 57.03
Prob > chi2 = 0.0000
Any thoughts on this would be very much appreciated.
Reference
Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European Journal of Epidemiology, 31(4), 337–350. https://doi.org/10.1007/s10654-016-0149-3
