st: Re: interpret dydx as probabilities after logistic or xtlogit

["Seyi Soremekun" <Seyi.Soremekun@lshtm.ac.uk>]

Hi All,
 
I have a model with a categorical (binary) by continuous interaction, which I estimate using logistic regression or RE logistic regression thus:
 
logistic infacility i.intvn##c.quintile 
xtlogit infacility i.intvn##c.quintile, re i(zone) or
 
I would like to estimate the change in probability (not odds) of my outcome "infacility" for a unit change in quintile, at intvn=0 and intvn=1, i.e. explain the interaction by looking at the actual estimated slopes of quintile, separately for intvn=0 and 1
 
 
Are the slopes obtained via a simple post-estimation margins dydx calculation?:
margins, dydx(quintile) over(intvn) continuous post 
or
margins, dydx(quintile) over(intvn) predict(pu0) continuous post
...where one then exponentiates the results to show the risk ratio for the unit change?
 
The reason I ask is that from graphing the raw proportions of infacility for each level of quintile separately for intvn=0 and 1 gives a very different picture to the results obtained from the above methods, even without the adjustment for clustering (i.e. via logistic model):
 
1. Logistic model
odds ratio for quintile (when intvn==0) = 0.4446739 
dydx for quintile (over intvn when =0) = -0.1383194, exponentiated to 0.87
 
2. Random effects model
odds ratio for quintile (when intvn==0) = 0.6044537
dydx for quintile (over intvn when =0) = -.0948134, exponentiated to .91
 
3. raw data when intvn=0
change in probability (% reduction) of infacility at:
quintile 2/1 = 0.73
quintile 3/2 = 0.68
quintile 4/3 = 0.59
quintile 5/4 = 0.38
 
One can see that the average pecentage reduction (~0.60) in the probability of infacility from the raw data (3.) is much higher than either logistic model.
So: 
1. Am I interpreting the dydx results from the logistic models in the correct fashion - as a percentage reduction in probability for a unit change in quintile (i.e. averaged risk ratio)?
2. If so any ideas why the model results look so different to the raw data - even in the simple logistic model without clustering adjustment? 
 
thanks, Seyi
 


Seyi Soremekun
Faculty of Epidemiology and Public Health 
London School of Hygiene and Tropical Medicine
London WC1E 7HT
+442079272464



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