st: Re: interpreting marginal effects of fractional logit with continuous independent variables

["Sandra Virgo" <Sandra.Virgo@lshtm.ac.uk>]

To Richard Williams: 
 
Thanks very much for your response - I'm familiar with your Margins01
and Margins02 documents, but I'm grateful you've sent me the Margins03
document as I think that will be very helpful for me - the marginscontplot command by Royston could be just what I'm after. I will also look
at discrete changes in the continuous variables (e.g. standard deviation
changes) as you suggest. And I will see if I can get the Long and Freese
book. 
I think that from what Austin has said I now have a way of interpreting
the margins output with my specific IV - it is perhaps the scaling of
that, rather than the fractional logit element that has made
interpretation so difficult. 
Many thanks. 
 

To David Hoaglin:
 
Hello David - thanks so much for your help. 
 
I get what you mean about all cases not having equal weight as
denominators and denominators might vary a lot. 
 
I think I understand what you mean about the 'region of predictor
space' - presumably you're asking how much of the variation in ple and
llti_stand is actually present when I hold covariates at their means? 
 
I am happy to ignore the 'all else held at means' assumption, and
therefore I won't try to calculate the Marginal Effects at the Mean as I
also know the limitations of this. 
 
However, I'd still be interested in calculating Average Marginal
Effects (i.e. with covariates taking on the actual values they have in
my data) in the way that Richard Williams describes. 
 
And I'm guessing that it would still be OK from what you say to
calculate predicted probabilities (fitted values/adjusted predictions to
use other terminology) for specific scenarios. I would also like to
calculate marginal effects at representative values (i.e. with
covariates at their existing values apart from any I choose to fix at a
series of values in order to explore 'interactions') as well as
exploring the effects of discrete changes in my continuous variable. 
 
Hopefully these analyses will be OK from what you say. 
 

To Austin Nichols:
 
Dear Austin - I'm very grateful for your help as it is either the
scaling of my IVs of interest or the fact it is fractional logit that is
making the output hard to interpret. 
 
Here's my output again: 
For the life expectancy variable the MEM: 
 
-
------------------------------------------------------------------------------
    | 	 Delta-method
    |   dy/dx   Std. Err.   z    P>|z| 
[95% Conf. Interval]
-
-------------+----------------------------------------------------------------
   ple |   .0018984   .0007678  2.47   0.013    
.0003935    .0034032
-
------------------------------------------------------------------------------
And for the illness prevalence variable the MEM: 
 
-
------------------------------------------------------------------------------
    | 	 Delta-method
    |   dy/dx   Std. Err.   z    P>|z| 
[95% Conf. Interval]
-
-------------+----------------------------------------------------------------
  llti_stand |  -.5630636   .0485536   -11.60   0.000  -.658227  
-.4679002
-
------------------------------------------------------------------------------
 
Does what you say mean for the interpretation of my llti_stand output
that: 
 
"For every one percentage-point increase in llti_stand
(age-standardised long-term limiting illness prevalence), the percentage
of conceptions ending in maternity decreases by 56 hundredths of a
percentage point (i.e. decreases by just over half a percentage point)?
 
This is substantively much more likely as it's more similar to the
result for life expectancy. Should my interpretation of the life
expectancy (ple) result be the same as before: "for every one-year
increase in life expectancy, the proportion of conceptions ending in
maternity increases by .18, with all else held at means" ?
 
As I have mentioned to David Hoaglin and Richard Williams, I'm happy
not to calculate marginal effects at the mean due to the other problems
with assumptions. But I'd still like to calculate Average Marginal
Effects and Marginal Effects at representative values as well as looking
at effects of discrete changes in the continuous variable, so being able
to interpret the output for my specific independent variables in the way
I think you have described is most helpful to me. 
 
Thanks everyone
 
Sandra
 
 
 
Sandra Virgo
PhD Researcher
Department of Population Health
London School of Hygiene & Tropical Medicine
0207 299 4681

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