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

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

Hello all
 
I am using a fractional logit model as my dependent variable is a proportion, specifically the proportion of conceptions ending in maternity. 
 
I have two independent variables of interest which are both continuous variables. One is life expectancy, scaled in years. The other is the age-standardised prevalence of long-term limiting illness, which is scaled as a proportion. There are other covariates, both continuous and factor variables. I have found significant relationships between my IVs and the DV, all else equal. 
 
I have used the margins command to interpret my findings, but am having trouble interpreting the output. 
Examples available online tend to use logistic regression rather than fractional logit, so I have had difficulties interpreting output in terms of my own DV. 
I have computed marginal effects at the mean (MEM), average marginal effects (AME) and marginal effects at representative values (MER). 
 
 
I am aware that getting the marginal effects for a continuous variable can be problematic as it is not a constant estimate. However, in computing MERs I found an interesting 'interaction' with one of my covariates so that is one way of getting around that problem and also a useful exercise. But I am having trouble putting the basic marginal effects into words. 
 
The output for my two independent variables is so different and substantively strange that I am finding it impossible to interpret: 
 
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
------------------------------------------------------------------------------
For the former it seems the marginal effect is tiny; for the latter enormous. 
There are similar issues when I compute the AME, so I know it's not just a problem with the MEM. 
 
 
Questions: 
 
1) Should I be interpreting the former as "for every one-year increase in life expectancy, the proportion of conceptions ending in maternity increases by .18, with all else held at means" and the latter "for every one-point increase in long-term limiting illness prevalence, the proportion of conceptions ending in maternity decreases by 56 points, with all else held at means"? 
The latter cannot be substantively possible. 
2) Should I therefore be using different language to deal with a proportional DV?
3) Are the apparent differences in marginal effects between the two variables due to their differences in scaling?
4) If scaling is a problem, should I be standardising the IVs before using a fractional logit and margins? 
5) Should I even be trying to compute the marginal effect of a continuous variable in the first place? 
 
Many thanks for your help!
 
Sandra


Sandra Virgo
PhD Researcher
Department of Population Health
London School of Hygiene & Tropical Medicine
0207 299 4681
( tel:02072994681) 


*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/