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

[Richard Williams <richardwilliams.ndu@gmail.com>]

Marginal effects for continuous variables measure the instantaneous 
rate of change. This may or may not correspond very well to the 
effect of a one unit change. It depends in part on how the variable 
is coded. For more, see

http://www3.nd.edu/~rwilliam/xsoc73994/Margins02.pdf

Maybe it is just me, but I personally don't find the MEs for 
continuous variables all that helpful. I would rather plot the 
effects of discrete changes in the continuous variable, e.g. the 
change from 0 to 1, from 1 to 2, etc. Patrick Royston's MCP command 
provides a convenient means for doing this. Either see his recent SJ 
article or look at my notes at

http://www3.nd.edu/~rwilliam/xsoc73994/Margins03.pdf

Finally, Long and Freese have several good methods for making the 
effects of variables in categorical models more understandable. They 
will hopefully have a new book out next year. The beta versions of 
their new commands look very promising.  Meanwhile, their old book 
and its spost9 commands may still be useful. See

http://www.stata.com/bookstore/regression-models-categorical-dependent-variables/index.html

Incidentally, I am not sure why fractional logit would be that much 
harder to explain than regular logit, but perhaps I am missing 
something. If you want some more basic background on the use of 
margins, you may wish to start with

http://www3.nd.edu/~rwilliam/xsoc73994/Margins01.pptx

At 11:49 AM 11/15/2013, Sandra Virgo wrote:
> 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)
>
>
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-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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