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

[David Hoaglin <dchoaglin@gmail.com>]

Hi, Sandra.

Would you please explain why you are unable to use an ordinary logit
model?  The proportions seem to be the usual sort of "counted
fractions" (as opposed to the continuous fractions in a fractional
logit model).  If you have the numerator and denominator of your
proportions, a binomial GLM should be appropriate, so perhaps you have
only the proportions and not the numerators and denominators.

Also, what are the individual observations?  How many do you have, and
how were the data collected?

David Hoaglin

On Fri, Nov 15, 2013 at 11:49 AM, Sandra Virgo <Sandra.Virgo@lshtm.ac.uk> 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

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