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

[Austin Nichols <austinnichols@gmail.com>]

Sandra Virgo <Sandra.Virgo@lshtm.ac.uk> :
Is   llti_stand  measured as a proportion between 0 and 1? If so, you
don't want to measure the effect as a one-unit change, but as one
hundredth of a unit.

On 11/15/13, 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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