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


From   Richard Williams <[email protected]>
To   [email protected], <[email protected]>
Subject   Re: st: interpreting marginal effects of fractional logit with continuous independent variables
Date   Fri, 15 Nov 2013 13:32:55 -0500

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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