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The pros and cons of generalized linear models (e.g. as implemented in
-glm-) versus other approaches are a rather large subject, but one key
point is that in -glm- it is the predicted mean which is fitted on a
transformed scale, which is not the exact equivalent of transforming
the data.
You need only realise that
* logit(0) and logit(1) are undefined whereas logit(mean) is perfectly
well defined for mean in (0,1)
or
* log(0) is also undefined, but Poisson models can accommodate observed zeros
to see the advantage. Another key point is that functional form and
distribution family are separate choices.
A very good expository paper, often cited on this list by Scott
Merryman and myself, is
Lane, P.W. 2002. Generalized linear models in soil science.
European Journal of Soil Science 53: 241-251.
Anyone going "soil science???" should know that the examples are not
difficult and seize this opportunity to impress your colleagues with
your eclectic erudition.
Abstract: Classical linear models are easy to understand and fit.
However, when assumptions are not met, violence should not be used on
the data to force them into the linear mould. Transformation of
variables may allow successful linear modeling, but it affects several
aspects of the model simultaneously. In particular, it can interfere
with the scientific interpretation of the model. Generalized linear
models are a wider class, and they retain the concept of additive
explanatory effects. They provide generalizations of the
distributional assumptions of the response variable, while at the same
time allowing a transformed scale on which the explanatory effects
combine. These models can be fitted reliably with standard software,
and the analysis is readily interpreted in an analogous way to that of
linear models. Many further generalizations to the generalized linear
model have been proposed, extending them to deal with smooth effects,
non-linear parameters, and extra compone
nts of variation. Though the extra complexity of generalized linear
models gives rise to some additional difficulties in analysis, these
difficulties are outweighed by the flexibility of the models and ease
of interpretation. The generalizations allow the intuitively more
appealing approach to analysis of adjusting the model rather than
adjusting the data.
Nick
[email protected]
On 19 December 2013 16:13, Richard Williams
<[email protected]> wrote:
> At 10:50 AM 12/19/2013, Scott Merryman wrote:
>>
>> One could also use the -expression()- option in -margins-
>>
>> margins race, expression(predict(xb)^2)
>> marginsplot, name(regress2,replace)
>
>
> Good point. I've used the expression option to do thing like multiply
> numbers by 100 so you get 37.3 instead of .373.
>
> That still leaves open the question of whether you should use regress
> (computing the square root of the dv yourself) or use glm (using the power
> link.) In my example it doesn't make too much difference. In general is it
> better to use glm or are there pros and cons of each approach?
>
>
>> Scott
>>
>>
>> On Thu, Dec 19, 2013 at 9:30 AM, Richard Williams
>> <[email protected]> wrote:
>> > Patrick Royston's -marginscontplot- (available from SSC) can be used
>> > when
>> > you've done a log or other transformation of an independent variable.
>> > See
>> > the help file example entitled "Example using a log-transformed
>> > covariate".
>> >
>> > For a dependent variable, I think you can use the glm command, at least
>> > some
>> > of the time. You should get a 2nd opinion on this, e.g. Austin Nichols
>> > is
>> > much better with these sorts of things than I am. When the dependent
>> > variable has been transformed I believe it is often better to use glm
>> > anyway. In the following you don't get exactly the same results from
>> > regress
>> > and glm but I don't think you are supposed to (and the results are
>> > similar).
>> >
>> > webuse nhanes2f, clear
>> > gen sqweight = weight ^.5
>> > reg sqweight i.race
>> > margins race
>> > marginsplot, name(regress)
>> > glm weight i.race, link(power .5)
>> > margins race
>> > marginsplot, name(glm)
>> >
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