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From |
Nick Cox <njcoxstata@gmail.com> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: Marginsplot on backtransformed data |

Date |
Thu, 19 Dec 2013 17:03:29 +0000 |

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 njcoxstata@gmail.com On 19 December 2013 16:13, Richard Williams <richardwilliams.ndu@gmail.com> 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 >> <richardwilliams.ndu@gmail.com> 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) >> > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Marginsplot on backtransformed data***From:*Daniel Herbert Opi <opi.herbert@gmail.com>

**Re: st: Marginsplot on backtransformed data***From:*Richard Williams <richardwilliams.ndu@gmail.com>

**Re: st: Marginsplot on backtransformed data***From:*Scott Merryman <scott.merryman@gmail.com>

**Re: st: Marginsplot on backtransformed data***From:*Richard Williams <richardwilliams.ndu@gmail.com>

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