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From |
William Hauser <whauseriii@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Re: xtmelogit convergence issues and log transforming IVs |

Date |
Wed, 25 Jan 2012 14:19:35 -0500 |

Nick and Maarten, I appreciate the advice. I think I prefer the intuitive interpretation of logs. I'm going to make the bold assumption that my interpretation of log base 1.1 as a 10% change is correct since I haven't been corrected : ) I also especially appreciate the suggestion of splines and the insightful example. Splines are not something that's ordinarily used in my field and I know little about it. I think a log transformation here makes for the most intuitive interpretation since the "knot(s)" in the spline would be arbitrary. That said, I have another research endeavor using this dataset and I think the use of a linear spline might be particularly useful - so Maarten's suggestion is, perhaps, more helpful than he could have realized. Thanks all, Will Hauser On Tue, Jan 24, 2012 at 3:24 PM, William Hauser <whauseriii@gmail.com> wrote: > Hi all, > I'm working with a dataset consisting of court cases nested within judges > nested within circuit. The model is specified as 2 levels (cases<judges) > with circuit represented as 19 dummy variables (20 circuits, 1 omitted as > reference). The outcome is dichotomous so I'm using the xtmelogit command. > Stata is version 12, intercooled. > > The problem is that the model simply will not converge unless I transform > two of the predictor variables which are, in their untransformed form, > highly overdispersed. These variables represent the number of points the > offender receives for their present offense and for their prior record if > they have one (more on that shortly). > > Problem is, I'm not sure how to interpret the resulting odds ratios for the > log transformed predictor variables (crime seriousness and prior record). > > Using the natural log, calculated as ln(xvar), I think the coefficient > represents the change in odds for increasing x by a factor of ~2.7 (the > value of e). This would seem to be very unintuitive if correct. > Alternatively, I can use the log to base 1.10 of the x vars, calculated as > ln(xvar)/ln(1.10), which I think might be interpreted as the odds ratio for > a 10% change in x but I'm not at all sure. > > So, what is the correct/best transformation for this application and how do > I interpret it? > > There is also the vexing issue the log of 0. For crime seriousness there > are no zeros since everyone committed a crime. But for prior record there > are those with no prior record. One solution that seems to be roundly > criticized is the addition of a constant such as .5 or 1 to all cases before > logging. Another solution is to keep the 0's as 0 and create a dummy coded > as 1 for all cases with that 0 value (i.e. those that would've been > undefined or "."). The syntax for the latter solution looks like this, > > gen log_priors=(ln(prior_record)/ln(1.10) > (a bunch of missing values result for all those cases where the offender has > no prior record) > replace log_priors=0 if prior_record==0 > gen no_priors=0 > replace no_priors=1 if prior_record==0 > > Anyone know if this is an acceptable solution or if perhaps another > transformation that is amenable to zeros is in order? > > Any insight or guidance would be greatly appreciated. > > Will Hauser * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: RE: Re: xtmelogit convergence issues and log transforming IVs***From:*Nick Cox <n.j.cox@durham.ac.uk>

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