Hi:

You might also want to look at the relogit() function in Zelig, which
implements a technique for rare events logistic regression. See the vignette
relogit.pdf in the Zelig package for further details. It's not a mixed
model, though....

HTH,
Dennis

On Mon, Aug 30, 2010 at 1:37 PM, David Atkins <datkins@u.washington.edu>wrote:

>
> Some colleagues have collected data from 184 females in dating
> relationships.  Data were collected daily using PDAs; the outcome is a
> binary indicator of whether any physical aggression occurred (intimate
> partner violence, or IPV).
>
> They are interested in 3 covariates:
>
> -- alcohol use: yes/no
> -- anger: rated on 1-5 scale
> -- verbal aggression: sum of handful of items, with 0-15 scale
>
> Their hypothesis is that the interaction of all 3 covariates will lead to
> the highest likelihood of IPV.  As you might expect, the outcome is very
> rare with 51 instances of IPV out of 8,269 days of data, and 158 women (out
> of 184) reported no instances of IPV.
>
> Question 1: Given that a GLMM will assume a normal distribution for the
> person-specific baserate in IPV, is this data even appropriate for GLMM or
> should they be looking elsewhere (perhaps GEE)?
>
> That said, for some (unknown) proportion of individuals, there probably
> would be instances of IPV if the data collection period were longer. Thus,
> perhaps there is some basis for assuming a distribution across people, even
> if the observed data for some individuals are all zeroes.
>
> To present some of the data (and I can check to see if it would be okay to
> make the data available), I dichotomized both anger and verbal aggression
> ("prov.cut" below):
>
>  ang.cut prov.cut alc.cut ipv.yes ipv.no
> 1       0        0       0       0     3918
> 2       0        0       1       0        1
> 3       1        0       0       5     2381
> 4       1        0       1       1      292
> 5       1        1       0      36     1471
> 6       1        1       1       9      257
>
> Thus, the instances of IPV are more likely when there is anger and verbal
> aggression; alcohol is a little less clear.  (And, if the association of
> anger and verbal aggression with IPV seems tautological, there has been
> debate about different forms of IPV, where some research has pointed to
> "cold" aggression.)
>
> Not surprisingly, analyses using either glmer() or MCMCglmm() show signs of
> partial separation, with some whopping odds-ratios and 95% CI spanning a
> couple orders of magnitude.
>
> I have read a bit about the problems of separation in logistic regression
> and know that Gelman et al suggest Bayesian priors as one "solution".
>  Moreover, I see in Jarrod Hadfield's course notes that his multinomial
> example has a "structural" zero that he addresses via priors on pp. 96-97,
> though I confess I don't quite follow exactly what he has done (and why).
>
> If I just let MCMCglmm cook on a regression with all 2-way interactions for
> a long while:
>
> prior = list(R = list(V = 1, fix = 1),
>                        B = list(mu = c(rep(0,7)), V = diag(7)),
>                        G = list(G1 = list(V = 1, nu = 0.002)))
> lr.mcmc <- MCMCglmm(ipv ~ (alc.cut + angc + log(provc + 0.03))^2, data =
> ipv.df,
>                                        family = "categorical", verbose =
> TRUE,
>                                        prior = prior,
>                                        nitt = 2000000, burnin = 1000000,
> thin = 1000,
>                                        random =  ~ person)
>
> The answers are less extreme than what I get with glmer, perhaps suggesting
> this is wandering toward the "correct" solution, though there are also
> plenty of indicators that we aren't there yet:
>
> > summary(lr.mcmc)
>
>  Iterations = 1999001
>  Thinning interval  = 1000001
>  Sample size  = 1000
>
>  DIC: 379.972
>
>  G-structure:  ~person
>
>       post.mean l-95% CI u-95% CI eff.samp
> person     2.287   0.6775    4.206    194.0
>
>  R-structure:  ~units
>
>      post.mean l-95% CI u-95% CI eff.samp
> units         1        1        1        0
>
>  Location effects: ipv ~ (alc.cut + angc + log(provc + 0.03))^2
>
>                          post.mean l-95% CI u-95% CI eff.samp  pMCMC
> (Intercept)                -2.58724 -3.49492 -1.65250   245.20 <0.001 ***
> alc.cut                     0.49512 -0.75268  1.99397  1000.00  0.464
> angc                        0.02664 -0.34227  0.41365   283.90  0.880
> log(provc + 0.03)           1.36626  0.98743  1.70863    28.69 <0.001 ***
> alc.cut:angc               -0.16519 -0.79299  0.41949   683.56  0.590
> alc.cut:log(provc + 0.03)  -0.02631 -0.53118  0.55065   157.34  0.898
> angc:log(provc + 0.03)     -0.26132 -0.40141 -0.10407    74.98  0.004 **
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> I haven't run multiple chains yet, but the effective sample sizes and trace
> plots already suggest we ain't there yet.  My specific question is whether
> there would be an alternative prior specification for the fixed-effects that
> would be more appropriate?
>
> I would appreciate any and all thoughts here, including if this just
> doesn't seem like an appropriate data/question for GLMMs.
>
> sessionInfo below.
>
> cheers, Dave
>
> > sessionInfo()
> R version 2.11.1 (2010-05-31)
> i386-apple-darwin9.8.0
>
> locale:
> [1] en_US.UTF-8/en_US.UTF-8/C/C/en_US.UTF-8/en_US.UTF-8
>
> attached base packages:
> [1] stats4    splines   stats     graphics  grDevices utils     datasets
> [8] methods   base
>
> other attached packages:
>  [1] MCMCglmm_2.06      corpcor_1.5.7      ape_2.5-3
>  [4] coda_0.13-5        Matrix_0.999375-44 lattice_0.19-10
>  [7] tensorA_0.35       Hmisc_3.8-2        modeltools_0.2-16
> [10] mvtnorm_0.9-92     survival_2.36-1
>
> loaded via a namespace (and not attached):
>  [1] cluster_1.13.1   coin_1.0-16      colorspace_1.0-1 gee_4.13-15
>  [5] grid_2.11.1      lme4_0.999375-35 nlme_3.1-96      party_0.9-9998
>  [9] rpart_3.1-46     tools_2.11.1
>
> --
> Dave Atkins, PhD
> Research Associate Professor
> Department of Psychiatry and Behavioral Science
> University of Washington
> datkins@u.washington.edu
>
> Center for the Study of Health and Risk Behaviors (CSHRB)
> 1100 NE 45th Street, Suite 300
> Seattle, WA  98105
> 206-616-3879
> http://depts.washington.edu/cshrb/
> (Mon-Wed)
>
> Center for Healthcare Improvement, for Addictions, Mental Illness,
>  Medically Vulnerable Populations (CHAMMP)
> 325 9th Avenue, 2HH-15
> Box 359911
> Seattle, WA 98104
> http://www.chammp.org
> (Thurs)
>
> _______________________________________________
> R-sig-mixed-models@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

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