[R-sig-ME] bivariate logistic/probit with hierarchical structure

[David Duffy]

On Wed, 11 May 2011, Jarrod Hadfield wrote:

> Quoting David Duffy <davidD at qimr.edu.au> on Wed, 11 May 2011 16:10:04 
>
>> On Fri, 6 May 2011, Arthur Charpentier wrote:
>> 
>>> I would like to fit a bivariate probit model, i.e. I observe Y=(Y1,Y2),
>>> I have some covariates X1,...Xk, and I assume that there is a hierarchical
>>> structure (and random effects), i.e. Y_i is actually a Y_{i,j} where j is 
>>> a
>>> subgroup index.
>>> So this yield two correlations levels,
>>> - within subgroup correlation between Y1_i's (if they belong to the same
>>> subgroup)
>>> 
>> 
>> Since you are doing "only" a bivariate, you might consider rewriting it as 
>> a univariate problem with appropriate random effects (that is Y1 and Y2 are 
>> in a lower level with variable specific random intercepts etc).
>
> The `residual' variances would not be identifiable even though the residual 
> correlation is, which I think would cause problems unless the variances are 
> fixed at some value (may be possible with the development version of lmer? )
>

I'm a bit slow, so I don't see where that would be a problem fitting in 
lmer per se.  Anyway, here is an example

library(Zelig)
require(VGAM)
data(sanction)
s1 <- sanction[,-5]
s2 <- sanction[,-4]
s1$group <- rownames(s1)
s2$group <- rownames(s2)
s1$type   <- "import"
s2$type   <- "export"
names(s2)[4] <- names(s1)[4] <- "response"
sanction2 <- rbind(s1,s2)
sanction2 <- sanction2[order(sanction2$group, sanction2$type),]
sanction2$type <- factor(sanction2$type)

lmer(response ~ coop + cost + target + type + (1|group),
      data=sanction2, family=binomial())
summary(vglm(cbind(import, export) ~ coop + cost + target,
              binom2.rho(exchangeable = TRUE), data = sanction))

lmer(response ~ type + type:coop + type:cost + type:target + (1|group), 
data=sanction2, family=binomial())
summary(vglm(cbind(import, export) ~ coop + cost + target,
              binom2.rho(exchangeable = FALSE), data = sanction))



-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v