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

David Duffy davidD at qimr.edu.au
Thu May 12 00:48:52 CEST 2011

```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) <- names(s1) <- "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

```