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

[Jarrod Hadfield]

Hi David,

Yes, I see, it can be done that way, but care has to be taken. In your  
example the observation-level correlation is actually negative which  
means the group variance gets set to zero. You could reverse the  
scoring for one of the responses though:

sanction2$response2<-sanction2$response

sanction2$response2[which(sanction2$type=="export")]<-as.numeric(sanction2$response2[which(sanction2$type=="export")]==0)

m2<-lmer(response2 ~ type + type:coop + type:cost + type:target +  
(1|group), data=sanction2, family=binomial())

which gives a positive estimate of the group variance (i.e. a negative  
observation-level correlation).

Cheers,

Jarrod





Quoting David Duffy <davidD at qimr.edu.au> on Thu, 12 May 2011 08:48:52  
+1000 (EST):

> 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
>
>



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