[R-sig-ME] confidence intervals with mvrnorm - upper value equal to inf

[Ben Bolker]

   A few clarifying points below.

On 10/14/20 3:11 PM, Alessandra Bielli wrote:
> Hi Ben
> 
> That's a good point, my parameters are not multivariate normal.
> But then, why was this method used in the Salamander example, where
> data are zero inflated and so, I assume, not multivariate normal?

   The multivariate normality refers to the sampling distribution of the 
*model parameters*, not to the distribution (marginal or conditional of 
the response variable).  In general the sampling distribution of the 
model parameters is multivariate normal if the data are "well enough 
behaved" (i.e., either the responses themselves are normal *or* there is 
enough data, and enough information in the data, for the log-likelihood 
to become quadratic in a sufficiently large neighborhood of the MLE ...)


> 
> I haven't simulated the data to share yet, but the "Inf" first appears
> at the line >pred.ucount.psim =
> exp(pred.cond.psim)*(1-plogis(pred.zi.psim))
> Only the first row, Used_piNgers=Y, shows "Inf".

    Hmm.  That's a little surprising, it implies that pred.cond.psim is 
a large number (>700 or so, which for a log-scale parameter is huge). 
Can you show us X.cond[1,] , beta.cond, vcov(m1)$cond ?
> 
> Thanks,
> Alessandra
> 
> On Sun, Oct 11, 2020 at 3:46 PM Ben Bolker <bbolker using gmail.com> wrote:
>>
>>     It's hard to troubleshoot this without a reproducible example. Unless
>> the answer is obvious -- which it's not, to me -- the easiest way to
>> troubleshoot is to work through the steps one at a time and see where
>> the infinite values first appear.  Can you create such an example either
>> by posting your data or by simulating data that looks like your data?
>>
>>     The posterior predictive simulation approach assumes that the
>> sampling distributions of the parameters are multivariate normal, which
>> is likely to be questionable in a low-information setting (which will be
>> the case if you don't have very many non-zero values ...)
>>
>>
>> On 10/10/20 7:28 AM, Alessandra Bielli wrote:
>>> Dear list,
>>>
>>> I am trying to predict a value and CI for two different treatments from a
>>> glmmTMB fitted model using posterior predictive simulations (mvrnorm
>>> function in the MASS package) as in the Salamander example, Brooks 2017
>>> appendix B
>>> <https://www.biorxiv.org/content/biorxiv/suppl/2017/05/01/132753.DC1/132753-2.pdf>.
>>> The dependent variable is a count, majority of values are zeros but some
>>> positive values appear.
>>>
>>> m1 <- glmmTMB(Dolphins.TOT ~ Used_piNgers + offset(log(Effort)) +
>>> (1|Trip_Code), ziformula =~1,
>>>                 data=x, family = "truncated_poisson")
>>>
>>>       newdata0 = with(x,
>>>                   expand.grid(
>>>                     Used_piNgers = c("Y","N"),
>>>                     Effort=1))
>>>
>>> X.cond = model.matrix(lme4::nobars(formula(m1)[-2]), newdata0)
>>>
>>> beta.cond = fixef(m1)$cond
>>> pred.cond = X.cond %*% beta.cond
>>> ziformula = m1$modelInfo$allForm$ziformula
>>> X.zi = model.matrix(lme4::nobars(ziformula), newdata0)
>>> beta.zi = fixef(m1)$zi
>>> pred.zi = X.zi %*% beta.zi
>>>
>>> pred.ucount = exp(pred.cond)*(1-plogis(pred.zi))
>>>
>>>
>>> set.seed(101)
>>> pred.condpar.psim = mvrnorm(1000,mu=beta.cond,Sigma=vcov(m1)$cond)
>>> pred.cond.psim = X.cond %*% t(pred.condpar.psim)
>>> pred.zipar.psim = mvrnorm(1000,mu=beta.zi,Sigma=vcov(m1)$zi)
>>> pred.zi.psim = X.zi %*% t(pred.zipar.psim)
>>> pred.ucount.psim = exp(pred.cond.psim)*(1-plogis(pred.zi.psim))
>>> ci.ucount = t(apply(pred.ucount.psim,1,quantile,c(0.025,0.975)))
>>> ci.ucount = data.frame(ci.ucount)
>>> names(ci.ucount) = c("ucount.low","ucount.high")
>>> pred.ucount = data.frame(newdata0, pred.ucount, ci.ucount)
>>>
>>> For my upper CI, I get a value equal to Inf:
>>>
>>> Used_piNgers Effort  pred.ucount ucount.low ucount.high
>>> 1            Y      1 6.758889e-11 0.00000000         Inf
>>> 2            N      1 1.575418e-02 0.00223033   0.1096139
>>>
>>> Is the Inf caused by the very low variability of values in my dataset? I
>>> tried to lower the upper bound of the CI ci.ucount =
>>> t(apply(pred.ucount.psim,1,quantile,c(0.025,0.975))) and only when reaching
>>> 0.475 ci.ucount = t(apply(pred.ucount.psim,1,quantile,c(0.025,0.475))) I
>>> obtained:
>>>
>>> Used_piNgers Effort  pred.ucount ucount.low  ucount.high
>>> 1            Y      1 6.758889e-11 0.00000000 7.117465e+12
>>> 2            N      1 1.575418e-02 0.00223033 1.454579e-02
>>>
>>> I found a related post
>>> <https://stackoverflow.com/questions/38272798/bootstrap-confidence-interval-with-inf-in-final-estimates-boot-dplyr-package>
>>> but
>>> the explanation is not clear to me. I would like to publish these results
>>> and I would like to know:
>>>
>>>      1. is this a sign that something is wrong? if yes, what is it?
>>>      2. if nothing is wrong, what does the Inf mean and what's the best way
>>>      to report it and plot it in a publication?
>>>
>>>
>>> I also posted this question on Cross validated
>>> https://stats.stackexchange.com/questions/491196/bootstrap-confidence-interval-with-mvrnorm-upper-value-equal-to-inf
>>>
>>> Thanks,
>>> Alessandra
>>>
>>>        [[alternative HTML version deleted]]
>>>
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>>
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