model check for negative binomial model

Dear Ben

Thanks for your quick response.

Yes, emergence success is usually between 60 and 80% or higher.
I am not sure how to use a binomial, if my data are counts?

Can you explain why the approximation doesn't work well if success gets
much above 50%? Does it make sense, then, to have "unhatched" as dependent
variable, so that I predict mortality (usually below 50%) using a nb with
offset(log(total clutch)) ?

summary(m.emerged)

Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: Negative Binomial(2.2104)  ( log )
Formula: Unhatched ~ Relocation..Y.N. + SP + offset(log(Total_Clutch)) +
   (1 | Beach_ID) + (1 | Week)
   Data: main

     AIC      BIC   logLik deviance df.resid
  5439.4   5466.0  -2713.7   5427.4      614

Scaled residuals:
    Min      1Q  Median      3Q     Max
-1.4383 -0.7242 -0.2287  0.4866  4.0531

Random effects:
 Groups   Name        Variance Std.Dev.
 Week     (Intercept) 0.003092 0.0556
 Beach_ID (Intercept) 0.025894 0.1609
Number of obs: 620, groups:  Week, 31; Beach_ID, 8

Fixed effects:
                  Estimate Std. Error z value Pr(>|z|)
(Intercept)       -1.38864    0.08227 -16.879  < 2e-16 ***
Relocation..Y.N.Y  0.32105    0.09152   3.508 0.000452 ***
SPL                0.22218    0.08793   2.527 0.011508 *
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Correlation of Fixed Effects:
            (Intr) R..Y.N
Rlct..Y.N.Y -0.143
SPL         -0.540 -0.038

Thanks,

Alessandra

On Tue, Feb 11, 2020 at 7:29 PM Ben Bolker <bbolker at gmail.com> wrote:

  Short answer: if emergence success gets much above 50%, then the
approximation you're making (Poisson + offset for binomial, or NB +
offset for negative binomial) doesn't work well.  You might try a
beta-binomial (with glmmTMB) or a binomial + an observation-level random
effect.

  (On the other hand, your intercept is -0.3, which corresponds to a
baseline emergence of 0.42 - not *very* high (but some beaches and years
will be well above that ...)

  Beyond that, are there any obvious patterns of mis-fit in the
predicted values ... ?

On 2020-02-11 8:09 p.m., Alessandra Bielli wrote:

Dear list

I am fitting a poisson model to estimate the effect of a treatment on
emergence success of hatchlings. To estimate emergence success, I use
number of emerged and an offset(log(total clutch).

However, overdispersion was detected:

overdisp_fun(m.emerged) #overdispersion detected

      chisq       ratio         rdf           p
3490.300836    5.684529  614.000000    0.000000

Therefore, I switched to a negative binomial. I know overdispersion is

not

relevant for nb models, but the model plots don't look too good. I also
tried to fit a poisson model with OLRE, but still the  plots don't look
good.
How do I know if my model is good enough, and what can I do to improve

it?

summary(m.emerged)

Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: Negative Binomial(7.604)  ( log )
Formula: Hatched ~ Relocation..Y.N. + SP + offset(log(Total_Clutch)) +

(1

|Beach_ID) + (1 | Year)
   Data: main

     AIC      BIC   logLik deviance df.resid
  6015.6   6042.2  -3001.8   6003.6      614

Scaled residuals:
    Min      1Q  Median      3Q     Max
-2.6427 -0.3790  0.1790  0.5242  1.6583

Random effects:
 Groups   Name        Variance Std.Dev.
 Beach_ID (Intercept) 0.004438 0.06662
 Year     (Intercept) 0.001640 0.04050
Number of obs: 620, groups:  Beach_ID, 8; Year, 5

Fixed effects:
                  Estimate Std. Error z value Pr(>|z|)
(Intercept)       -0.29915    0.04055  -7.377 1.62e-13 ***
Relocation..Y.N.Y -0.16402    0.05052  -3.247  0.00117 **
SPL               -0.08311    0.04365  -1.904  0.05689 .
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Correlation of Fixed Effects:
            (Intr) R..Y.N
Rlct..Y.N.Y -0.114
SPL         -0.497 -0.054


Thanks for your help,

Alessandra