Clash Royale CLAN TAG#URR8PPP

0 values in glm binomial family with link=logit => do not treat them correctly

I have this model that run well:

glm(formula = cbind(Number_F, Nbre_dead) ~ Temperature + Population +
Size + Number_I, family = binomial(link = logit), data = marine_data_T2)


Number_F (total of individuals at the end of the experiment) = Number_I (total of individuals at the beginning of the experiment) - Nbre_dead (number of individuals that died). So, data look like this : 6=6-0 (if all individuals survived); 5=7-2 (if two of them died); 8=7-1 (if only one died).

However, when I run the summary of this model and look at the p-values, I think that the model does not work 'correctly':

summary

Call:
glm(formula = cbind(Number_F, Nbre_dead) ~ Temperature + Population +
Size + Number_I, family = binomial(link = logit), data = marine_data_T2)

Deviance Residuals:
Min 1Q Median 3Q Max
-2.56056 0.00008 0.27646 0.63662 1.75879

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -4.0006 1.8824 -2.125 0.033565 *
Temperature20 20.0504 2125.4089 0.009 0.992473
Temperature22.5 2.8416 0.5617 5.059 4.22e-07 ***
Temperature25 3.8333 0.7880 4.865 1.15e-06 ***
Temperature27.5 2.9741 0.5992 4.964 6.92e-07 ***
Temperature30 1.9170 0.5044 3.800 0.000145 ***
PopulationPAC 0.9571 0.6115 1.565 0.117536
PopulationSAR -0.1583 0.5259 -0.301 0.763443
Size6-7mm 2.5652 0.8782 2.921 0.003489 **
Number_I 0.6097 0.2675 2.280 0.022636 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 154.626 on 89 degrees of freedom
Residual deviance: 61.112 on 80 degrees of freedom
AIC: 125.82

Number of Fisher Scoring iterations: 18


Indeed, I am completely sure I have a significative difference between 15°C and 20°C (temperature treatments) as I have a 50% mortality at 15°C and 0% at 20°C but I think that because at 20°C I did not have any individual of my experiment that died (consequently, I have Number_dead = 0), the model does not know how to 'react'. I have 6 temperature treatments (15, 20, 22.5, 25, 27.5 and 30°C).

Do you a way to make it work fine ?

I have the same model for another transect (I studied two transects of three populations) and for that one, there was no problem because there were individuals that died in all treatments.

Here are my data:

marine_data_T2 <-
structure(list(Population = c("PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR", "PAC", "MOR", "SAR", "PAC", "MOR",
"SAR", "PAC", "MOR", "SAR"), Temperature = structure(c(1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L,
6L, 6L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L,
3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L,
6L, 6L, 6L, 6L, 6L, 6L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L,
4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L), .Label = c("15", "20", "22.5",
"25", "27.5", "30"), class = "factor"), Size = c("4-5mm", "4-5mm",
"4-5mm", "6-7mm", "6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm",
"6-7mm", "6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm", "6-7mm",
"6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm", "6-7mm", "6-7mm",
"6-7mm", "4-5mm", "4-5mm", "4-5mm", "6-7mm", "6-7mm", "6-7mm",
"4-5mm", "4-5mm", "4-5mm", "6-7mm", "6-7mm", "6-7mm", "4-5mm",
"4-5mm", "4-5mm", "6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm",
"4-5mm", "6-7mm", "6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm",
"6-7mm", "6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm", "6-7mm",
"6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm", "6-7mm", "6-7mm",
"6-7mm", "4-5mm", "4-5mm", "4-5mm", "6-7mm", "6-7mm", "4-5mm",
"4-5mm", "4-5mm", "4-5mm", "6-7mm", "6-7mm", "4-5mm", "4-5mm",
"4-5mm", "4-5mm", "6-7mm", "6-7mm", "4-5mm", "4-5mm", "4-5mm",
"4-5mm", "6-7mm", "6-7mm", "4-5mm"), Number_I = c(6, 8, 6, 4,
3, 4, 6, 8, 6, 4, 3, 4, 5, 7, 6, 5, 3, 4, 4, 7, 6, 5, 4, 4, 6,
7, 7, 4, 4, 3, 6, 7, 6, 4, 3, 4, 5, 7, 5, 2, 3, 5, 6, 8, 6, 4,
3, 4, 5, 7, 6, 5, 4, 4, 5, 7, 6, 5, 4, 4, 6, 7, 7, 4, 4, 3, 5,
6, 5, 2, 4, 5, 5, 6, 5, 3, 4, 5, 5, 6, 5, 3, 4, 5, 5, 6, 5, 3,
4, 5), Number_F = c(2, 4, 4, 3, 2, 4, 6, 8, 6, 4, 3, 4, 5, 7,
6, 5, 3, 4, 4, 7, 6, 5, 4, 4, 6, 7, 6, 4, 4, 3, 6, 7, 6, 4, 3,
3, 3, 4, 1, 1, 3, 1, 6, 8, 6, 4, 3, 4, 5, 7, 6, 5, 4, 4, 5, 7,
6, 5, 4, 4, 6, 7, 7, 4, 4, 3, 4, 6, 3, 2, 2, 3, 5, 4, 5, 3, 4,
2, 5, 6, 4, 3, 4, 4, 5, 6, 4, 3, 3, 4), Nbre_dead = c(4, 4, 2,
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 1, 0, 4, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 3, 0, 0, 1, 0, 0, 1, 0, 0, 1,
0, 1, 1)), .Names = c("Population", "Temperature", "Size", "Number_I",
"Number_F", "Nbre_dead"), row.names = c(NA, -90L), class = "data.frame")

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