R interpretation summary (hurdle model)

Question

I have litte experience with GLMM's and I need to use Hurdle models for the first time. I'm not sure if I interpret the output correct. Also, are there any other parameters from the summary I should check before making conclusions?

Data Counts of insects caught in traps with 2 different luring products (A & B). The traps were emptied every 3-4 days for a few months. The sex and morph of the insects was determined. The df looks like this:

Date       value  morph sex product
2016-04-05     5 Winter   M     A
2016-04-05     1 Summer   M     A
2016-04-05    18 Winter   F     A
2016-04-05     3 Summer   F     A
...

The main questions are: Which product is better? Does this differ between morphs?

Model Because of excess zeros I used a Hurdle model. I have Date as random effect. The functionglmmADMB::glmmadmb() can make hurdle models with mixed effects. For the truncated part neg.bin. was a lot better than poisson with AIC 890 vs 1400. After comparing AIC's, these are my final models:

# binairy part
hurP1 <- glmmadmb(as.numeric(data2$value > 0) ~ product * morph + (1 | Date), 
                  data = data2, family = "binomial")

# truncated part
hurP2 <- glmmadmb(value ~ product * morph + sex + (1 | Date),
                  data = subset(data2, value > 0), family = "truncnbinom1")

Summary

# binairy part
Coefficients:
                   Estimate Std. Error z value Pr(>|z|)  
(Intercept)              0.0946     0.4612    0.21    0.838  
productB                -1.0569     0.4513   -2.34    0.019 *
morphWinter              0.1898     0.4361    0.44    0.663  
productB:morphWinter    -1.4064     0.6574   -2.14    0.032 *

# truncated part
Coefficients:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)               2.473      0.210   11.76  < 2e-16 ***
sexM                      0.436      0.134    3.25  0.00117 ** 
productB                 -0.105      0.161   -0.66  0.51245    
morphWinter              -0.719      0.189   -3.80  0.00015 ***
productB:morphWinter     -0.619      0.324   -1.91  0.05569 .

My interpretation From the binairy model I understand there are less often insects caught (regardless of number) in B traps and this result is even stronger for winter morphs. The truncated model I find more difficult. Anyway I do understand that 1) significantly more males are caught 2) sign. less winter morphs are caught. I assume the intercept means that I have the highest number of summer females in product A?

Am I interpreting it correct? Any corrections and other insights are welcome!

Answer 1

I think you are basically correct. As English is not your first language I think the way you expressed the binary model is not in fact what you understood (if that makes sense). Let me put it another way. What the model shows is that the chances that any insect at all will be caught is less for B traps. And so on. I think your interpretation of the truncated part is correct.

Presumably you know that if you exponentiate the coefficients you get odds ratios and multipliers respectively for the two models?