# Interpreting effect size for binomial GLM (power analysis with simr)

I am doing a power analysis to determine how many sites I need to sample (recording an animal’s presence/absence) to detect a difference between the animal's presence before and after a fire has gone through. We have already surveyed the sites (around 200) before the fire and so I want to know if we can do less post-burn sampling (to save money). The results will be analysed using a binomial glm. I am using the simr packing and powersim function. Here is the model that will be used:

m3 <- glm(animal.present ~ fire, family=binomial, data=data)

I am predicting there to be a reduction in animal presence of 50% post fire. Given it’s a binomial model and the coefficient represents a logit, I think the coefficient should be -0.7 (as the exponentiate of that is -0.5):

exp(-0.7)
 0.4965853


I do this to change the coefficient:

coef(m3)['firepost'] <- -0.7

Running the model I get the below output. I want to know if I have specified the correct effect size and have I put the effect in the correct direction (e.g. less animals in post fire):

glm(formula = koala.present ~ fire, family = binomial, data = koala.fire)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-0.8949  -0.8949  -0.6614   1.4892   1.8040

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  -0.7084     0.1515  -4.675 2.94e-06 ***
firepost     -0.7000     0.2143  -3.267  0.00109 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 499.7  on 393  degrees of freedom
Residual deviance: 499.7  on 392  degrees of freedom
AIC: 503.7

Number of Fisher Scoring iterations: 4


Running the power analysis then shows we should sample the same number of sites as before (197) to have have enough power


Power for predictor 'fire', (95% confidence interval):================================================|
85.00% (82.63, 87.16)

Test: Likelihood ratio

Based on 1000 simulations, (0 warnings, 0 errors)
alpha = 0.05, nrow = 394

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