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This plot, which I previously created, shows predicted probabilities of claim onset based on two variables, PIB (scaled across the x-axis) and W, presented as its 75th and 25th percentiles. Confidence intervals for the predictions are presented alongside the two lines.

Probability of Claim Onset

As I theorize that W and PIB have an interactive effect on claim onset, I'd like to see if there is any significance in the marginal effect of W on PIB. Confidence intervals of the predicted probabilities alone cannot confirm that this effect is insignificant, per my reading here (https://www.sociologicalscience.com/download/vol-6/february/SocSci_v6_81to117.pdf).

I know that you can calculate marginal effect easily from predicted probabilities by subtracting one from the other. Yet, I don't understand how I can get the confidence intervals for the marginal effect -- obviously needed to determine when and where my two sets of probabilities are indeed significantly different from one another.

The function that I used for calculating predicted probabilities of the zeroinfl() model object and the confidence intervals of those predicted probabilities is derived from an online posting (https://stat.ethz.ch/pipermail/r-help/2008-December/182806.html). I'm happy to provide more code if needed, but as this is not a question about an error, I am not sure it is needed.

Sam Driggers
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1 Answers1

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So, I'm not entirely sure this is the correct answer, but to anyone who might come across the same problem I did:

Assuming that the two prediction lines maintain the same variance, you can pool SE before then calculating. See the wikipedia for Pooled Variance to confirm. 

SEpooled <- ((pred_1_OR_pred_2$SE * sqrt(simulation_n))^2) * (sqrt((1/simulation_n)+(1/simulation_n)))
low_conf <- (pred_1$PP - pred_2$PP) - (1.96*SEpooled)
high_conf <- (pred_1$PP - pred_2$PP) + (1.96*SEpooled)

##Add this to the plot
lines(pred_1$x_val, low_conf, lty=2)
lines(pred_1$x_val, high_conf, lty=2)
Sam Driggers
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