Hi all,

I'm working on a single-season two-species spotted owl/barred owl analysis where I'm focused on detection probabilities, not occupancy (sites are non-randomly selected so estimates of occupancy are invalid). The pertinent covariate in this model is a z-transformed weekly measurement of background noise levels at each site.

I'm using the PsiBA (Richmond et al 2010) parameterization and have coded my encounters in the condensed 0-3 method. Models are running without any problems but I'm having trouble understanding the relationships between my beta estimates. My model structure on p is coded as:

p ~ SP+INT_o+INT_d + SP:INT_o + Noise + SP:Noise

Plotting real estimates makes sense, nothing misbehaving or acting strangely (image in link):

https://imgur.com/a/am1oLPC

Coefficient estimates are:

B1_pA[1] 0.285612 0.093490

B2_pB[1] 0.238717 0.499941

B3_rA[1] -0.135319 0.135049

B4_rBa[1] -0.411427 0.157263

B5_pA[1].Noise_pA -1.096682 0.075720

B6_rBA[1] -1.141336 0.497547

B7_pB[1].Noise_pB 0.383992 0.117759

Here's the question: How are the beta estimates referring to each other?

Noise_pB is definitely a negative effect according to real estimates, but the betas don’t tell the same story. I’m reporting these estimates to describe the relationships between probabilities and can’t figure out how to explain B4-7. Is the magnitude of the rBa effect relative to rBA? Similarly, is Noise_B relative to Noise_A?

I tested back-transforming beta estimates for pA, pB and rA into real estimates on a model without covariates using:

logit2prob <- function(logit){

odds <- exp(logit)

prob <- odds / (1 + odds)

return(prob)

}

real pA: logit2prob(betapA)

real pB: logit2prob(betapA + betapB)

real rA: logit2prob(betapA + betarA)

However, this method doesn't work for rBa or rBA, at least not in the combinations of coefficient estimates I’ve tried.

I would greatly appreciate any help on this! Happy to provide more output if necessary. I’ve scoured all sources I can think of--my deepest apologies if this question has already been addressed.

Thanks!

Leila