Standard error overlapping 0

questions concerning analysis/theory using program PRESENCE

Standard error overlapping 0

Postby dmh1454 » Wed Jul 29, 2020 3:10 pm

Good afternoon,

I am currently running single-species, single-season occupancy models in PRESENCE. However, I ran into a problem with some of my models. I ran my models first with a constant occupancy to determine the top detection model. After showing my colleague the models however, he claims that something is wrong with my data as the standard error of my beta models overlaps 0. Here is the null model, where psi overlaps 0.

Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 psi.a1 : 0.133281 0.287953
B1 P[5].b1 : 0.727036 0.195763


However, when I run models with a variable in occupancy, it no longer shows standard error overlapping 0.

Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 psi.a1 : 0.887288 0.428300
A2 psi.Waterbody_Type : -1.643238 0.627444
B1 P[5].b1 : 0.724914 0.196107

I am unsure now whether my models ran properly or not. I was under the assumption that any models that overlap 0 just show that the model is nonsignificant. I thought that whats being shown (in the first model) is that the null for occupancy is nonsignificant but the constant for detection is significant. I am aware that beta values are not usable in their current form and must be calculated to determine the confidence intervals for true significance but I would rather not do all the calculations just to find out I am wasting time.

Does anyone have any thoughts on this or have a resource that may give me more insight? Please let me know if you need more information. Thank you.
dmh1454
 
Posts: 11
Joined: Fri Aug 02, 2019 12:35 pm

Re: Standard error overlapping 0

Postby jhines » Wed Jul 29, 2020 3:41 pm

The beta estimates are on the logit scale, meaning they range from minus infinity to plus infinity. Translating that to the real probability scale (zero to one) means that negative values for beta correspond to probabilities less than 0.5 and positive values correspond to probabilities > 0.5 (when we're talking about intercept terms). For the beta associated with psi, you have a value > 0, so the prob. of occupancy will be > 0.5 The conf. interval using the std. error would be 0.13 - 1.96*0.29 = -0.44 to 0.13+1.96*0.29 = 0.70. Those values are on the logit scale, so the conf. interval of the prob. of occ. would be from the inverse-logit of -0.44 to the inv. logit of 0.70 ( from 0.39 to 0.67). The point here is that the beta estimates can be negative and std. errors can overlap zero. When converted to probabilities, they will fall between zero and one. The fact that the std. error of beta overlaps zero just means that the conf. interval of the real parameter (psi) overlaps 0.5. So, nothing wrong with the data.

The 2nd model has an intercept and slope for psi, meaning that occupancy can be different for each waterbody type. You can interpret the first beta in the same way as the first model for all sites where the waterbody type equals zero. The fact that the conf. interval doesn't overlap zero simply means that the 95% conf. interval lower limit for occupancy when waterbody=0 > 0.5.

Since the waterbody beta is negative, it means that there is a negative relationship between waterbody type and occupancy (ie., as waterbody type increases, occupancy decreases). The conf. interval for that beta doesn't overlap zero, so you can be fairly confident that there is truly a negative effect of waterbody type on occupancy. If the conf. interval did overlap zero, then you would be less confident that the true effect of waterbody type was negative. With a strong effect of that covariate, I suspect that the 2nd model has a much lower AIC value than the 1st model.

Again, nothing from these two models indicate a problem with the data.
jhines
 
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Re: Standard error overlapping 0

Postby dmh1454 » Wed Jul 29, 2020 3:57 pm

Ok, so like I thought. Thank you for your time.
dmh1454
 
Posts: 11
Joined: Fri Aug 02, 2019 12:35 pm


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