Normalize and Scale Covariate

[hoarybat]

Hello,

Under the Edit menu on the Data Input Window, there are two options: 1. Normalize covariate and 2. Scale covariate. Can someone please explain the stats behind these two options? Does the scale covariate option merely obtain the z-scores? What does the normalize covariate option do? A log-transformation?

I am having a hard time get my data to numerically converge in my models and I think I need to scale or normalize my covariates, but I don't know which option to take. Or should I do both? Any suggestions? My values for my covariates are often highly variable, ranging from 0 up to 5000. Also, can I input covariates with negative values? I ran a Pricinpal Component Analysis and some of the covariates are the factors from the PCA and they have negative values.

All of my models give me the numerical convergence error with significant digits... For my detection models the standard errors are within reason, but the SE for psi is well over 300,000. I don't get it????

Thanks.

[jhines]

Covariate values can be negative, and there are no limits on the values that they can take. That said, the optimization routine in PRESENCE will sometimes have trouble when there is a wide range in the covariates. (It is due to the transformation function taking the exponential of very large positive or negative values.) In cases where this happens, you can 'scale' the covariates to reduce the range of values without changing the models. When you 'scale' a covariate, you simply divide the covariate by a constant, resulting in the associated beta parameter being multiplied by a constant such that the product of the two is the same. So if your covarite ranges from -50 to 5000, and you divide by 100, the new covariate will range from -0.5 to 50. If the beta estimate associated with that covariate was 0.0123 with the un-scaled covariate, the beta estimate for the scaled covariate would be 1.23. All 'real' parameters (psi, p, eps,...) will remain unchanged. The advantage of scaling covariates is that it's easy to convert the beta's back to what they would have been with the original covariates, however, the actual values of the beta estimates are not usually all that interesting. What most people are interested in is the value of the beta estimate relative to it's standard error. So, if the beta estimate is 'significantly' different from zero for the un-scaled covariate, it will be 'significant' with the scaled covarite as well. It's the same as changing the units, which are arbitrary anyway.

The 'normalize' option is similar to the 'scale' option except that it computes the mean and standard deviation of the covariate and computes a new covariate by subtracting each covariate value from the mean and dividing by the standard deviation. This results in covariate values which are centered around zero and range from approximately -2.0 to 2.0. As with scaling, the result will be that the beta estimates will be altered, but the value of the beta estimates relative to their estimated standard errors will be the same, and the 'real' parameters will be the same. This option tends to perform better in cases where scaling doesn't work.

If you're still having trouble with convergence after trying one of these options, check the data to make sure you have at least some variation in the covariates with respect to the estimates. For example, if all sites have detections, then occupancy will be estimated as 1.0, and can't vary with respect to any covariate. Or, if detections only happen when a covariate has one particular value and non-detections happen for all other values of the covariate, there probably won't be enough variation in the covariate to model detection as a function of that covariate.

Jim

[hoarybat]

Jim,

I am trying to run prelim data, so I am using data from only half of my sites (I still have another field season). I have sampled 35 sites for 2 nights each, and the amount of detections is very low. I had only 4 detections over the 70 sampling periods. Is this preventing the numerical convergence and proper estimates? I plan on sampling 70 sites total over 2 seasons and each site 2 times. I've read that for rare species it is better to sample more sites less often than fewer sites more often. From these errors I am receiving, I am concerned I may be undersampling.

[jhines]

With only 4 detections, I doubt that you will be able to run a model with covariates. The only model which might run is the simple one, psi(.),p(.). I've heard people recommend at least 10 detections per covariate as a 'rule of thumb'. I don't like those types of 'rules', but in this case, 4 detections isn't going to be enough to model a relationship between a covariate and a parameter.

There is a section in the 'Occupancy Estimation and Modeling' book which talks about the optimal number of sites and surveys and it indicates that when detection probability is low, you should have many surveys. There are tables, starting on page 168 which should help with designing your surveys.

Jim