Beta SEs on categorical detection covariates

[kmruppert]

Hello,

I'm relatively new to PRESENCE and occupancy modeling in general, but I have scoured manuals, forums, and the internet in general and have not yet been able to find a solution for my current problem.

I am trying to assess the impacts of variables on detection. Occupancy at my sites for my species does not change, so I've set psi to 1 for a single-season, single-species model. All of my covariates are sampling-specific, and I do not have any site-specific covariates. I have the continuous covariates of water temperature and trap hours (Z-transformed), and the categorical covariates of recent rain (binary), weather, and meteorological season (converted to indicators). I have 5 sites and 72 sampling occasions for each site.

My issue lies in the beta outputs for my categorical models. The standard error for betas is coming back as -1.#IND00. When I do not include all the covariates (for example, if I run a model including spring, summer, and fall, excluding winter), I do not have the issue with the SE. The model is reaching convergence with 7.8 significant digits, but the output does read ***** neg. std.err(s) in VC matrix.

Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
A1 psi.a1 : 0.000000 118632.832030
B1 P[72].b1 : -1.756447 -1.#IND00
B2 P[1].Spring : 0.370153 -1.#IND00
B3 P[1].Summer : -2.463060 -1.#IND00
B4 P[1].Fall : 0.542003 -1.#IND00
B5 P[1].Winter : -0.203647 -1.#IND00

Is there a problem with the way I am inputting/running things, or is my data set unable to work with this? Is there anything I can do to fix it? Season is coming up as my top model and makes biological sense, but I obviously don't want to include something that is incorrect. I would really appreciate any guidance that anyone is able to give me, and I'm happy to supply any further information requested.

Thanks,

Krista

[jhines]

In some cases, Presence can get std. errors of other parameters when one parameter (eg., psi) is not estimated. In other cases, that beta parameter screws up the computation of the variance-covariance matrix and none of the standard errors can be computed. A solution is to delete the column from the occupancy (psi) design matrix in Presence when you fix psi=1.

[kmruppert]

Thank you so much for the quick response! I tried deleting the column from the occupancy design matrix, but unfortunately the standard errors have not changed.

Untransformed Estimates of coefficients for covariates (Beta's)
======================================================================
estimate std.error
B1 P[72].b1 : -1.756447 -1.#IND00
B2 P[1].Spring : 0.370153 -1.#IND00
B3 P[1].Summer : -2.463060 -1.#IND00
B4 P[1].Fall : 0.542003 -1.#IND00
B5 P[1].Winter : -0.203647 -1.#IND00

Do you know of anything else I can try? Thanks again for your help!

[jhines]

If you send me the most recent backup zipfile in your project folder, I'd be happy to diagnose.

Jim (jhines@usgs.gov)

[jhines]

The reason for the problems with the variances is that there are too many beta columns. For categorical covariates, if you have N covariates, you can either have N betas (columns in the design matrix), one for each category, or an intercept column (column of 1's) and N-1 betas. In your output, you have an intercept (B1 p[72].P1) and 4 betas for the 4 seasons, totaling 5 betas to estimate 4 parameters. Either get rid of the intercept column, or (any) one of the season covariate columns.

Also, since you're not estimating psi, get rid of the column in the occupancy design matrix.

[kmruppert]

Thank you so much for the help! That fixed the issue with the categorical covariates!

Just for clarity, for continuous covariates, does the same hold true, or should it be the intercept column and the covariate column? Additionally, can models be run including continuous and categorical covariates, and if so, should the intercept column be included?

Thanks again!

[jhines]

For continuous covariates, you need an intercept column and a covariate column. The intercept beta corresponds to where the plot of the parameter (eg., p) is zero. The covariate beta corresponds to the slope (on the logit scale), or how the parameter changes with changes in the covariate. If you have both a categorical and continuous covariate, you only need 1 intercept, N-1 columns for the N categorical covariates, and 1 column for the effect of the continuous covariate, assuming an 'additive' model (no interaction between covariates). If you have interaction (eg., different effects of continuous covariate for different categories of the categorical covariate), then you have an 'interaction' or 'multiplicitive' model and need to add interaction covariates. These are the products of each categorical covariate and the continuous covariate. The total number of columns for the interaction model would be 2*N.