Design matrix question - using covariate and constant recap

[tswannack]

Hi, my name is Todd Swannack and I am a PhD student at Texas A & M University. I am working with some of my mark-recap data on Houston toads and I have a question or two about the design matrix. I have been working my way through ‘A Gentle Introduction’ want to make sure I am on the right track.

I have one group and have run the CJS model. I would like to test a model with a covariate (precipitation) while keeping recapture probability constant. I have set up my design matrix as follows:


B1 _ B2 _ Parm _ Pint
1 _ 41.49 _ 1:Phi _ 0
1 _ 44.56 _ 2:Phi _ 0
1 _ 45.27 _ 3:Phi _ 0
1 _ 26.41 _ 4:Phi _ 0
0 _ 0 _ 5:p _ 1
0 _ 0 _ 6:p _ 1
0 _ 0 _ 7:p _ 1
0 _ 0 _ 8:p _ 1

My main question is: does this look right?, and if not, does anyone have any suggestions on how to fix it? Thanks for any assistance. I really appreciate it.

Take care,

Todd

[abreton]

For starters, lets make sure you built the appropriate PIM model before you opened the design matrix (DM). If so, then the following should be true: your study occurs over five occasions; phi 1-4 (from your PIMs and DM) represent apparent survival probabilities from occasion 1-2, 2-3, 3-4, 4-5 respectively; and p 5-8 (from your PIMs and DM) represent encounter (resight, recapture...etc) probabilities on occasions 2, 3, 4, 5. Next, I'll assume that after building this PIM structure, you closed the PIMs, and proceeded to build all models (or all except the Phi (t) p (t) = CJS model) in the design matrix. Bad things can occur if you manipulate the PIMs as your building and running models in the DM! As you probably know, you should build your most general and uncontrained model into the PIMs, close the PIMs, and run/build all models int eh design matrix - even the global PIM model but this wouldn't be critical for not-to-sparse datasets.

Okay, so onto your question. Assuming you said yes to my inquires, i.e., all "true", then your DM is correct. However, I'd suggest renaming your B1 and B2 columns to Phi Int and Phi Precip respectively. And more importantly, you should transform your covariate so that values are between about -3 and +3 (I often use cov/10 or 100). Values above -3 and +3 can cause convergence problems in the logLikelihood function underlying the model. Lastly, be careful with your wording - your not "testing" a model per se, instead you're fitting data to a model and then assessing it's support relative to a set of models which are all conditional on the same data.

[cooch]

And more importantly, you should transform your covariate so that values are between about -3 and +3 (I often use cov/10 or 100). Values above -3 and +3 can cause convergence problems in the logLikelihood function underlying the model.

True, but standardizing to ensure numerical convergence is now handled internally in MARK - using the 'standardize' covariates option explicitly simply constrains values to have a mean of 0, and a range of apx. [-3,3]. There are some advantages in doing this. This is all discussed in Chapter 12 - specifically, see p. 9 in chapter 12, and section 12.5.

[tswannack]

Cool. Thank you for your suggestions. I really appreciate it. Take care.

T