binary covariates or groups???

[jln]

I am new at and attempting to learn program Mark…and thus I have a couple of basic questions. Any help you could provide me with would be fabulous. I am primarily confused with the covariates vs grouping methods. I have read through several messages on similar topics and the "gentle intro", but none appeared to clarify my questions. Here is what I have so far….

I am using the band recovery model. After my encounter history, I grouped age (adult and juveniles), then I have land at harvest site and movement as covariates (both of which are binary).
EH
Age groups (adult or juv)
land at harvest site (public or private)
movement (yes or no)

Ex:
000000000010000000 3 1 0 0;

I have entered in the PIM an age model for juvs that turn to adults the following year. Ok…so I got this far and was able to model age and time, etc… that was great.

So now my confusion lies with the covariates--- which again are all binary variables (land at harvest site [0= private or 1 = public] and movement [0=yes or 1=no]). I am uncertain if this is the correct way of doing this or if I should have groups within groups?

Ultimately, I would like to use Mark’s models to see if age, harvest site, and movement influence survival rates….Am I doing this correctly? If not could you please lead me in the correction direction?

[jlaake]

This is a bit confusing because categorical (factor) covariates like you have can be used via groups or as an individual covariate as you have specified them. The choice is up to you and there are advantages and disadvantages however you go. Using individual covariates can result in slower execution times but unless you have lots of data that won't be a problem. Also, individual covariates require the use of a design matrix so you can't use the sin link with PIM coding which can make it harder on MARK to count parameters in some cases. Using groups for categorical covariates means you have lots of PIMS to manipulate. For example, in your case you could have 8 groups. 2ages*2 movement*2 land. That means you would have 8 PIMS for every parameter. Not my idea of fun. Age is a natural one to use for groups because it really is a time-varying covariate (age changes with time) although you can still have time-varying individual covariates (you have a variable for each time). If you are going to use a factor variable as an individual covariate then you need to have k-1 variables for the k-levels. In your case k=2 so you have one variable. You choose 1 level as the intercept and the other k-1 levels have a 1 in the column that represents the value of the level for that animal. If they are all zero then that animal has the intercept factor level. If you think about it, this is the same way you would enter a column in the design matrix if it was for the parameters in the model. You can think of individual covariates as simply columns of the design matrix that change from animal to animal. Instead of entering the values in the design matrix, you enter the names of the individual covariates. You will only have one column (per parameter eg Phi,p for CJS if more than one) for each of your covariates unless you want the covariate to interact with time or some other variable. If you had a factor variable with 3 levels then you would have 2 variables and 2 columns. Look through the book material on individual covariates.

--jeff

[cooch]

I am new at and attempting to learn program Mark…and thus I have a couple of basic questions. Any help you could provide me with would be fabulous. I am primarily confused with the covariates vs grouping methods. I have read through several messages on similar topics and the "gentle intro", but none appeared to clarify my questions. Here is what I have so far….

Jeff provided a detailed answer in his posted reply, and (at the risk of sounding self-serving) I'll echo his suggestion to read the 'guide' as much as you can.

But, the basic issue which Jeff raises is that you *can* in many instances save yourself some time by expressing binary classification variables (e.g., sex, adult/juvenile) as a simple linear covariate, since it can save you a lot of time when you are working with models, since using the covariate approach reduces the number of PIMs you have to wrestle with. This is often a good thing, especially for big ugly data sets.

However, the trade-off is that you need to know what you're doing, especially when it comes to handle interaction terms in a factorial design. If you have some background in linear models, this is perhaps not a big issue, but for new MARK users, this can lead you into trouble.

So, my general suggestion is that it is often less confusing to using explcit groups (PIMS) for group variables, and not the individual covariates 'short-cut', until you're really comfortable with things. The 'guide' was written assuming that most users will want to work this way, so the added advantage in using PIMs is that you have a fair chunk of long-winded documentation at your disposal.

Having said that, its probably time to update the individual covariates chapter to discuss this issue, which seems to come up here with some frequency. That won't happen overnite, so in the interim, I'd suggest the PIM approach.

[Paul Lukacs]

This is a more complicated case than a standard covariate or group situation. You only have the covariate information for individuals that are recovered. All the unrecovered animals have missing data for their covariates (or if grouping what group would you put them in?). So the example history

000000000010000000 3 1 0 0;

actually isn't valid because a 0 in the first covariate refers to an individual recovered on private land, yet the individual wasn't ever recovered. MARK doesn't currently handle missing covariate data.

Paul

[cooch]

<snip>
MARK doesn't currently handle missing covariate data.

Paul

Issues concerning how you can 'approximately' handle missing covariate data in MARK are discussed in some detail in Chapter 11 (the individual covariates chapter).

[sbonner]

I'm not sure I completely understand your experiments design, but it seems to me that this be handled as a multistate model. You could include land type as a state variable and model the probability of moving between public and private land (if that's at all meaningful) and the capture and survival probabilities for each state.

This would handle the problem with the unobserved covariates on each capture occasion, because that's exactly what the states in a multistate model are -- discrete covariates that you only observe when an individual is captured.

Multistrata (state) models are covered in Chapter 10 of The Gentle Introduction.

[cooch]

I'm not sure I completely understand your experiments design, but it seems to me that this be handled as a multistate model. You could include land type as a state variable and model the probability of moving between public and private land (if that's at all meaningful) and the capture and survival probabilities for each state.

This would handle the problem with the unobserved covariates on each capture occasion, because that's exactly what the states in a multistate model are -- discrete covariates that you only observe when an individual is captured.

Multistrata (state) models are covered in Chapter 10 of The Gentle Introduction.

In addition, using MS models to handle time-varying covariates (which often arise) is covered in some detail in Chapter 11. May not apply in this case, but for future reference...

[cooch]

In partial response to a fair number of recent questions concerning the relative pros and cons of coding for groups using individual covariates (rather than handling them explicitly as attribute groups), I've added a bunch of text to Chapter 11 (the individual covariates chapter), which covers the issue is some detail (perhaps enough, perhaps not - let me know - it always looks right to me The new version hasn't been rolled into the 'single PDF file' version of the book yet, so to look at the new stuff (specifically, new section 11.6), access the individual file for chapter 11.

Beyond feedback on whether or not I should change anything, please let me know if there are any outright errors.