attribute groups and interaction in Royle Count (Biometrics)

[caique]

Dear all,
Do someone know how set up interaction in Desing Matrix when dealing with Royle Count's data type?
There are always 2 rows in the DM even whem I have more tham one group.
Actually, I'm not able to set up groups in PRESENCE as I do in MARK (by "attribute groups"at Specification for Analyses).
Maybe it is my problem and I take this oportunity to confirm how set up grups in Presence.
Please,let me know if it is a misunderstand: I'm seting up groups as sites covariates in Presence. Does someone agree?
Maybe it is a silly question, but I didn't find this subject in the Forum, sorry.
Any help will be very much appreciated, please.
Cheers,
Carlos

[jhines]

Dear Carlos,

Since there are only 2 parameters estimated in the Royle model, there are always 2 rows in the design matrix. If you have N groups, you need to add N-1 site covariates. You can then estimate a different parameter for each group by adding 2*(N-1) columns to the design matrix. For example, if you have 3 groups, you would have 2 indicator covariates which are 1 if the site belongs to that group, zero otherwise. The design matrix for the model where the parameters for each group are estimated separately would be:

Code: Select all

           a1     a2      a3      a4      a5       a6
p           1   Grp1    Grp2     0      0          0
lambda      0     0       0       1     Grp1     Grp2


[caique]

Thank you, Hines.
Nice, there was not a misunderstand about seting up the groups, thanks.
But I'm still not sure about seting up the additive and interaction.
I understand that the groups are an additive terms, like in your example.
But how to set up a continuos covariable (e.g. WEIGHT) with intereaction with group?
Keeping your example, if more one beta (a7) is add to represent WEIGHT (only for lambda) in DM , it would also be additive, like this:

Code: Select all

      a1   a2   a3   a4   a5   a6   a7
p     1    Grp1 Grp2 0   0    0     0
lambda  0   0   0   1  Grp1  Grp2   Wgt



if it is possible, could you exeplain or give some reference where I can find how to set up interaction "groups and continuos convariables" in PRESENCE, please?
Sorry, it may be too obvious to be explained it that I found it anywhere. Anyway it would be very helpfull.
Thanks.
Carlos

[jhines]

Carlos,

For a model with 3 groups and interaction with a continuous covariate, you will need 6 (=3*2) columns for lambda. The design matrix would look like this:

Code: Select all

        a1    a2    a3   a4  a5    a6    a7    a8      a9
p       1    Grp1  Grp2   0   0     0     0     0       0
lambda  0      0     0    1  Grp1  Grp2  Wgt  G1xWgt  G2xWgt


where G1xWgt is a new covariate created by multiplying the Grp1 covariate by the Wgt covariate. G2xWgt is another new covariate ( = Grp2 * Wgt).

The estimate of A4 will be the 'intercept' term (or log(lambda) when weight is zero) for lambda(group 3) and a7 will be the 'slope' term (or effect of weight on lambda) for group 3.
A5 is the difference in intercepts between group 3 and group 1, and a8 is the difference in 'slopes' between group 3 and group 1.
A6 is the difference in intercepts between group 3 and group 2, and a9 is the difference in 'slopes' between group 3 and group 2.

Cheers,

Jim

[caique]

Thanks, Jim.
It is much more clear now.
Cheers,
Carlos