apparent missing beta parameters in RMark results

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apparent missing beta parameters in RMark results

Postby rmark4salamanders » Mon Oct 09, 2017 1:08 pm

I'm running a multistate model with 5 states (2,3,4,5, and 6). I have year and season as covariates: there are 7 years in the study (1 through 7), and 3 seasons (fall, spring, and summer). As an example, when I run the model S~year+season+stratum and keep other parameters constant I get the following list of betas:

Code: Select all
$beta
                   estimate        se         lcl         ucl
S:(Intercept)     3.7452911 0.9689498   1.8461495   5.6444327
S:yearyear2      -1.2621913 0.9540269  -3.1320841   0.6077014
S:yearyear3       0.5552285 1.0356145  -1.4745759   2.5850329
S:yearyear4       0.5278407 0.9183120  -1.2720509   2.3277323
S:yearyear5      -1.3551528 0.9529783  -3.2229903   0.5126848
S:yearyear6      -2.6475072 0.9585767  -4.5263176  -0.7686968
S:yearyear7      -1.1512225 1.0988442  -3.3049571   1.0025121
S:seasonspring   17.6266590 0.0000000  17.6266590  17.6266590
S:seasonsummer   15.1923610 0.0000000  15.1923610  15.1923610
S:stratum3        1.8536932 0.3363387   1.1944694   2.5129170
S:stratum4        1.9240445 0.4177686   1.1052181   2.7428709
S:stratum5        2.4906431 0.3738151   1.7579655   3.2233207
S:stratum6      -21.8775480 0.0000000 -21.8775480 -21.8775480
Psi:(Intercept)  -0.7718812 0.0362026  -0.8428382  -0.7009242
p:(Intercept)    -2.3290458 0.0228745  -2.3738798  -2.2842119
c:(Intercept)    -1.7671490 0.0369619  -1.8395944  -1.6947037
f0:(Intercept)    4.5564466 0.0316342   4.4944436   4.6184495


Now I know i have a few singularities in this model, and it isn't one I would end up using, but what i'm curious about is the fact that there is no beta for the season fall, or for the stratum 2. I get that year 1 is being used an intercept.

So why isn't there a beta for fall or stratum 2? and how are the real parameter estimates for survival in stratum 2 or season fall being made?

Any help understanding this would be much appreciated.
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Re: apparent missing beta parameters in RMark results

Postby jlaake » Mon Oct 09, 2017 4:45 pm

Whenever you have a formula with more than one factor variable the intercept is for the first level of each factor variable when you are using the default of treatment contrasts. It works that way for any modelling in R or any other stats package for that matter - except that for SAS it is the last factor variable rather than the first I believe.

So for your model the intercept is for fall - year 1 - stratum 2.

--jeff
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