## Keeping track of betas

questions concerning analysis/theory using programs M-SURGE, E-SURGE and U-CARE

### Keeping track of betas

Hi,

I would like to know the relation between the sentence in GEMACO and the position of each beta in the output file.
Here I let two examples, if you might clarify them it would be very useful to understand how it works.

For instance, leaving out the EVENT stuff, it could be in GEPAT:
INITIAL STATE=p*
TRANSITION=
*-p
-*p
--p
In GEMACO:
Scenario 1)
IS[i+t*x(1)]
TRANSITION1[shortcut1+t(1 7)+[t([2:6;8:13]).[i+t*x(8)]]]
where shortcut1 represents a group with two levels

In total, how many betas for these sentences? (I guess six), which would be the correspondence between each beta position in the output and the GEMACO sentence?
May you complete this?
beta1= Intercept (initial state)
beta2= covariate1 slope (initial state)
beta3=...

and for Scenario 2)
IS[i+t*x(1)]
TRANSITION1[f+t(1 7)+[t([2:6;8:13]).[i+t*x(8)]]]

Again I would expect six betas, may you complete this?
beta1= intercept (initial state)
beta2= covariate1 slope (initial state)
beta3= ...
simone77

Posts: 148
Joined: Mon Aug 10, 2009 2:52 pm

### Re: Keeping track of betas

The positions of the beta in the output file are the same than the position of the beta in the IVFV
knowing that:
1) betas for initial states are the first followed by transitions and event.
2) Inside the transitions or events: step 1 are the first followed by step 2), etc
3) fixed parameters are removed.
CHOQUET

Posts: 211
Joined: Thu Nov 24, 2005 4:58 am
Location: CEFE, Montpellier, FRANCE.

### Re: Keeping track of betas

Sorry to revive this post, but I am having difficulty finding out the order of beta parameters for slopes, because there are no clear references in IVFV like for intercept parameters.

Imagine that "group" has three levels, initial state is fixed and that I have the following sentence in the survival step:
group.[i+xind(1,2)]

In this case I am not sure of the order of the slopes. Betas parameters 1-3 are clear, because they show in IVFV:

#1 = intercept for group 1
#2 = intercept for group 2
#3 = intercept for group 3

However, what is the order of betas 4-9? In my view, there are two options.

Option 1:
#4 slope xind1 for group 1
#5 slope xind2 for group 1
#6 slope xind1 for group 2
#7 slope xind2 for group 2
#8 slope xind1 for group 3
#9 slope xind2 for group 3

Option 2:
#4 slope xind1 for group 1
#5 slope xind1 for group 2
#6 slope xind1 for group 3
#7 slope xind2 for group 1
#8 slope xind2 for group 2
#9 slope xind2 for group 3

My guess is for option 1, but I'd like to be sure!

Thank you
wisc88

Posts: 9
Joined: Mon Nov 06, 2017 11:35 am

### Re: Keeping track of betas

This answer comes very late but, as this is a source of confusion for many E-SURGE users, I think it may be useful for others.

I would think the same, that the right answer is your "option 1".
The GEMACO sentence is:
group.[i+xind(1,2)]

Algebraically, in my mind, it corresponds to something like:
group.i + group.xind(1,2)

As a consequence, I would expect that:
alpha1(g1) + alpha2(g2) + alpha3(g3) +
beta4(group1) * xind(1) + beta5(group1) * xind(2) +
beta6(group2)*xind(1) + beta7(group2)*xind(2) +
beta8(group3)*xind(1) + beta9(group3)*xind(2)
where "alpha" refer to the intercepts and "beta" to the slopes, I have followed a sequential numeration to keep track of them in the IVFV.

Also, one might want to so a subset of data exluding some group, repeating the same model with the same GEMACO phrase and compare the beta estimates between the two datasets to confirm who is who.
simone77

Posts: 148
Joined: Mon Aug 10, 2009 2:52 pm