stratum-specific linear and nonlinear models

[steven]

I'd like someone to clarify the proper way to fit stratum-specific age trends. assume that individuals can be up to age n and that there are 2 strata.

An overall (all strata) linear model would be, say,

1 1
1 2
1 3
. .
1 n

Would a stratum-specific linear model be

1 1 0
1 2 0
1 3 0
. . .
1 n 0
1 0 1
1 0 2
1 0 3
. . .
1 0 n


OR

1 1 0
1 2 0
1 3 0
. . .
1 n 0
1 0 n+1
1 0 n+2
1 0 n+3
. . .
1 0 2n


These give different answers (both regression coefficients and deviances).

Similarily for a stratum-specific quadratic analysis, does one fit

1 1 1 0
1 2 4 0
1 3 9 0
. . . .
1 n n^2 0
1 1 0 1
1 2 0 4
1 3 0 9
. . . .
1 n 0 n^2

OR

1 1 1 0
1 2 4 0
1 3 9 0
. . . .
1 n n^2 0
1 n+1 0 (n+1)^2
1 n+2 0 (n+2)^2
1 n+3 0 (n+3)^2
. . . .
1 2n 0 (2n)^2

Many thanks for your help!

[ganghis]

Go for the first approach you outline IF you want the regression intercept to be the same for each strata. If not, use

1 1 0 0
1 2 0 0
. . . .
1 n 0 0
0 0 1 1
0 0 1 2
. . . .
0 0 1 n

Or, look more at additive models if you want to consider a model where
there are parallel models for each strata (on the logit scale).

The second DM you outline doesn't make much sense.

Paul