NONLINEAR MODELS

[steven]

I'd like to fit a quadratic term for age, such that

logit (survival) = 1 +ax +bx^2.

I understand from the manual (page 7-38) that this should be fitted with a design matrix like this


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

assuming that individuals can be up to age n. Is this correct? the reason I ask is that the resulting model does not appear to pick up the nonlinearity in any meaningful way. In other words, the age-specific survivorships estimated separately (with an identity design matrix and not with the "quadratic" design matrix) increase with age, level off, and then decrease, i.e., they have an obvious inverted-U-shaped pattern (on the arithmetic scale). The values fitted with the quadratic function come nowhere close; they look essentially linear (on the arithmetic scale). In addition, the deviances associated with the linear model (logit = = 1 + ax) and the quadratic model (logit = 1 +ax +bx^2) are the same, implying that a quadratic model is not being fit.

any thoughts about this would be helpful.

thanks,
S.

[Bill Kendall]

First, although it's probably a typo, your model is
logit(survival) = c + ax +bx^2.

Other than that, your last column does not represent a square term. It should be

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

[cooch]

I'd like to fit a quadratic term for age, such that

logit (survival) = 1 +ax +bx^2.

I understand from the manual (page 7-38) that this should be fitted with a design matrix like this


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

You're misreading the text. The part you're referring to is simply describing the conceptual structure of linear trend, in general - ordinal values reflecting a constant difference in Y for each step in X. Nothing more.

Look at the example for a simple linear trend on page 7 - 38, and then read the paragraph at the bottom of the page. It describes, in words, exactly what Bill put in his reply.