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Given the model, $\log(A_i) = \alpha + \beta \, covar_i$, with $i=1,\dots,1000$, $\alpha=4$, $\beta=0.2$, and covariate $covar \sim U(-1,1)$, I derived $\log(A)$ values (in $\texttt{R}$) as:

alpha <- 4; beta <- 0.2; ni <- 1000
covar <- runif(ni, -1.0, 1.0)
log_A <- alpha + beta * covar

Now, I want to derive intercept ($\gamma$) and slope ($\delta$) of the following model, by using the information I have from the first model:

$\text{logit}(A_i/400) = \gamma+ \delta \, covar_i$.

Please note that the two models differ from the link function (log and logit link respectively) and the scaled response variable.

Is the following relationship correct? $\gamma = \text{logit}(\exp(\alpha) \, 400))$.

How can I derive $\delta$?

Simon74
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  • None of your models have error terms. Are you running regressions (i.e OLS and logit) and estimating parameters that fit the data best or are you saying there are actual true values of alpha, beta,...) – Greg Mar 10 '15 at 17:37
  • Edit: I guess that might have been a dumb question since we're in the regression tab :-). – Greg Mar 10 '15 at 19:32
  • Thanks Greg. The values reported correspond to truth. I'm simulating data and in a next step (not shown) I consider stocasticity by drawing values from the expectation $A$. I am still not able to derive the intercept and slope of the second model. Thanks again. – Simon74 Mar 10 '15 at 20:58

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