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 $\delta$?