Lognormal linear regression

Question

I would like to fit a linear regression model with a lognormal distribution that has a linear expectation in the $X$, $Y$ space. So, I need a model with the following properties:

$$ Y|X \sim Lognormal $$ $$ E[Y|X] = X*β^T $$

Can you offer any suggestions? Thank you in advance.

Answer 1

If you're looking for a software to fit this model, you can use R with the logNormReg package. Example:

library(logNormReg)

# covariate
x <- 1:100
# "conditional mean" of the response
mu <- 50 + 2*x
# standard deviation of log(response)
s <- 0.4
# simulate the response
y <- rlnorm(100, log(mu)-s^2/2, s)

# fit the lognormal regression model
lognlm(y ~ x)

If you're look for mathematical details, look at the references given in the above link.