I am looking to obtain parameter estimates for one predictor when constraining another predictors to specific values in a negative binomial glm in order to better explain an interaction effect.
My model is something like this:
model <- glm.nb(outcome ~ IV * moderator + covariate1 + covariate2)
Because the IV:moderator term is significant, I would like to obtain parameter estimates for IV at specific values of moderator (i.e., at +1 and -1 SD). I can obtain slope estimates for IV at various levels of moderator using the visreg package but I don't know how to estimate SEs and test statistics. moderator is a continuous variable so I can't use the multcomp package and other packages designed for finding simple slopes (e.g., pequod and QuantPsyc) are incompatible with negative binomial regression. Thanks!
If you want to constrain one of the values in your regression, consider taking that variable out of the model and adding it in as an offset. For example with the sample data.
dd<-data.frame(
x1=runif(50),
x2=runif(50)
)
dd<-transform(dd,
y=5*x1-2*x2+3+rnorm(50)
)
We can run a model with both x1 and x2 as parameters
lm(y ~ x1 + x2,dd)
# Call:
# lm(formula = y ~ x1 + x2, data = dd)
#
# Coefficients:
# (Intercept) x1 x2
# 3.438438 4.135162 -2.154770
Or say that we know that the coefficient of x2 is -2. Then we can not estimate x2 but put that term in as an offset
lm(y ~ x1 + offset(-2*x2), dd)
# Call:
# lm(formula = y ~ x1 + offset(-2 * x2), data = dd)
#
# Coefficients:
# (Intercept) x1
# 3.347531 4.153594
The offset() option basically just create a covariate who's coefficient is always 1. Even though I've demonstrated with lm, this same method should work for glm.nb and many other regression models.