Assuming that you're using glm()
, which is the standard/most-used tool for fitting Poisson regressions in R: the $p$-values in the table printed by summary()
are so-called Wald p-values, which make a specific assumption about the sampling distribution of the parameter estimates (specifically that they are [multivariate] Normal, or equivalently that the log-likelihood surface is quadratic). The $p$-values that you get from a likelihood ratio test (e.g., with anova(full_model, restricted_model)
where restricted_model
omits the focal parameter, or drop1(full_model)
) also makes an assumption (that 2 x the log-likelihood difference between the models follows a chi-squared distribution when the null hypothesis is true), but the LRT assumption is much weaker than the one assumed by the Wald p-values, so the LRT $p$-values are in general more accurate.
As a side note, your statement that "... this variable is significant and should be included ..." makes me a bit nervous, as it suggests that you are using hypothesis testing to decide on the structure of your final model, which may be problematic (see this answer) ...
As an example from UCLA OARC:
p <- read.csv("https://stats.idre.ucla.edu/stat/data/poisson_sim.csv")
p <- within(p, {
prog <- factor(prog, levels=1:3, labels=c("General", "Academic",
"Vocational"))
id <- factor(id)
})
m1 <- glm(num_awards ~ prog + math, family="poisson", data=p)
Wald (summary())
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.24712 0.65845 -7.969 1.60e-15 ***
progAcademic 1.08386 0.35825 3.025 0.00248 **
progVocational 0.36981 0.44107 0.838 0.40179
math 0.07015 0.01060 6.619 3.63e-11 ***
LRT (drop1)
drop1(m1, test= "Chisq")
Single term deletions
Model:
num_awards ~ prog + math
Df Deviance AIC LRT Pr(>Chi)
<none> 189.45 373.50
prog 2 204.02 384.08 14.572 0.0006852 ***
math 1 234.46 416.51 45.010 1.96e-11 ***
You'll note a few differences here ...