# What does a p-value of exactly 0 mean - lme (nlme) function fixed effects

Using the nlme package in R, I ran a multilevel regression model model with a random intercept and a fixed linear effect of time with REML estimation:

lme(fixed = outcome ~ 1 + day, random = ~ 1 | ID, data = data, method = "REML", na.action = na.exclude)

The p-values for the fixed effects are exactly 0 - not 0.0000 as I've seen before. Does this indicate that something is wrong with my model?

## 1 Answer

Without seeing the data and the model it is hard to be absolutely sure, but I would think that it just means that the p value is extremely small. We can do a simulation to show this quite easily:

N <- 1000
group <- rep(c(1,2,3,4,5,6,7,8,9,10),100)
x <- seq(1:N)
y <- rnorm(N, 100, 1) + x + group/10

group <- as.factor(group)
lmm.lme <- lme(fixed = y ~ x, random = ~ 1 | group)
summary(lmm.lme)


which gives:

Fixed effects: y ~ x
Value  Std.Error  DF  t-value p-value
(Intercept) 100.56748 0.11300572 989  889.933       0
x             0.99998 0.00010884 989 9187.745       0


A lot of other functions show <2e-16 for such p values, but not lme apparently.

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