# 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?

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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