# Fixed effect turns insignificant when including random effect - Multilevel

I have a data set from a diary study in which stress was assessed for 30 days. I want to build multilevel regressions (level 1: measurements, level 2: persons) to investigate the effect of different time-variant predictors on stress. I have a level 1 predictor, which I have within-person-centred, and I am reintroducing the respective person-means on level 2. When I estimate a model with only a fixed effect of my predictor, as such:

fit1 <- lme(fixed = stress ~ 1 + predictor_centred + predictor_mean, random = ~ 1 |ID, data = data, method = "REML", na.action=na.exclude)
summary(fit1)

Value  Std.Error   DF   t-value p-value
(Intercept)        1.9348732 0.10978983 2959 17.623428  0.0000
predictor_centred  0.0128509 0.00569165 2959  2.257845  0.0240
predictor_mean    -0.0076657 0.05816799 2959 -0.131785  0.8952


I get a significant effect of the within-person centred predictor and a nonsignificant effect of the person-means. When I add a random effect of my predictor, a likelihood ratio test indicates that there is significant variation in the slope between persons. The fixed effect of my centred predictor turns insignificant. What does this mean/how do I interpret this and what does it mean for model-building? Thank you in advance!

fit2 <- lme(fixed = stress ~ 1 + predictor_centred + predictor_mean, random = ~ 1 + predictor_centred|ID, data = data, method = "REML", na.action=na.exclude)
anova(fit1, fit2)

Model df      AIC      BIC    logLik   Test  L.Ratio p-value
fit1       1  5 7467.134 7497.275 -3728.567
fit2       2  7 7393.375 7435.572 -3689.688 1 vs 2 77.75881  <.0001

summary(fit2)

Value  Std.Error   DF   t-value p-value
(Intercept)       1.934587  0.10980636 2959 17.618166  0.0000
predictor_centred 0.0058862 0.01121010 2959  0.525081  0.5996
predictor_mean    0.0039029 0.05785693 2959  0.067457  0.9462