In my data, the RT (gaze) of individuals (ID) is examined as a function of a visual conditions, the factor size (small, medium, large).

Base model:

`print(Base <- lmer(RT ~ Size + (1|ID), data=rt), cor=F) `

Random effect:

`print(NoCor <- lmer(RT ~ Size + (0+Size|ID) , data=rt)) print(WithCor <- lmer(RT ~ Size + (1+Size|ID), data=rt)) `

Addition of ID slopes improves the Base model. My question is, how can a significant random effect (Size/ID) be interpreted when there is no relationship between the random and fixed effect, i.e., when the correlation between the random factor and the fixed facor does not improve the model [the anova(NoCr, WithCor) does not show a significant improvement]?

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#### Best Answer

First, you should compare models from lmer after fitting with ML (maximum likelihood) since the default is REML. So something like:

`fit.nc <- update(NoCor, REML=FALSE) fit.wc <- udpate(WithCor, REML=FALSE) anova(fit.nc, fit.wc) `

It would help to see the output of the random effects variation from your fits. For example, to answer: is there a strong correlation between the intercept and slope and what are the variation sizes?

If you find that the random slope only model (NoCor) provides the best fit, then this means that the Size variable has a different effect between groups (depending on the variation). But the no intercept implies that the mean response at some zero level (baseline for your factor Size) is the same across all groups.

A random slope only model is not as common unless informed by theory — usually we assume baseline variation between groups (random intercept) and then let effects (slope) vary as well. If you don't think there's a good reason to accept the slope-only model, then you may want to keep the random intercept & slope model since it may conform better to theory.

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