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It seems wise to usually include random slopes in addition to the fixed slopes for lower level predictors as described in some previous questions:

When should I *not* permit a fixed effect to vary across levels of a random effect in a mixed effects model?

Varying group coefficients in lme4

My question is interpretation of the significance of the fixed effect when it is highly significant without letting the slopes vary but loses significance when the slopes do vary.

This predictor is obviously important but is it only important for certain upper level effects and should not be generalized to the population of interest?

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