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Say I have the following output:

Fixed effects:
  intercept: Estimate = 50
  X1: Estimate = 20
  X2: Estimate = -10

Random effects: 
  intercept: Variance = 16, SD=4
  X1: Variance = 9, SD = 3 Corr = -.5
  X2: Variance = 4, SD = 2 Corr = .5
Residual Variance = 4

In interpreting this, can I say that a one standard deviation increase in the intercept yields a half standard deviation decrease in the slope with respect to X1? For example, if obs 1's intercept is 58 (2 SD's above the mean) then the slope estimate with respect to X1 is 17 (i.e. 20 -(2 X -.5 X 3)). Is that a correct interpretation of the change in estimates?

where SD = standard deviation and Corr = correlation between the random effect and intercept

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I don't think so. It sounds like you're interpreting your random-effects structure as if there's a dependency between the random slopes and the random intercept, but without seeing your model, I would guess that it postulates that these are independent, because to do otherwise would be unusual.

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  • $\begingroup$ I should specify that the corr value is the correlation between the intercept and random slope $\endgroup$ – JWH2006 Feb 14 '17 at 18:21
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    $\begingroup$ @JWH2006 It would help to specify the full model. $\endgroup$ – Kodiologist Feb 14 '17 at 19:06

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