If the model has multiple random effects, I'm not sure the standard deviations would be very meaningful. You could take, e.g., the standard deviations of all the data points in a given 'cell' of the design (assuming that your independent variables are all categorical), but this will be ignoring related clusters of data (e.g., subjects or items). A mixed effect model provides standard errors for the marginal means (at least, it does in R; I assume it also does in SPSS); normally you would be able to convert a standard error to a standard deviation by multiplying it by √N, but I am not sure if the appropriate N for a mixed-effect model is known (for the same reason that the appropriate degrees of freedom for a t-test of mixed-effect model coefficients is not known).

Hi Stephen,

Thank you for your input. I found some source suggesting to use the square root of the sum of covariance parameters (residual and intercept) as denominator, however, the pooled SD then differs from the 'classical' approach to derive the SD from the SE. Currently, I favor calculating the SD from the SE of the estimated marginal means for the pooled SD. At least, this is more transparent and straight forward.