The standard error of a conditional fitted value equals the square root of the following variance expression.
X is the design matrix for the fixed effect terms and Z is the design matrix for the random terms.
The range in which the mean response for a given set of predictor values is expected to fall.
is the conditional fit. is the standard error of he fit.
The degrees of freedom use this formula for the conditional case:
For further details on the notation, go to Conditional fits and residuals in Fit Mixed Effects Model.
The conditional prediction interval is:
is the conditional fit at the new variable setting.