# Methods and formulas for conditional statistics in Predict for Fit Mixed Effects Model

Select the method or formula of your choice.

## Conditional fitted value

The conditional fitted values are calculated using the following equation:

### Notation

TermDescription the vector of the new settings for the fixed effect terms the estimated coefficients for the fixed effect terms The vector of the new settings for the random terms he BLUP predictions for the random terms

## Standard error of the conditional fitted value (SE Fit)

The standard error of a conditional fitted value equals the square root of the following variance expression.

where

X is the design matrix for the fixed effect terms and Z is the design matrix for the random terms.

## Confidence intervals for conditional means

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:

where
and ### Notation

TermDescription
Wthe asymptotic variance-covariance matrix of For further details on the notation, go to Conditional fits and residuals in Fit Mixed Effects Model.

## Conditional prediction interval

The conditional prediction interval is: is the conditional fit at the new variable setting. =  = The degrees of freedom use this formula for the conditional case:

where

### Notation

TermDescription
W the asymptotic variance-covariance matrix of the variance component estimates
Ithe identity matrix the variance component for the ith random effect term the vector of the new settings for the fixed effect terms the vector of the new settings for the random terms
cthe number of random terms in the model
B C21
G
mithe number of levels for the random effect
Xthe n x p design matrix for the fixed effects terms,  the inverse of the variance-covariance matrix the n x mi design matrix for the random term in the model