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

Select the method or formula of your choice.

## Marginal fitted value

The marginal 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

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

The standard error of the marginal fitted values in the mixed model depend on the test method for the fixed effects. For both methods, the standard error equals the square root of the variance for the fitted value.

where

where

## Confidence intervals for marginal means

The confidence interval for the marginal mean response at the new setting is: is the marginal fit. is the standard error of the fit.

The degrees of freedom use this formula for the marginal case:

where

## Marginal prediction interval

The marginal prediction interval is: =  = The degrees of freedom use this formula for the marginal case:

where

### Notation

TermDescription
W the asymptotic variance-covariance matrix of the variance component estimates the estimated coefficients for the fixed effect terms the vector of the new settings for the fixed effect terms the vector of the new settings for the random terms the variance component for the ith random effect term
cthe number of random terms in the model
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
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