Methods and formulas for conditional fits and residuals in Fit Mixed Effects Model

The conditional fitted values are calculated using the following equation:

For further details on the notation, see the Methods section, the Test of Fixed Effects Section, and the Random Effect Predictions section.

The standard errors of the conditional fitted values are the square roots of the diagonal elements of the following matrix:

where

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

Term	Description
W	the asymptotic variance-covariance matrix of

For further details on the notation, go to the Methods section and the Test of Fixed Effects section.

A residual is the difference between an observed value and a fitted value. This part of the observation is not explained by the fitted model.

The conditional residual is calculated by the following expression:

Notation

Term	Description
yi	the response value
	the conditional fitted value

Standardized residuals are also called "internally Studentized residuals."

where the standard deviation of the residual is the appropriate diagonal square root of the residual variance matrix:

where

Notation

Term	Description
ei	the residual
Std(ei)	the standard deviation of the residual