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

Select the method or formula of your choice.

Marginal fitted value

The predicted y or ; the mean response value for the given the values of the fixed factors, and covariates using the marginal fitted equation. The marginal equation does not include coefficients for any random factors.

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

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 errors are the square roots of the diagonal elements of the variance matrix of the fits.

Kenward-Roger's method


Satterthwaites approximation


Confidence intervals for marginal means

The confidence interval for the marginal mean response is calculated using the following expression:

is the marginal fit. is the standard error of the fit.

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



the row of the X matrix

Marginal residuals

The marginal residual is calculated by the following expression:


yithe response value
the marginal fitted value

Standardized residuals

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:



eithe ith residual
Std(ei)the standard deviation of the ith residual

Leverages (Hi) for marginal data

The leverage matrix has the following form:

The Hi column displays the diagonal elements of H.