# Methods and formulas for coefficients in Fit Mixed Effects Model

Select the method or formula of your choice.

## Coefficients in mixed models

In matrix terms, the vector of estimated coefficients follows:

For further details on the notation, go to the Methods section.

## Standard errors of the coefficients in mixed models

The standard errors of the coefficients depend on the test method for the fixed effects. For further details on the notation, go to the Methods section and the Tests of Fixed Effects section.

### Kenward-Roger's approximation

The standard errors of the estimated coefficients are the square roots of the dialgonal elements of the matrix .

where

### Satterthwaite Approximation

The standard errors are the square roots of the diagonal elements of the matrix, .

where

## Degrees of freedom for coefficients

The following hypotheses are for the tests of the coefficients:
The following equations give the degrees of freedom for the coefficient: where

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

## Confidence intervals for coefficients

The (1 − α)% confidence limits for the coefficient has the following equation:

### Notation

TermDescription the estimated coefficient the 1 − α/2 percentile from the t distribution with df degrees of freedom the standard error of the estimated coefficient

## T-value

### Notation

TermDescription test statistic for the coefficient  estimated coefficient standard error of the estimated coefficient

## p-value (P)

The following equation gives the two-sided p-value for the null hypothesis that a coefficient equals 0:

### Notation

TermDescription The probability that under the null hypothesis T is less than the absolute value of the calculated . Here, T follows a t-distribution with df degrees of freedom. The t value for the coefficient.
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