Mixed models degrees of freedom

[Whitney Fosco]

I am confused about how SPSS calculates degrees of freedom in the MIXED
procedure. I understand that it uses Satterthwaite approximation, but my level
1 predictors have fewer dfs than my level 2 predictors, which seems backward.
It also is inconsistent with other resources I've read regarding how to
compute degrees of freedom for level 1 and level 2 variables. Does anyone know
the exact formula for how these two levels are approximated in SPSS or why
there would be more dfs for my level 2 predictors than level 1? Thanks for any
help that you can provide!

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[Hart, Kimberly (hartkb)]

I will be out of office until June 14th, with limited access to email. I will respond to your email when I return.

Best, Kim

 

[Ryan]

Whitney,

 

It's generally easier for list members to help when syntax is posted, along with additional details regarding the variables, data, and design.

 

To answer your question, there is no simple formula to calculate df using Satterwhaite's approximation in a linear mixed model. The simple formula [that is not based on the Satter's approx.] for calculating df for level-2 predictors regression coefficients is:

 

df = N_level_2 - k -1

 

where

 

N_level_2 = number of level-2 groups

k = number of level-2 predictors

 

Usually, the df produced by SPSS for  regression coefficients of level-2 predictors are relatively close to the df produced by the formula above.

 

There is a scenario under which df for a level-1 regression coefficient will be based on the number of level-2 groups...If level-1 slopes are permitted to vary across level-2 groups, that is, treated as "random," then the sample size will based on the number of level-2 groups. Factoring in Satter's approx. can lead to the situation you describe.

 

Ryan

On Wed, Jun 19, 2013 at 1:33 PM, Whitney Fosco <[hidden email]> wrote:

I am confused about how SPSS calculates degrees of freedom in the MIXED
procedure. I understand that it uses Satterthwaite approximation, but my level
1 predictors have fewer dfs than my level 2 predictors, which seems backward.
It also is inconsistent with other resources I've read regarding how to
compute degrees of freedom for level 1 and level 2 variables. Does anyone know
the exact formula for how these two levels are approximated in SPSS or why
there would be more dfs for my level 2 predictors than level 1? Thanks for any
help that you can provide!

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD