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Mixed model ANOVA degrees of freedom

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Mixed model ANOVA degrees of freedom

Kambiz
Typically when reporting test results from a GLM I use  the format
(F(df_factor_term,df_error_term)=F-stat, p=p-value), i.e.,
(F(n,n-1)=statistic,p=pvalue). My question is what is the equivalent
format for a reporting results from a linear mixed model. For example
if I have a fixed effect for term X SPSS outputs numerator and
denominator degrees of freedom(df), I am assuming that
F(df_numerator,df_denominator) is equivalent to
F(df_factor_term,df_error_term), and in both instances the
significance level for the F is from the F distribution with the
degrees of freedom for the numerator and denominator mean squares. If
that is correct, why does the denominator df in the mixed model not
take on the value of n-1(or some constant, where n=number of factor
levels)? Thanks in advance for your comments.

--
-K.
------------------------------------------------------------
Kambiz Tavabi PhD
Biomedical Imaging Laboratory
The Children's Hospital of Philadelphia
34th Street and Civic Center Boulevard
Philadelphia, Pa. 19104
Tel: 267.426.0302
------------------------------------------------------------

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Re: Mixed model ANOVA degrees of freedom

Alex Reutter

The denominator df are computed using Satterthwaite's approximation.  More details are in the MIXED algorithms documentation (Help > Algorithms).

Alex


From: Kambiz <[hidden email]>
To: [hidden email]
Date: 07/22/2010 06:33 PM
Subject: Mixed model ANOVA degrees of freedom
Sent by: "SPSSX(r) Discussion" <[hidden email]>





Typically when reporting test results from a GLM I use  the format
(F(df_factor_term,df_error_term)=F-stat, p=p-value), i.e.,
(F(n,n-1)=statistic,p=pvalue). My question is what is the equivalent
format for a reporting results from a linear mixed model. For example
if I have a fixed effect for term X SPSS outputs numerator and
denominator degrees of freedom(df), I am assuming that
F(df_numerator,df_denominator) is equivalent to
F(df_factor_term,df_error_term), and in both instances the
significance level for the F is from the F distribution with the
degrees of freedom for the numerator and denominator mean squares. If
that is correct, why does the denominator df in the mixed model not
take on the value of n-1(or some constant, where n=number of factor
levels)? Thanks in advance for your comments.

--
-K.

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Re: Mixed model ANOVA degrees of freedom

Kambiz
In reply to this post by Kambiz
Thanks Alex. So is it safe to say that the mixed model, and how the df (apparently related to a covariance matrix) is computed, is a non-parametric alternative to the GLM? Such that there is no assumption that the underlying population variances are equally distributed.And so the denominator value is the effective df for the chi-squre distribution of the linear combination of sample variances? I am just trying to put in words the equations in the algorithm.
 
----- Original Message -----
Sent: Friday, July 23, 2010 12:17 PM
Subject: Re: Mixed model ANOVA degrees of freedom


The denominator df are computed using Satterthwaite's approximation.  More details are in the MIXED algorithms documentation (Help > Algorithms).

Alex


From: Kambiz <[hidden email]>
To: [hidden email]
Date: 07/22/2010 06:33 PM
Subject: Mixed model ANOVA degrees of freedom
Sent by: "SPSSX(r) Discussion" <[hidden email]>





Typically when reporting test results from a GLM I use  the format
(F(df_factor_term,df_error_term)=F-stat, p=p-value), i.e.,
(F(n,n-1)=statistic,p=pvalue). My question is what is the equivalent
format for a reporting results from a linear mixed model. For example
if I have a fixed effect for term X SPSS outputs numerator and
denominator degrees of freedom(df), I am assuming that
F(df_numerator,df_denominator) is equivalent to
F(df_factor_term,df_error_term), and in both instances the
significance level for the F is from the F distribution with the
degrees of freedom for the numerator and denominator mean squares. If
that is correct, why does the denominator df in the mixed model not
take on the value of n-1(or some constant, where n=number of factor
levels)? Thanks in advance for your comments.

--
-K.

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Re: Mixed model ANOVA degrees of freedom

Alex Reutter

Satterthwaite is not a nonparametric method, but it is robust under unequal variances... however, I would think it would be better to incorporate the heteroscedastic variances directly into the model.  In a really simple scenario, look at the salesperformance.sav dataset that ships with the product and run the following syntax.  The first MIXED command fits a model that assumes equal variances across the categories of the grouping variable, while the second MIXED command fits a separate residual variance parameter for each group.

COMPUTE case = $casenum.

MIXED perform BY group
  /FIXED=group
  /PRINT=R SOLUTION TESTCOV.

MIXED perform BY group
  /FIXED=group
  /PRINT=R SOLUTION TESTCOV
  /REPEATED=group | SUBJECT(case) COVTYPE(DIAG).

Alex



From: Kambiz <[hidden email]>
To: [hidden email]
Date: 07/24/2010 08:00 PM
Subject: Re: Mixed model ANOVA degrees of freedom
Sent by: "SPSSX(r) Discussion" <[hidden email]>





Thanks Alex. So is it safe to say that the mixed model, and how the df (apparently related to a covariance matrix) is computed, is a non-parametric alternative to the GLM? Such that there is no assumption that the underlying population variances are equally distributed.And so the denominator value is the effective df for the chi-squre distribution of the linear combination of sample variances? I am just trying to put in words the equations in the algorithm.
 
----- Original Message -----
From: Alex Reutter
Sent: Friday, July 23, 2010 12:17 PM
Subject: Re: Mixed model ANOVA degrees of freedom


The denominator df are computed using Satterthwaite's approximation.  More details are in the MIXED algorithms documentation (Help > Algorithms).


Alex


From: Kambiz <ktavabi@...>
To: [hidden email]
Date: 07/22/2010 06:33 PM
Subject: Mixed model ANOVA degrees of freedom
Sent by: "SPSSX(r) Discussion" <[hidden email]>






Typically when reporting test results from a GLM I use  the format
(F(df_factor_term,df_error_term)=F-stat, p=p-value), i.e.,
(F(n,n-1)=statistic,p=pvalue). My question is what is the equivalent
format for a reporting results from a linear mixed model. For example
if I have a fixed effect for term X SPSS outputs numerator and
denominator degrees of freedom(df), I am assuming that
F(df_numerator,df_denominator) is equivalent to
F(df_factor_term,df_error_term), and in both instances the
significance level for the F is from the F distribution with the
degrees of freedom for the numerator and denominator mean squares. If
that is correct, why does the denominator df in the mixed model not
take on the value of n-1(or some constant, where n=number of factor
levels)? Thanks in advance for your comments.

--
-K.


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