SPSSX Discussion

Response to "unequal variances" post

classic Classic list List threaded Threaded
♦
♦
 3 messages Options
Ryan
Reply | Threaded
Open this post in threaded view
♦
♦
|

Response to "unequal variances" post

Ryan
SPSS-L,
 
 
The purpose of this post is to demonstrate how one would fit group-speccific covariance structures in a linear mixed model...
 
 
When dealing with repeated measures, we assume that observations made by the same subject are correlated. Within a linear mixed modeling framework, we would usually account for this dependency by adding a REPEATED statement, along with the appropriate subject identification variable [so the procedure knows which observations should be permitted to be correlated].
 
 
With only two levels of a within-subjects variable, we would normally be comfortable specifying a compound symmetric covariance structure for the error matrix, as follows:
 
             Subject=1    Subject=2  ...
             ---------    ---------
             t1    t2     t1    t2   ...
        -                                -
  Cov = | V1+V2    V2     0     0    ... |
        |    V2 V1+V2     0     0    ... |
        |     0     0   V1+V2  V2    ... |
        |     0     0   V2    V1+V2  ... |
        |   ...   ...   ...   ...    ... |
        -                                -
 
The covariance structure above assumes that the same error variance and covariance apply to all subjects.
 
 
However, if the elements of the compound symmetric covariance structure vary across 2 groups, assuming 100 subjects per group, for example, then we would have:
 
 
               Group=1                  Group=2
         ----------------------- --------------------------------
subject      1      2       100    101    102         200
       -                                                          -
 Cov = | block1    [0]  ...    [0]    [0]    [0]  ...    [0]  ... |
       |    [0] block1  ...    [0]    [0]    [0]  ...    [0]  ... |
       |    ...    ...  ...    ...    ...    ...  ...    ...  ... |
       |    [0]    [0]  ... block1    [0]    [0]  ...    [0]  ... |
       |    [0]    [0]  ...    [0] block2    [0]  ...    [0]  ... |
       |    [0]    [0]  ...    [0]    [0] block2  ...    [0]  ... |
       |    ...    ...  ...    ...    ...    ...  ...    ...  ... |
       |    [0]    [0]  ...    [0]    [0]    [0]  ... block2  ... |
       |    ...    ...  ...    ...    ...    ...  ...    ...  ... |
       -                                                          -
 
where
 
            -                -
   block1 = | V11+V12     V12|
            |     V12 V11+V12|
            -                -

            -                -
   block2 = | V21+V22     V22|
            |     V22 V21+V22|
            -                -

and
            -       -
      [0] = |0     0|
            |0     0|
            -       -
 
 
How would we fit a linear mixed model in SPSS that conforms to the covariance structure of the error matrix in which group-specific independent blocks are incorporated?
 
 
One way would be to employ the GENLINMIXED procedure as follows:
 

GENLINMIXED
 /DATA_STRUCTURE SUBJECTS=subject REPEATED_MEASURES=<Ws variable> GROUPING=group COVARIANCE_TYPE=COMPOUND_SYMMETRY
 /FIELDS TARGET=y
 /TARGET_OPTIONS DISTRIBUTION=NORMAL LINK=IDENTITY
 /FIXED EFFECTS=group <Ws variable> group*<Ws variable> USE_INTERCEPT=TRUE.
 
The GROUPING keyword produces group-specific independent blocks discussed previously. This keyword is not available in the MIXED procedure, which is why I resorted to the GENLINMIXED procedure.
 
 
Ryan
 
Ryan
Reply | Threaded
Open this post in threaded view
♦
♦
|

Re: Response to "unequal variances" post

Ryan
SPSS-L,
 
 
I received a couple of comments off-list that there was difficulty reading the entire message I posted recently. For those having difficulty reading a message I have posted to SPSS-L, I suggest searching the SPSS-L archives. My most recent post resides here:

Also, I was asked off-list to provide an explanation of how the dataset needs to be structured to successfully run the GENLINMIXED code I provided in the previous post.

Answer: It is no different than how one would construct a dataset in long (a.k.a vertical) form for any mixed model.

Ryan

 
On Wed, Jun 5, 2013 at 9:58 PM, Ryan Black <[hidden email]> wrote:
SPSS-L,
 
 
The purpose of this post is to demonstrate how one would fit group-speccific covariance structures in a linear mixed model...
 
 
When dealing with repeated measures, we assume that observations made by the same subject are correlated. Within a linear mixed modeling framework, we would usually account for this dependency by adding a REPEATED statement, along with the appropriate subject identification variable [so the procedure knows which observations should be permitted to be correlated].
 
 
With only two levels of a within-subjects variable, we would normally be comfortable specifying a compound symmetric covariance structure for the error matrix, as follows:
 
             Subject=1    Subject=2  ...
             ---------    ---------
             t1    t2     t1    t2   ...
        -                                -
  Cov = | V1+V2    V2     0     0    ... |
        |    V2 V1+V2     0     0    ... |
        |     0     0   V1+V2  V2    ... |
        |     0     0   V2    V1+V2  ... |
        |   ...   ...   ...   ...    ... |
        -                                -
 
The covariance structure above assumes that the same error variance and covariance apply to all subjects.
 
 
However, if the elements of the compound symmetric covariance structure vary across 2 groups, assuming 100 subjects per group, for example, then we would have:
 
 
               Group=1                  Group=2
         ----------------------- --------------------------------
subject      1      2       100    101    102         200
       -                                                          -
 Cov = | block1    [0]  ...    [0]    [0]    [0]  ...    [0]  ... |
       |    [0] block1  ...    [0]    [0]    [0]  ...    [0]  ... |
       |    ...    ...  ...    ...    ...    ...  ...    ...  ... |
       |    [0]    [0]  ... block1    [0]    [0]  ...    [0]  ... |
       |    [0]    [0]  ...    [0] block2    [0]  ...    [0]  ... |
       |    [0]    [0]  ...    [0]    [0] block2  ...    [0]  ... |
       |    ...    ...  ...    ...    ...    ...  ...    ...  ... |
       |    [0]    [0]  ...    [0]    [0]    [0]  ... block2  ... |
       |    ...    ...  ...    ...    ...    ...  ...    ...  ... |
       -                                                          -
 
where
 
            -                -
   block1 = | V11+V12     V12|
            |     V12 V11+V12|
            -                -

            -                -
   block2 = | V21+V22     V22|
            |     V22 V21+V22|
            -                -

and
            -       -
      [0] = |0     0|
            |0     0|
            -       -
 
 
How would we fit a linear mixed model in SPSS that conforms to the covariance structure of the error matrix in which group-specific independent blocks are incorporated?
 
 
One way would be to employ the GENLINMIXED procedure as follows:
 

GENLINMIXED
 /DATA_STRUCTURE SUBJECTS=subject REPEATED_MEASURES=<Ws variable> GROUPING=group COVARIANCE_TYPE=COMPOUND_SYMMETRY
 /FIELDS TARGET=y
 /TARGET_OPTIONS DISTRIBUTION=NORMAL LINK=IDENTITY
 /FIXED EFFECTS=group <Ws variable> group*<Ws variable> USE_INTERCEPT=TRUE.
 
The GROUPING keyword produces group-specific independent blocks discussed previously. This keyword is not available in the MIXED procedure, which is why I resorted to the GENLINMIXED procedure.
 
 
Ryan
 
John McConnell-2
Reply | Threaded
Open this post in threaded view
♦
♦
|

Automatic reply: Response to "unequal variances" post

John McConnell-2

Hi

 

I'll be out of the office today - - Thursday 6 June.

 

I will check mail intermittently and get back to you as soon as i can

 

Thanks

John

 

 

 
Free forum by Nabble Edit this page