GEE correlation matrix

[spssdummy]

Hey, I'm doing analyses with binary logistic GEE. I was wondering if using
"independent" as working correlation structure takes into account the
repeated measurements in the data or if this would be the same as using
normal logistic regression and ignoring the fact that there are repeated
measurements. (My goal is to correct for repeated measurements but I have no
assumption regarding the correlation).

Thanks!



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[Jon Peck]

From the dialog box help...

Working Correlation Matrix. This correlation matrix represents the within-subject dependencies. Its size is determined by the number of measurements and thus the combination of values of within-subject variables. You can specify one of the following structures:

• Independent. Repeated measurements are uncorrelated.
• AR(1). Repeated measurements have a first-order autoregressive relationship. The correlation between any two elements is equal to rho for adjacent elements, rho2 for elements that are separated by a third, and so on. is constrained so that –1<<1.
• Exchangeable. This structure has homogenous correlations between elements. It is also known as a compound symmetry structure.
• M-dependent. Consecutive measurements have a common correlation coefficient, pairs of measurements separated by a third have a common correlation coefficient, and so on, through pairs of measurements separated by m−1 other measurements. For example, if you give students standardized tests each year from 3rd through 7th grade. This structure assumes that the 3rd and 4th, 4th and 5th, 5th and 6th, and 6th and 7th grade scores will have the same correlation; 3rd and 5th, 4th and 6th, and 5th and 7th will have the same correlation; 3rd and 6th and 4th and 7th will have the same correlation. Measurements with separaration greater than m are assumed to be uncorrelated. When choosing this structure, specify a value of m less than the order of the working correlation matrix.
• Unstructured. This is a completely general correlation matrix.

On Mon, Dec 7, 2020 at 6:16 AM spssdummy <[hidden email]> wrote:

Hey, I'm doing analyses with binary logistic GEE. I was wondering if using
"independent" as working correlation structure takes into account the
repeated measurements in the data or if this would be the same as using
normal logistic regression and ignoring the fact that there are repeated
measurements. (My goal is to correct for repeated measurements but I have no
assumption regarding the correlation).

Thanks!



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[spssdummy]

Thanks Jon:) However, I read through this before already and I'm still not
sure about my question and what choosing for 'independent' actually implies!



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[Jon Peck]

All I can suggest is that you work through the GENLIN topic in the Algorithms doc.

On Mon, Dec 7, 2020 at 8:22 AM spssdummy <[hidden email]> wrote:

Thanks Jon:) However, I read through this before already and I'm still not
sure about my question and what choosing for 'independent' actually implies!



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Jon K Peck
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[Bruce Weaver]

Alternatively, you can try it and see what happens.  I would work out an
example in SPSS if I had more time.  But in all honesty, I find the code for
estimating models with GEE much simpler in Stata, and therefore, was able to
whip up this example quite quickly.  

To make things line up properly, you'll have to change the font to a fixed
font such as Courier.  (You may have to copy & paste into a text editor or
word processor.)  

Compare the coefficients, SEs, z- and p-values and 95% CIs for Models 2 and
3.  They are the same (to 3 decimals, at least).  Model 2 was estimated
using the -xtgee- command but with the corr(independent) option.  Model 3
was estimated with the -logit- command, one of the commands that can be used
to estimate ordinary binary logit models.  

HTH.


. * Use a variation on the example shown here:
. * https://www.stata.com/features/generalized-estimating-equations/
. clear

. webuse nlswork
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. * Use logit link function rather than probit
. * Model 1:  GEE with corr(exchangeable)
. xtgee union age not_smsa, i(idcode) ///
> family(binomial) link(logit) corr(exchangeable)

Iteration 1: tolerance = .08812485
Iteration 2: tolerance = .00597886
Iteration 3: tolerance = .00022492
Iteration 4: tolerance = 7.966e-06
Iteration 5: tolerance = 2.747e-07

GEE population-averaged model                   Number of obs     =    
19,226
Group variable:                     idcode      Number of groups  =    
4,150
Link:                                logit      Obs per group:
Family:                           binomial                    min =        
1
Correlation:                  exchangeable                    avg =      
4.6
                                                              max =        
12
                                                Wald chi2(2)      =    
29.83
Scale parameter:                         1      Prob > chi2       =    
0.0000

------------------------------------------------------------------------------
       union |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
         age |      0.008      0.002    3.259   0.0011        0.003      
0.013
    not_smsa |     -0.250      0.056   -4.482   0.0000       -0.360    
-0.141
       _cons |     -1.446      0.083  -17.404   0.0000       -1.609    
-1.284
------------------------------------------------------------------------------

. * Model 2:  GEE with corr(independent)
. xtgee union age not_smsa, i(idcode) ///
> family(binomial) link(logit) corr(independent)

Iteration 1: tolerance = 4.743e-09

GEE population-averaged model                   Number of obs     =    
19,226
Group variable:                     idcode      Number of groups  =    
4,150
Link:                                logit      Obs per group:
Family:                           binomial                    min =        
1
Correlation:                   independent                    avg =      
4.6
                                                              max =        
12
                                                Wald chi2(2)      =    
102.32
Scale parameter:                         1      Prob > chi2       =    
0.0000

Pearson chi2(19226):              19227.17      Deviance          =  
20828.88
Dispersion (Pearson):             1.000061      Dispersion        =  
1.08337

------------------------------------------------------------------------------
       union |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
         age |      0.010      0.003    3.726   0.0002        0.005      
0.016
    not_smsa |     -0.380      0.040   -9.522   0.0000       -0.458    
-0.301
       _cons |     -1.409      0.089  -15.804   0.0000       -1.583    
-1.234
------------------------------------------------------------------------------

. * Model 3:  An ordinary logit model
. logit union age not_smsa

Iteration 0:   log likelihood = -10467.433  
Iteration 1:   log likelihood = -10414.653  
Iteration 2:   log likelihood =  -10414.44  
Iteration 3:   log likelihood =  -10414.44  

Logistic regression                             Number of obs     =    
19,226
                                                LR chi2(2)        =    
105.99
                                                Prob > chi2       =    
0.0000
Log likelihood =  -10414.44                     Pseudo R2         =    
0.0051

------------------------------------------------------------------------------
       union |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
         age |      0.010      0.003    3.726   0.0002        0.005      
0.016
    not_smsa |     -0.380      0.040   -9.522   0.0000       -0.458    
-0.301
       _cons |     -1.409      0.089  -15.804   0.0000       -1.583    
-1.234
------------------------------------------------------------------------------

.
end of do-file


Here is the code, in case anyone wants it.

* Use a variation on the example shown here:
* https://www.stata.com/features/generalized-estimating-equations/
clear
webuse nlswork
* Use logit link function rather than probit
* Model 1:  GEE with corr(exchangeable)
xtgee union age not_smsa, i(idcode) ///
family(binomial) link(logit) corr(exchangeable)
* Model 2:  GEE with corr(independent)
xtgee union age not_smsa, i(idcode) ///
family(binomial) link(logit) corr(independent)
* Model 3:  An ordinary logit model
logit union age not_smsa


spssdummy wrote

> Thanks Jon:) However, I read through this before already and I'm still not
> sure about my question and what choosing for 'independent' actually
> implies!
>
>
>
> --
> Sent from: http://spssx-discussion.1045642.n5.nabble.com/
>
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> To manage your subscription to SPSSX-L, send a message to

> LISTSERV@.UGA

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Bruce Weaver
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"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
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