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lmer versus glm results

5 messages · Thomas Levine, Yuqing Ren, John Maindonald

Original
Yuqing Ren
# 
Dear All,

I have a quick questions about comparing results from lmer and from
glm. We are running analysis to predict a person's likelihood of
leaving a project with some people affiliated with multiple projects
(binary outcome and crossed random effects).

The data consist of three levels: projects, members (crossed with
projects with 70% members with one project and 30% with multiple
projects), and time series nested within individuals. I ran the
analysis with first glm (family=binomial) and then lmer
(family-binomial and + (1 | projectid) + (1 | memberid) to account for
the random effects). The two analyses have the same covariates:
project size and scope and some individual member attributes such as
tenure and past performance.

Theoretically, I expect the coefficients to be similar between the two
results with some differences in the significance test or confidence
intervals. However, I found three coefficients flipped signs between
the two, which is very puzzling. I ran another set of analysis with a
continuous dependent variable (quantity of work completed) and found
similar coefficients between the two (results from lm and lmer).

So my question is: should we expect the results from glm and lmer to
be similar? If we should see different results, is it because of the
distribution being binomial rather than normal or other reasons? Which
set of results is more reliable and should be included in our paper?

Thanks very much.

Ching Ren
Yuqing Ren
# 
Dear Tom,

Thanks very much for your response. Here are the commands I ran.

glm(leaving ~ quarter + project_scope + project_size + tenure +
pastwork, family=binomial("logit"), data=all)
lmer(leaving ~ quarter + project_scope + project_size + tenure +
pastwork + ( 1 + quarter | project_id) + (1 + quarter | user_id),
family=binomial, data=all)

Ching
On Wed, May 25, 2011 at 3:38 PM, Thomas Levine <tkl22 at cornell.edu> wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      John Maindonald
    

    

      
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The more relevant comparison is between
1) {
glm(leaving ~ quarter + project_scope + project_size + tenure + pastwork
+ <additional fixed effect terms that account, now as fixed effectsm for the same 
main effects and interactions as ( 1 + quarter | project_id) + (1 + quarter | user_id)>,
family=binomial("logit"), data=all)

[replacing the part between the diamond brackets (< >) by something that R can
interpret is left as an exercise for anyone who might welcome such a challenge!]
}

and 2) {
lmer(leaving ~ quarter + project_scope + project_size + tenure +
pastwork + ( 1 + quarter | project_id) + (1 + quarter | user_id),
family=binomial, data=all)
}

Note that the coefficient estimates are conditional on other effects for which the
relevant equation accounts.  Change those other effects and you are likely to
change the coefficients, and the coefficient estimates.

What is probably a second order effect (& not needed to explain what you see 
here) is that the relative weighting of the observations will be different in the
random effects analysis, even for a 'relevant' comparison.

The following makes the point re interpretation of regression coefficients well, 
albeit in a standard least squares regression context:  
"Interpreting Regression Coefficients", at:
http://www.mosaic-web.org/MCAST/videos/MCAST-2010-09-10/lib/playback.html

This is one in a series of "M-casts".  A complete list is at:
http://www.causeweb.org/wiki/mosaic/index.php/Pub100

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

        
On 26/05/2011, at 2:53 PM, Yuqing Ren wrote:

        

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Yuqing Ren
    

    

      
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Excellent! This is exactly the answer I was looking for and it makes
perfect sense.

Thank you, John and Tom for your help.

Ching

On Thu, May 26, 2011 at 3:03 AM, John Maindonald

        
<john.maindonald at anu.edu.au> wrote: