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bigglm() results different from glm()

8 messages · John Fox, Thomas Lumley, Francisco J. Zagmutt

Francisco J. Zagmutt
# 
Dear all,

I am using the bigglm package to fit a few GLM's to a large dataset (3 
million rows, 6 columns).  While trying to fit a Poisson GLM I noticed 
that the coefficient estimates were very different from what I obtained 
when estimating the model on a smaller dataset using glm(), I wrote a 
very basic toy example to compare the results of bigglm() against a 
glm() call.  Consider the following code:


 > require(biglm)
 > options(digits=6, scipen=3, contrasts = c("contr.treatment", 
"contr.poly"))
 > dat=data.frame(y =c(rpois(50000, 10),rpois(50000, 15)), 
ttment=gl(2,50000))
 > m1 <- glm(y~ttment, data=dat, family=poisson(link="log"))
 > m1big <- bigglm(y~ttment , data=dat, family=poisson(link="log"))
 > summary(m1)

<snipped output for this email>
Coefficients:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)  2.30305    0.00141    1629   <2e-16 ***
ttment2      0.40429    0.00183     221   <2e-16 ***

     Null deviance: 151889  on 99999  degrees of freedom
Residual deviance: 101848  on 99998  degrees of freedom
AIC: 533152

 > summary(m1big)
Large data regression model: bigglm(y ~ ttment, data = dat, family = 
poisson(link = "log"))
Sample size =  100000
              Coef  (95%   CI)    SE p
(Intercept) 2.651 2.650 2.653 0.001 0
ttment2     4.346 4.344 4.348 0.001 0

 > m1big$deviance
[1] 287158986


Notice that the coefficients and deviance are quite different in the 
model estimated using bigglm(). If I change the chunk to 
seq(1000,10000,1000) the estimates remain the same.

Can someone help me understand what is causing these differences?

Here is my version info:

 > version
                _
platform       i386-pc-mingw32
arch           i386
os             mingw32
system         i386, mingw32
status
major          2
minor          8.1
year           2008
month          12
day            22
svn rev        47281
language       R
version.string R version 2.8.1 (2008-12-22)


Many thanks in advance for your help,

Francisco
Thomas Lumley
# 
This is a surprisingly interesting problem that took a while to debug, because the computations all seemed correct.

Your model hasn't converged yet.  You can get the right answer either by running longer:
Large data regression model: bigglm(y ~ ttment, data = dat, family = poisson(link = "log"),
     chunksize = 100000, maxit = 20)
Sample size =  100000
              Coef  (95%   CI)    SE p
(Intercept) 2.304 2.301 2.307 0.001 0
ttment2     0.405 0.401 0.408 0.002 0

or supplying starting values:
Large data regression model: bigglm(y ~ ttment, data = dat, family = poisson(link = "log"),
     chunksize = 100000, start = c(2, 0))
Sample size =  100000
              Coef  (95%   CI)    SE p
(Intercept) 2.304 2.301 2.307 0.001 0
ttment2     0.405 0.401 0.408 0.002 0


The bug is that you weren't told about the lack of convergence.  There is a flag in the object, but it is only set after the model is converged, so it is not there when convergence fails.
NULL
[1] TRUE
[1] TRUE

For the next version I will make sure there is a clear warning when the model hasn't converged.  The default maximum number of iterations is fairly small, by design --- if it isn't working, you want to find out and specify starting values rather than wait for dozens of potentially slow iterations.  This strategy obviously breaks down when you don't notice that failure. :(

      -thomas
On Mon, 16 Mar 2009, Francisco J. Zagmutt wrote:

            

      
      
      
    

        

      
      
    

        
Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

  
  


  


      

    

    

      
      

        


  

        

      John Fox
    

    

      
      #
    

  


  

      
Dear Francisco,

I was able to duplicate the problem that you reported, and in addition
discovered that the problem seems to be peculiar to the poisson family.
lm(y~ttment, data=dat) and biglm(y~ttment, data=dat) produce identical
results, as do glm(y~ttment, data=dat) and bigglm(y~ttment, data=dat).
Another example, with the binomial family:

            

      
      
      
    

        
ttment=gl(2,50000))

            

      
      
      
    

        
(Intercept)     ttment2 
   -1.33508     2.34263

            

      
      
      
    

        
(Intercept)     ttment2 
   -1.33508     2.34263

            

      
      
      
    

        
[1] 109244

            

      
      
      
    

        
[1] 109244

I'm copying this message to Thomas Lumley, who's the author and maintainer
of the biglm package.

Regards,
 John

            

      
      
      
    

        
On

            

      
      
      
    

        

      
      
    

        
http://www.R-project.org/posting-guide.html

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Thomas Lumley
    

    

      
      #
    

  


  

      
Yes, the slow convergence is easier to get with the log link.  Overshooting the correct coefficient vector has more dramatic effects on the fitted values and weights, and in this example the starting value of (0,0) is a long way from the truth.   The same sort of thing happens in the Cox model, where there are real data sets that will cause numeric overflow in a careless implementation.

It might be worth trying to guess better starting values: saving an iteration or two would be useful with large data sets.

      -thomas

        
On Tue, 17 Mar 2009, John Fox wrote:

        

            

      
      
      
    

        

      
      
    

        

      
      
    

        
Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

  
  


  


      

    

    

      
      

        


  

        

      Francisco J. Zagmutt
    

    

      
      #
    

  


  

      
Dear Thomas and John,

Thanks for your prompt reply and for looking at your code to explain 
these differences. I see you replied very late at night, so I am sorry 
if my little problem kept you awake!

As you pointed out, the model indeed converges (as reported in 
model$converged) once I specify a larger number of iterations.

A very minor comment: it seems that the reporting of the estimates in 
summary.biglm() is not taking the parameters from options(digits).  For 
example, using the same data and models as before:

 > require(biglm)
 > options(digits=8)
 > dat=data.frame(y =c(rpois(50000, 10),rpois(50000, 15)), 
ttment=gl(2,50000))
 > m1 <- glm(y~ttment, data=dat, family=poisson(link="log"))
 > m1big <- bigglm(y~ttment , data=dat, family=poisson(link="log"), 
maxit=20)

 > summary(m1)
<Snipped>
Coefficients:
              Estimate Std. Error z value  Pr(>|z|)
(Intercept) 2.3019509  0.0014147 1627.21 < 2.2e-16 ***
ttment2     0.4052002  0.0018264  221.86 < 2.2e-16 ***

 > summary(m1big)
              Coef  (95%   CI)    SE p
(Intercept) 2.302 2.299 2.305 0.001 0
ttment2     0.405 0.402 0.409 0.002 0


To get more digits I can extract the point estimates using coef(m1big), 
but after looking at str(m1big) the only way I could figure to extract 
the p-values was:

 > summary(m1big)$mat[,"p"]
(Intercept)     ttment2
           0           0

Is there a way I can get summary.biglm() to report more digits directly?

Thanks again,

Francisco

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Francisco J. Zagmutt
    

    

      
      #
    

  


  

      
Dear Thomas and John,

Thanks for your prompt reply and for looking at your code to explain 
these differences. I see you replied very late at night, so I am sorry 
if my little problem kept you awake!

As you pointed out, the model indeed converges (as reported in 
model$converged) once I specify a larger number of iterations.

A very minor comment: it seems that the reporting of the estimates in 
summary.biglm() is not taking the parameters from options(digits).  For 
example, using the same data and models as before:

 > require(biglm)
 > options(digits=8)
 > dat=data.frame(y =c(rpois(50000, 10),rpois(50000, 15)), 
ttment=gl(2,50000))
 > m1 <- glm(y~ttment, data=dat, family=poisson(link="log"))
 > m1big <- bigglm(y~ttment , data=dat, family=poisson(link="log"), 
maxit=20)

 > summary(m1)
<Snipped>
Coefficients:
              Estimate Std. Error z value  Pr(>|z|)
(Intercept) 2.3019509  0.0014147 1627.21 < 2.2e-16 ***
ttment2     0.4052002  0.0018264  221.86 < 2.2e-16 ***

 > summary(m1big)
              Coef  (95%   CI)    SE p
(Intercept) 2.302 2.299 2.305 0.001 0
ttment2     0.405 0.402 0.409 0.002 0


To get more digits I can extract the point estimates using coef(m1big), 
but after looking at str(m1big) the only way I could figure to extract 
the p-values was:

 > summary(m1big)$mat[,"p"]
(Intercept)     ttment2
           0           0

Is there a way I can get summary.biglm() to report more digits directly?

Thanks again,

Francisco

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Thomas Lumley
    

    

      
      #
    

  


  

      
There's a digits= argument to the print method.

            

      
      
      
    

        
Large data regression model: bigglm(ff, data = trees, chunksize = 10, sandwich = TRUE)
Sample size =  31
                 Coef     (95%      CI)      SE p
(Intercept) -6.63162 -8.08729 -5.17595 0.72783 0
log(Girth)   1.98265  1.87132  2.09398 0.05567 0
log(Height)  1.11712  0.73339  1.50085 0.19186 0
Sandwich (model-robust) standard errors


I suppose I should make it take its default from options(digits)-3 or something.

      -thomas

        
On Tue, 17 Mar 2009, Francisco J. Zagmutt wrote:

        

            

      
      
      
    

        

      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        
Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

  
  


  


      

    

    

      
      

        


  

        

      Francisco J. Zagmutt
    

    

      
      #
    

  


  

      
That's a much cleaner solution!  It would be nice if biglm takes the 
defaults from options(digits), but off course we can also just use 
print() as you pointed out.

Thanks again for your replies and for making this library available to 
the community.

Francisco