paradox about the degree of freedom in a logistic regression model

Fri, Dec 7, 2007 6:14 AM

Bin Yue wrote:

 Dear all:
   "predict.glm" provides an example to perform logistic regression when the
response variable is a tow-columned  matrix. I find some paradox about the
degree of freedom  .

 > summary(budworm.lg)

Call:
glm(formula = SF ~ sex * ldose, family = binomial)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-1.39849  -0.32094  -0.07592   0.38220   1.10375  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -2.9935     0.5527  -5.416 6.09e-08 ***
sexM          0.1750     0.7783   0.225    0.822    
ldose         0.9060     0.1671   5.422 5.89e-08 ***
sexM:ldose    0.3529     0.2700   1.307    0.191    
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 124.8756  on 11  degrees of freedom
Residual deviance:   4.9937  on  8  degrees of freedom
AIC: 43.104

Number of Fisher Scoring iterations: 4

This is the data set used in regression:
  numdead numalive sex ldose
1        1       19   M     0
2        4       16   M     1
3        9       11   M     2
4       13        7   M     3
5       18        2   M     4
6       20        0   M     5
7        0       20   F     0
8        2       18   F     1
9        6       14   F     2
10      10       10   F     3
11      12        8   F     4
12      16        4   F     5

     The degree of freedom is 8. Each row in the example is thought to be
one observation. If  I extend it to be a three column data.frame, the first
denoting the whether the individual is alive , the secode denoting the sex,
and the third "ldose",there will be 12*20=240 observations. 
     Since my data set is one of the second type , I wish to know whether
the form of data set affects the result of regression ,such as the degree of
freedom.
   Dose anybody have any idea about this? Thank all who read this message.
   Regards,
   Bin Yue

Yes. Never use the deviance in binary logistic regression. Only use
differences in deviance between models, each of which satisfy
requirements for asymptotic theory (in your case, you could compare your
model with that described by sex*factor(ldose)). Another striking
example is this

y <- rbinom(1000, prob=.5, size=1)
summary(glm(y~-1,binomial))

now try it with different data

y <- rbinom(1000, prob=.01, size=1)
summary(glm(y~-1,binomial))

and think about it. Then consider the same thing with y~1.

As Brian keeps telling me, there IS a sense in which the residual
deviances make sense in such cases, but it is not as a means of testing
the model adequacy.

O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

paradox about the degree of freedom in a logistic regression model

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