Hello everyone,
I have a query which again relates to deviance as a ‘goodness of fit’
statistic. Minitab provides an example for the binary logistic case where
log likelihood is -46.820 and Deviance is 51.201. There are 50 covariate
patterns (i.e. N=50) and the number of paramters, p, in the model are 3,
hence df=47.
Deviance, or the log likelihood ratio statistic is defined in texts as:
D= 2[l(b_max;y) - l (b;y)]
b_max and b are MLEs of the maximal (saturated) model and model of interest
respectively.
l(b_max;y) is the log likelihood funtion of the maximal model
l(b;y) is the log likelihood funtion of the model of interest
Am I correct in thinking that Deviance, D, is zero for the maximal model
(N=p)?
For the Minitab example LL (which is presumably (-2l(b;y)/-2) ) is -46.820
and Deviance (which presumably defined as D above) is 51.201.
Bearing Minitab’s result in mind, am I correct in thinking that ‘Deviance’,
D, for the model of interest is not simply -2l(b;y) and hence -2l(b_max;y)
of the maximal model is not zero? Hence this explains why in the Minitab
example Deviance and -2LL are not the same in the example?
SPSS says that if a model fits the data perfectly, the likelihood is 1 and
hence its -2LL is zero - doesn’t this imply that -2l(b_max;y) should equal
zero?, hence I’m a little confused as to the difference between Minitab’s
quoted -2LL and Deviance. I have tried another example in Minitab
(Vaso-constriction of the skin data,Finney, 1947 where there are 39 cases
but 38 covariate patterns) and the -2LL and Deviance for this example are
the same -which is confusing!
Many thanks for your help,
Kim.
[log in to unmask]
|