Hello everyone,
A question about logistic regression.....
Question 1
For the ungrouped situation (n_i=1) [as opposed to the events/trials set
up], it is recommended that the Pearson's statistic and Deviance
statistic should not be used to assess 'goodness of fit' of a binary
logistic model (e.g. Statistical Modelling in GLIM, Aitkin et al. and
http://www.ms.unimelb.edu.au/~rayw/ms372/37201sw8.pdf). Instead the
'Hosmer Lemeshow test' is recommended.
When we have ordinal logistic regression, I assume that the same problem
holds (i.e. we cannot use the Pearson's statistic and Deviance statistic
to assess 'goodness of fit') when we have the usual 'ungrouped data'
scenario. Therefore, how should goodness of fit of an ordinal logistic
model be assessed ?. SPSS prints McFadden's R^2 for ordinal regression
and I have read that this can be used to assess 'goodness of fit' for a
logistic model (with the *adjusted* McFadden's R^2 recommended)
(http://www.lrz-muenchen.de/~wlm/ST004.pdf ), but is it acceptable for
the ungrouped case?
Question 2
Also, I'd like to ask....in various examples I have seen it looks like
R^2 (adjusted) for regression models (be it multiple regression or
logistic regression) can be used to compare the fit of nested models
e.g. if we are predicting Y1 using multiple regression and we determined
models 1 and 2, model 1 could have variables A and B; model 2 could have
variables A, B, C and D and we could use R^2 (adj) to compare the two
models' fit the data. However, my question is, can R^2 (adjusted) for
regression models (be it multiple regression or logistic regression) be
used to compare models which have no variables in common? i.e. If in
an obesity study we were looking at model 1 to predict 'weight' and
our explanatory variables were A and B and our R^2(adj)=0.87 and in
model 2 we predicted 'hours of daily exercise' and our explanatory
variables were C,D and E and our R^2(adj)=0.68.....could we report that
Model 1 was a better fit than model 2?
Question 3
For ordinal logistic regression Minitab prints the measures of
association: Somers' D, Goodman & Kruskal's Gamma and Kendall's Tau-a
which measure the association between "the observed responses and the
predicted probabilities" (I guess they mean predicted categories)
generated by the model. I assume that these statistics are valid (I
cannot see a reason why not as both variables are on an ordinal scale).
I notice that these statistics are also printed for binary logistic
regression...I assume here that they are treating the binary response as
being 'ordered' e.g. whether cancer is present or absent(?).....and I
assume here that these statistics are valid for the 'ungrouped
situation'.
Many thanks,
Kim
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