Dear all,
I would appreciate your views on the following:
For Binary Logistic Regression with binary (0/1) explanatory variables :
Log (odds of event) = B0+B1*X_1 + B2*X_2 etc....
For a particular variable (say X_1) the odds ratio e^B1 tells me that
someone with characteristic X1 is e^B1 more likely to have the 'event'
than someone without characteristic X1 (with other variables remaining
the same).
For ordinal logistic regression I would like to ask how the odds ratio
is interpreted. Say if we had 3 response categories: good reading
skills, medium reading skills, poor reading skills and 4 binary (0/1)
explanatory variables. We derive the constant, alpha1, which is
associated with 'good' category and constant,alpha2, associated with
'good' or 'medium' category . I use the ordinal regression procedure in
SAS so that increasing 'score': B1*X_1 + B2*X_2 +B2 X_3 + B3 X_4 means
tendency towards better reading skill. Now would we say that the odds
ration e^B1 means *both* that
(i) someone with X_1=1 is e^B1 times more likely to have good reading
skill compared to someone without X_1
(ii) someone with X_1 is e^B1 times more likely to have good or medium
reading skill compared to someone without X_1.
Or , for simplicity, would it be acceptable to say that someone with
X_1=1 is e^B1 times more likely to be *better* at reading than someone
without X_1?
Many thanks for your views on this,
All the Best,
Kim
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