Hello everyone
I have two questions:
1. My aim is to model an ordered categorical response thus I have used
SAS/Minitab to create an ordinal logistic model.
My first question relates to the determination of the goodness of fit
of the model. The packages allow me to test:
1) Ho the predictors are equal to zero vs H1 at least one of the
predictors differs from zero
2) Ho the model fits the data adequately
vs H1 the model does not fit adequately (using the 'Pearson' and
'deviance' goodness-of -fit tests in Minitab).
3) the predictive
ability of the models (by looking at 'measures of association'
between response variable and predicted probabilities).
1) 2) and 3) indicate that my model is OK.
I know that for the binary logistic regression case, the value of
-2log-likelihood (for the intercept and covariates) - which is akin
to deviance- can be used to test the null hypothesis that the model is
a good fit to the data. If the model is appropriate, the statistic
has approximately the chi-squared distribution with N-s degrees of
freedom (N=number of observation, s=number of parameters in
model)_..by the way, can we say in this case that the larger the
significance (p>0.05), the better the model fits the data?
Now, I'd like to ask, is it valid for *ordinal logistic regression*to
test -2 log likelihood (for the intercept and covariates) in the same
way (i.e. deriving the significance from the chi-squared distribution
with N-s degrees of freedom)? I ask this because even though the
'goodness of fit' tests indicate my ordinal logistic model is OK,
my -2LL is quite large.
Also, for *ordinal logistic regression* if :
D_0 = deviance of model with q parameters
D_1=deviance of model with s parameters
(q<s)
Can we compare the two models using the value of D_0 - D_1 and
find the significance of this value from the chisquared
distribution with s-q degrees of freedom?
2. My second question is: is it valid to use objective and
subjective variables in a model to predict a subjective (or objective)
response? In the models I am currently studying a certain subjective
response seems to be an extremely good predictor of a specific
subjective response - exclusion of this predictor would result in a
much inferior model.
Many thanks (in advance) for your help,
Kim.
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