I am using this method for interpreting the proportion of each predictor variable in a disease occurrence which contains 3 outliers, then I cannot use multiple linear regression, now I want to know that what are the assumptions of Probit-Logit model.
Parallel regression/ proportional odds assumption: all coefficients on the predictors/independent variables are equal for every category of the outcome. Hence, the slopes of the estimated equations are identical. Brant's test is used to test this assumption.
I don't understand why 3 outliers would lead you to switch from MLR to ordinal regression. If the data were suitable for MLR I'd suggest a robust regression approach instead.
Dear Thom,
The output R-square of the MLR is below 0.3, and I think it is nothing reliable for judging the output model.
on the other hand, ordinal regression resulted in R-square of some 0.7 which is much more reasonable.
isn't it? May I have your comments or ideas?
I agree with Thom: if you're variable is suited for MLR, hence continuous, it's not clear how you can apply ordinal regression on it, which needs ordinal qualitative variable. Unless you convert it into classes, which is quite arbitrary and may give spurious results more dramatically than the 3 outliers... All of this has very little to do with the presence or absence of outliers.
You'd better think about 1) why is the some outliers, 2) how to handle them, 3) do they influence the results of your MLR and 4) find robust methods that allow outliers still staying in agreement with the kind of your variable.
If for any reason you stay with ordinal regression, there is conditions to have interpretable estimates (on the number of case of any combination of the explanatory variables - don't forget that 1) its asymptotic and 2) its non-linear, hence algorithm may have difficulties to converge) and assumptions, of linearity in the logit/probit scale depending on the link you choose. These links also assume that there is a kind of symmetry in the effects of the Xs on the failure and success probabilities.
R^2 isn't defined for ordinal regression - s I'm assuming you have a pseudo-R^2 measure (which can be problematic). It isn't a surprise that R^2 increases when you trim or delete outliers, so the comparison between the models isn't really appropriate IMO. One should choose the model because it captures the structure of the data not because it maximises R^2 or pseudo-R^2. Indeed the latter approach will invariably lead to overfitting and a model that generalises poorly.
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