[R] [Not R question]: Better fit for order probit model

[adschai at optonline.net]

Hi,

I have a model which tries to fit a set of data with 10-level ordered responses. Somehow, in my data, the majority of the observations are from level 6-10 and leave only about 1-5% of total observations contributed to level 1-10. As a result, my model tends to perform badly on points that have lower level than 6. 

I would like to ask if there's any way to circumvent this problem or not. I was thinking of the followings ideas. But I am opened to any suggestions if you could please. 

1. Bootstrapping with small size of samples each time. Howevever, in each sample basket, I intentionally sample in such a way that there is a good mix between observations from each level. Then I have to do this many times. But I don't know how to obtain the true standard error of estimated parameters after all bootstrapping has been done. Is it going to be simply the average of all standard errors estimated each time?

2. Weighting points with level 1-6 more. But it's unclear to me how to put this weight back to maximum likelihood when estimating parameters. It's unlike OLS where your objective is to minimize error or, if you'd like, a penalty function. But MLE is obviously not a penalty function.

3. Do step-wise regression. I will segment the data into two regions, first points with response less than 6 and the rest with those above 6. The first step is a binary regression to determine if the point belongs to which of the two groups. Then in the second step, estimate ordered probit model for each group separately. The question here is then, why I am choosing 6 as a cutting point instead of others? 

Any suggestions would be really appreciated. Thank you.

- adschai