Which classification method to use?

Question

I have a topsoil stoniness data which consists of ~300 sample plots. The stoniness data (stoniness index(SI)) is set in five classes 1 through 5 and class number one represents extremely low SI and class number five extremely high SI. My goal is to study how well is it possible predict the SI for new plots. As independent variables I am using two types of variables: gamma-variables (continuous values) and dummy-variables (0 or 1).

I have trouble deciding which classification/analysis method would be the most suitable for my data. My professor suggests using Linear discriminant analysis but what I've read and heard, I don't think my data passes all the preconditions to use this analysis and so I can't expect to get reliable results.

Second analysis that I have been thinking is multinomial logistic regression. This analysis seems to be suitable for my data but all the examples I've seen about this analysis deal with problems such as choosing correct study program or car type which are not "ordered" unlike the SI classes in my data (low to high).

Third and in my opinion the best option: Ordinal regression which takes in to consideration the order of the categories. Biggest concern I have regarding this analysis is that in many studies distances between the categories is not known unlike in my data the distances between different SI categories are measured and specific.

In Summary: Data consists of Dependent variable which has five ordered classes (SI) and independent continuous gamma-values and dummy-variables.

Which analysis method is the best option for this kind of data, Linear discrimination analysis, multinomial logistic regression or Ordinal regression. Or is there some other analysis which would be better that these three?

Answer 1

I agree that of the three options you considered, ordinal regression is the most appropriate one, for the reasons you gave. In fact, if the distances between neighboring SI categories are all the same, an ordered logistic regression (proportional odds) model could be a very good choice.

If the SI bins are unevenly spaced, the best approach may actually be to relabel the bins with their midpoint SI values and treat this as a continuous dependent variable, e.g. by performing a simple linear regression.