How to perform ordinal regression with rank-based dependent variable?

Question

I have a dataset I'm about to use for some preliminary testing. However, I've stumbled onto a puzzle which I cannot seem to figure out.

https://drive.google.com/file/d/0BzfbOrk7Ans7UGdEbzZtR2NqT0k/view?usp=sharing

I'm trying to figure out the effect various variables have on the level of diplomatic recognition a country receives. In order to measure the level of recognition, I managed to calculate the Google PageRank score for each country. What PR assumes is that a link sent from site A to site B is a vote for B's importance. If site B links to site C, B's vote is worth more than it was before site A linked to site B, and thus increasing the importance of page C. Thus, in transforming this into the 'real world', I've replaced 'sites' with countries and 'links' with diplomatic ties. After running the algorithm I ended up with a score which can be used to rank the different countries on their level of diplomatic recognition.

Here comes the problem. While I managed, eventually, to figure out how to apply the algorithm to my dataset, I'm fairly new to the world of regressions. I've conducted a couple of linear regressions using various dubious surveys, but I imagine I should use ordinal regression when dealing with such a rank-based variable; and here I am completely blank.

With the help of youtube, google and some stat-aquaintances, I've managed to run the ordinal regression on the dataset you see attached in the link. I've tried running it with various independent variables (those listed in dataset in the link), including Gross National Income, military expenditures, military personell, GNI per capita and Hub-rank (which is another network centrality measure). I've also transformed the independent variables into rank variables similar to the dependent variable. However, my results are rather useless as I get the following message: "There are xxx (xxx) cells (i.e., dependent variable levels by combinations of predictor variable values) with zero frequencies."

Now, I think I understand that the reason for this message is basically that I have as many unique categoris as there are observations, meaning that there are no variation in the dataset. What I don't know is how to overcome this obstacle.

Should I rescale the dependent variable somehow? Should I consider rescaling the independent variables? Should I consider not doing ordinal regression at all?

Oh, by the way, I'm using SPSS.

Any help would be greatly appriciated!

https://drive.google.com/file/d/0BzfbOrk7Ans7UGdEbzZtR2NqT0k/view?usp=sharing

Answer 1

It sounds as if your dependent variable is a count variable, not an ordinal variable, given that it is the total number of diplomatic ties for each country. As such, you need to use a Poisson Regression Model (PRM). There is the standard Poisson Regression, and then several generalizations depending on the nature and distribution of the counts. For example, if the variance exceeds the mean (very likely), then you probably want to use negative binomial regression. Or, if you have a lot of zeros on your DV, perhaps a zero-inflated model. If the countries in your dataset have to have >1 counts in order to be included, then a truncated Poisson model may be what you need.