Ordered logistic regression

[Zuhumnan Dapel]

Dear All,
Is it plausible to transform into logarithm controls (continuous) before carnying out estimation?

Thanks,
Dapel

[Clyde Schechter]

Your question isn't very clear. Do you mean using the logarithms of your predictor variables, instead of their original values, in an ordered logistic regression model?

If that's the question, the answer depends on two things. First, the variables you want to take logarithms of have to take on exclusively positive values. Second, there is the question of whether it makes any sense to do this. That depends on your subject matter--what is the research question and what kinds of variables are in play here--and can't be answered in the abstract. What do others in your discipline do when using these variables? If there is nothing to go on from the earlier work of others, have you graphically explored and seen whether the original variables or their logarithms provide better model fits?

[Zuhumnan Dapel]

Thanks dear Clyde. Your description of the question is correct. Sorry that mine was not very clear. The dependent variable is categorical (corruption perceptions index) with three outcomes: 1=extremely corrupt, 2=highly corrupt and 3=not extremely corrupt (taking 3 as base category ). The predictors are govt’s capital expenditure and total debt stock, both reported in billions of local currency. But instead of using 4,500,000,000, I used 4.5, i.e. dividing everything by a billion. Is this OK? Also, what is the link between Linear Probability Model (LPM) and ordered logistic regression? Is the later a subset of the former? The idea is that the probability of finance-related corruption increases whenever there is more money to be spend as public officials often take advantage of this to divert some amount for private use. The same with debt. When govt borrows, such borrowings induce corruption officials to steal from.

[Zuhumnan Dapel]

Dear Clyde,
Any more thought(s) on post #3?

[daniel klein]

The predictors are govt’s capital expenditure and total debt stock, both reported in billions of local currency. But instead of using 4,500,000,000, I used 4.5, i.e. dividing everything by a billion. Is this OK?

Well, it has nothing to do with taking logs. This will give you (raw logit) coefficients that are one billion times larger than the original ones, as they now represent the linear change in log-odds given a one billion increase in govt’s capital expenditure. There is nothing wrong with this.

Best
Daniel

[Clyde Schechter]

And the impact of having rescaled by a factor of a billion is that if you log transform, the log transformed variables will be log(1000000000) = 20.7 smaller than they otherwise would have: this will show up in the constant term.

I guess that government capital expenditure and debt stock would always be positive? Is that right? If so, log transforming is possible. Whether it is sensible to do this really requires doing some exploration. I might start by simplifying my outcome variable (temporarily) to a dichotomy by combining extremely and highly corrupt into a single category(1) contrasted with not very corrupt(0) and then look at -lowess- plots (with logit option) of that outcome against the predictor variables in their transformed and untransformed versions. Whichever looks like a more linear relationship may be more sensible. I would also try this maneuver with the outcome dichotomized as extremely corrupt (1) vs not very or highly corrupt (0) to confirm that it seems to work the same either way.

In any case, my guess is that others have investigated this question before using similar variables: I would see what they have done and perhaps follow suit if they have had success or present good reasons for their approach.

[Zuhumnan Dapel]

Thanks you all very much. Dear Clyde, yes, you are right. Government capital expenditure and debt stock are positive. Since one is dealing with odd ratio between 0 and 1 is it still necessary to log transform, given that our interest for the transformation is to be able to interpret results in the context of elasticity? I have been wanting to know the link between Linear Probability Model (LPM) and ordered logistic regression? Is the later a subset of the former?

[Clyde Schechter]

Maybe I'm missing something but I don't see any connection between the OR being between 0 and 1 and whether it is appropriate to log transform or not. The appropriateness of log transformation depends on the fit to the data. "Elasticity" is a technical economics term that I have a limited understanding of, but it is outside of my domain of expertise, so I won't comment on it here.

Ordered logistic regression is not a type of linear probability model. Both ordered logistic regression and linear probability models are types of generalized linear models. A linear probability model is nothing more than a linear regression in which the outcome is thought of as a probability, and the predicted values are anticipated (not always correctly) to fall between 0 and 1. In an ordered logistic regression, your outcome is an ordinal variable and you are developing a linear combination of predictors that (attempts to) model the log odds of the outcome being at each of those ordinal levels conditional on the covariates. If your ordinal outcome had only two levels, then you could do a linear probability model instead--which is better depends on the situation. But with 3 or more levels, unless you choose to combine some to reduce to a dichotomy, it is hard to see how an ordinary linear regression of the outcome would lead to meaningful results.

[Zuhumnan Dapel]

Thank for the detailed response