# Regression model for ordinal dependent variable and categorical independent variables

If I'm using R, which regression model should I use for my dataset? (I need to get the R-squared value.) I have 1 dependent variable and 6 independent variables as follows:

1 dependent variable:

• concern {-2, -1, 0, 1, 2}

6 independent variables:

• org { scl_msg, scl_pg, fin}
• type_d { prsnl, activ, log}
• type_f { x-t, user-x, t-x}
• gender { male, female}
• age { 18-25, 26-30 , 31-35, 36-40, 40+}
• awareness { fully-aware , partially-aware, not-aware}
• Are you saying that your dv can only take the values -2, -1, 0, 1, 2? – gung Oct 16 '14 at 2:33
• yes it is only {-2, -1, 0, 1, 2} – sdj Oct 16 '14 at 14:25
• Then your dependent variable isn't continuous. Eg, you can't have a 1.5 or a -3, etc. Do you have good reason to believe that the difference between 2 & 1 is the same as -1 & -2? These look like ordinal data to me. – gung Oct 16 '14 at 15:27
• it is representing concern levels , so -2 means extremly concened, 0 means neutral and 2 means not concerned. in this case if it ordinal do you think logistic regression model should be the corect model to use ? or do you have another seggastions ? – sdj Oct 16 '14 at 15:56

## 1 Answer

You will be best off using ordinal logistic regression. There are at least four ways to do this in R (meaning different functions in different packages). The uniformly excellent UCLA statistics help site has a fairly comprehensive tutorial (albeit using only polr in MASS) here. There is a nice overview of the different possibilities here (it is primarily code you can run, with less explanation).

Note that there isn't really such a thing as R-squared for generalized linear models such as ordinal logistic regression. There are a number of so-called pseudo R-squareds, but it is important to understand what each one measures (there is a nice guide here), and their value is debatable (for an overview of the issues, see this excellent CV thread: Which pseudo $$R^2$$ is the one to report for logistic regression).

• I found this post from googling, and perhaps you'd be able to answer: do you know of any papers/references in which the consequences of using OLS with an ordinal dependent variable are studied and compared to e.g. ordinal logistic regression (I'm thinking in terms of consistency, unbiasedness, hypothesis testing, etc)? – hejseb Apr 7 '15 at 14:58
• @hejseb, no not really. It's pretty obvious that OLS would be totally inappropriate. – gung Apr 7 '15 at 14:59
• @gung I completely agree, and I am well aware this is the 'truth' (if you will). But I was curious as to knowing when the OLS estimator would be decent (in some sense) or the opposite. Basically, I have a paper I want to criticize (which does this mistake), but I was hoping I could just make a reference and not reinvent the wheel and demonstrate the inappropriateness myself... Thanks anyway! – hejseb Apr 7 '15 at 15:03
• @hejseb, you could ask a new question seeking a reference. You could also cite something generic, like Agresti (2013). I'm afraid I don't know of a reference. From intuition, OLS would be vaguely acceptable if your levels are approximately equal interval, don't bunch up near the extremes & you have a lot of data. – gung Apr 7 '15 at 15:06