# Ordinal or binomial regression?

I have designed a question and now intend to use SPSS to analyse the results:

My dependent variable is: intention to vote. Yes or No.

My independent variables are: a series of question ranked on a scale from strongly disagree to strongly agree.

Do I need to use ordinal regression, if the dependent variable is Dichotomous? Even thought the independent variables are ordinal.

Or do I need to use binomial logistic regression, as my dependent variable is simply yes or no? Would it be possible to do this with ordinal independent variables?

Many thanks.

• Since the DV is dichotomous, you may use any of the three: binary logistic, ordinal, nominal regressions. They all are logistic. They should yield identical or almost identical results whenever data are enough "good" for such analysis. The first one is somewhat different algorithmically, computationally from the other two. This is, btw mentioned in SPSS Help. I quoted it here. Commented Mar 18, 2016 at 17:55
• Even thought the independent variables are ordinal "Ordinal" regression means ordinal DV, not ordinal IVs. There is no universal or ideal manner to treat ordinal predictors in regression. Some approaches are mentioned here. Commented Mar 18, 2016 at 18:00
• Thanks, for binomial logistic would I need to use dummy variables for all of my IV's then? Commented Mar 19, 2016 at 11:13

The model you choose is based on the structure of your outcome variable, not on your model covariates (or independent variables, as you refer to them here), because it is the outcome variable that imposes restrictions on the predicted values from your model. If your outcome is dichotomous, you would use a model where the predicted values would fall between 0 and 1. In this case, as you correctly pointed out above, an ordinary logit or probit would suffice. You would enter your ordinal independent variable as (k-1) dummy variables, where k is the number of categories in that ordinal variable. Standard interpretation applies where the odds ratios or marginal effects for each dummy variable is interpreted relative to the excluded category.

• Thanks! Are you suggesting then that I need to have dummy variables for each of my independent variables then? Commented Mar 19, 2016 at 14:45
• you need (k-1) dummy variables for each of your categorical independent variables, where k is the number of categories for the independent variable. For example, if you have age (5 categories), income bracket (4 categories), and number of hours of exercise per week (5 categories) as independent variables, you would need 4 age dummies, 3 income dummies, and 4 exercise dummies Commented Mar 19, 2016 at 17:59
• Thanks. How would I then input this into SPSS within the context of my question? Would I have "Intention to vote" as the Dependent, and then each individual dummy variable across the independent variables - which will be 4 for each category so 16 in total? Commented Mar 19, 2016 at 20:01
• with the ultimate goal of trying to see which category influences the intention to vote the greatest? Commented Mar 19, 2016 at 20:05
• @MatthewRogers The answer depends on what people in your field usually do. In some fields, it may be commonplace to enter the Likert scale responses as dummy variables. In other fields, it is commonplace to dichotomize the scale variable (for example, recode "strongly agree" and "agree" to 1, and recode remaining responses to 0). A third option is to create some kind of composite measure from more than 1 questionnaire item, e.g. using PCA or factor analysis if it makes sense in your context. Without knowing too much about your ordinal independent variables, it's hard to make a suggestion Commented Mar 26, 2016 at 22:15

You should use binomial logistic regression and not ordinal regression, though there are some concerns that you should be aware of when using ordinal predictors in a logistic regression.

Notably, if you're representing your ordinal variables numerically but the relationship between the rising levels of ordinality of an independent variable and the response of the dependent variable are not linear, the model can falsely estimate the linear response.

For example, given an independent variable with ordinal levels (a, b, c) and a response variable, consider two possible variable responses:

[A]

[B]

In [A], the ordinal predictors would very poorly model the binomial response, whereas in B the linear response would be just fine.

In [A], you would definitely want to use the ordinal predictor as a categorical variable instead of as a numeric representation, whereas in [B] the numeric representation of ordinal levels would be just fine.

• many thanks - if using binomial would I therefore need to use dummy variables for my IV's? Commented Mar 19, 2016 at 11:20
• That would be one way to handle the concern, yes. Commented Mar 19, 2016 at 15:09
• Thanks, how would I then input my new data into SPSS within the context of my question? Would I have "Intention to vote" as the Dependent, and then each individual dummy variable across all the independent variables - which will be 4 for each category so 16 in total? Commented Mar 19, 2016 at 20:02
• with the ultimate goal of trying to see which category influences the intention to vote the greatest? Commented Mar 19, 2016 at 20:05
• Again, yes- that would be one way of doing so. Commented Mar 21, 2016 at 14:07