# Ordinal regression vs. summated score

It seems quite common to see scientific researches using a summated score to represent an overall scale that consists of many individual scale items (ex. Likert scale items). I assume that regular statistical tools (ex. ANOVA, linear regression, etc.) can be used on these data, which are treated as quantitative data.

However I've came upon another tool when dealing with ordinal data - ordinal regression (or ordered logistic regression). My initial question was: would it be better if I just used ordinal regression rather than calculating summated score first then use multiple regression? But I found out that ordinal regression seemed applicable only when all individual scales were included to fit a dependent variable. In cases where scales are made up of subscales, then generating summated scores is a must (or perhaps not?), meaning that data are treated as quantitative already.

I'm not sure if what I understand here is correct or not. Verification is greatly appreciated.

• If the resulting scale is not an interval scale, that is, the meaning of a particular gap is not the same across the scale (e.g. is the difference between 1 and 3 the same as the difference between 101 and 103?) then treating it as a continuous measurement does not make any sense. So, this really translates to a question about whether or not you can make a rational argument that your outcome is an interval scale - if so, you can treat as you would any other continuous variable. – Macro Jan 6 '13 at 22:11

## 1 Answer

Ordinal regression is appropriate whenever the dependent variable is ordinal: That is, when you can assume that the levels are in order, but not that the gaps between the levels are equal.

If you analyze individual Likert items (each scored 1-5 or 1-7 or whatever) then this could be a very reasonable assumption. But other methods might be good too; this post on my blog might be helpful.

However, if you sum a bunch (say 10) Likert items (each, say, 1-5) then your total ranges from 10 to 50 and ordinal regression, while technically correct, will be hard to implement and interpret (there would be a huge number of parameters). In this case, I suggest that OLS regression could be the default.

You could, certainly, do ordinal logistic regression on each of the 10 Likert items, but then you have 10 regressions to interpret, which might lead to confusion.

In any case, you should start with a bunch of graphs to see what's going on. Before summing (or otherwise combining) the Likert items, I'd also check how they relate to each other using factor analysis and Cronbach's alpha.

• I see now. Your link is also informative. I've tried OLS regression and indeed that sheer amount of parameters is difficult to understand. I think I'll just do the very basic using multiple regression (path analysis) and Cronbach's alpha. Thanks anyways! – yongtw123 Jan 10 '13 at 16:53