# Nonparametric multiple linear regression with SPSS

#### Aldus

##### New Member
Is there a way to conduct nonparametric multiple regression analysis using SPSS?
If yes, can you provide some explanations on this regard.

I have three IVs and one DV with nonparametric data from a Likert scale.
I trying to identify if I can use the IVs to predict the DV. Also, I want to know which possible combination of IVs are most significant for the prediction.

However, I was told that if I'm going to run multiple regression analysis I have to add assumptions to elevate ordinal variables to parametric status so that the general linear model is appropriate. I don't know how to justfiy bringing Likert data to metric levels (Let me know if you have an answer on that one too. Preferably with a link to a valid academic source). Therefore, I'm looking for a way to complete the analysis using a nonparametric alternative to multiple regression

To gather data, I'm using a 7-point Likert scales with 4 items per variable.
My sample is N=150

#### CB

##### Super Moderator
Hi aldus,

When you say "nonparametric multiple regression", the main actual analysis that springs to mind is quantile regression. This isn't available in SPSS though.

You mention your data not being parametric... really "parametric" and "nonparametric" are labels we usually apply to tests rather than data as such. In terms of your data there may be two distinct sets of concerns that might lead you to be hesitant about using a parametric test:

1) The distributional assumptions of multiple linear regression - most notably that the residuals from the regression model are independently and identically distributed. You may also wish to assume that the residuals are normally distributed in order to perform inferential tests, although your fairly sizeable sample provides some robustness to this assumption. Likert data is arguably not fully conducive to some of these assumptions since it isn't truly continuous, but note that you can only really evaluate these assumptions once you've actually run your analysis. You can't evaluate them on the basis of your raw data alone. (There are some other possibly relevant assumptions I haven't mentioned above, like linearity and absence of multicollinearity).

2) Measurement level issues. Some researchers argue that Likert scale data represents ordinal data according to the S.S Stevens measurement levels. Other researchers argue that it can safely be treated as interval (you can find plenty of articles on this with a Google Scholar search). If we follow the logic of the S.S Stevens measurement levels and the associated measurement theory (representationalism), and believe that Likert scale data is only ordinal, then performing parametric analysis with Likert data would not be appropriate. Note that "interval data" is not an intrinsic assumption of multiple linear regression; rather it's representational measurement theory that suggests we should not use such a test with ordinal data.

However, not all researchers believe that the S.S. Stevens measurement levels are actually useful or important. There are certainly other measurement theories than representationalism (e.g. latent variable theory, classical test theory), which lead us to different concerns.

Hopefully that helps clarify things a little!

#### Aldus

##### New Member
Thanks for your feedback Cowboy. I want to conduct regular parametric tests, and somewhat understand the assumptions for multiple linear regression--including those that you don't go in detail.
The problem is with measurement levels, where I really don't know how to justify my approach using a solid academic document that backs my position. I'll read more on latent variable theory and classical test theory to see if it gives me the answer.

In the mean time, keep me posted if you know of a good article that helps me justify the use of Likert data--and more importantly, that explains well how to use it.

#### Aldus

##### New Member
Coming back for the same information, I just read about the possibility of using 'Ordinal Logistic Regression'. However, I'm not familiar with this type of test.
What would be the assumptions to run OLR?