I have a query regarding which type of regression analysis to use for my study. I have used a scale (dependent variable) that contains 9-items and each item is marked on a 5-point Likert scale. Scores of each item are summed and ranges from 9 to 45. Higher score indicates the respondent has more characteristics of that construct.
Similarly, there are two independent variable. One IV has 20-items and each item is marked on a 4-point Likert scale. Score ranges from 20 to 80. Second IV has 7-items and each item is marked on a 5-point Likert scale. Score ranges from 7 to 28.
The reviewer has suggested me to use non-parametric tests since my data is ordinal. However, previous studies have used Multiple Linear Regression using similar types of constructs.
Which type of regression analysis is appropriate in this case - ordinal regression or multiple linear regression? Any literature explaining this would be highly useful.
Your reviewer is technically correct, but very much out of date. Linear regression have been used for these kinds of variables for decades, at least in the social sciences. As an alternative to linear regression, you could show him (or her) the results of the analogous ordered (ordinal) regression model for your data, which typically yields similar results as the linear model. (That's why the linear model is prefferred in most cases.) Most standard softwares have the ordered/ordinal regression model as an option. BR, Chris
Your reviewer is technically not correct. Once you take the individual Likert-type questions and combine them into a scale, you are treating your data as interval data, and not strictly ordinal. It really makes no sense at that point to then say the scale is ordinal in nature.
That being said, if you don't have too many distinct values in your dependent variable, using ordinal regression would make sense. (Although, how does the software handle the supposedly ordinal independent variables?)
Really, the appropriateness of using traditional OLS general linear model regression depends on whether it's reasonable to do so. If, for example, the residuals from your analysis reasonably meet the assumptions of normal-ish distribution and homoscedasticity (and other assumptions), then the model might be reasonable. No real data or real population meet these assumptions perfectly.
I'd normalize the DV (that is, rescale it so that the value will be with 0...1) and use a beta-model or a quasi-binomial (regression) model.
I think the reviewer's comment makes sense in a way that for interval scale, it requires the adjacent values are equally spaced. For example, the difference between 10 and 11 oC (temperature) is exactly equal to the difference btween 11 and 12 oC. This almost does not happen to the Likert scale; for example, the change from highly unsatisfied to unsatisfied might be greater than from unsatisfied to neutral. Therefore, even though you combine your items to make a larger scale that looks like an interval scale, it doesn't guarantee that it's actually interval (and MLR is appropriate).
I would suggest you to perform some exploratory factor analyses (EFA) to examine whether your items load on a few factors and make sure that your scale can be numerically combined. You may also want to use SEM (structural equation modeling) to model your data because both your independent and dependent variables appear to be latent.
Long Bao Hoang , The thing is, once the results of several Likert items are averaged into a single scale, the analyst is already treating them as interval data. ... To say that (3, 4, 5) and (4, 4, 4) average to the same value, you have to assume that the values have equal spacing. (Or at least assume some pre-determined spacing). If this isn't a reasonable assumption, then the analyst shouldn't have conducted that averaging in the first place. It does no good to average values from individual items, and then think the result isn't interval.
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