# How to justify the choice of independent variables in multiple regression

I am trying to measure the effect of atmospheric factors as smell or light (IV) on purchase behavior (DV). In total I have xx likert scales that contain 5 likert items and responses are coded from 1 to 5.

I am wondering which approach would be the best to show that my IVs have some relevance. Could someone check if my approach makes sense?

1. Clean out the data (delete monotone, take values & outliers into account, check normality)
2. Conduct a reliability test with Cronbach's alpha
3. Construct validity (convergent and discriminant)
4. Harman single factor test
5. Factor analysis
6. Check if the 5 assumptions about MR are met (linearity, normality etc.)

Do you think that this approach is sufficient in order to show that my model has some value?

• Welcome to CV. You should probably tag your question as "self-study." As research checklists go, this is fine. One thing you might consider adding would be checks for model "overfitting" based, e.g., on a bootstrap analysis (there are published papers on this) as well as using some variant of k-fold cross-validation to demonstrate out-of-sample predictive validity and accuracy. Nov 13, 2015 at 20:26
• @DJohnson, this isn't really self-study in the sense we're worried about. Nov 13, 2015 at 20:35
• Is your 5 (factor analysis) EFA or CFA? Note that Cronbach's alpha is meaningless if the data aren't unidimensional, so you should run your factor analysis first. Likewise, checking the construct validity only makes sense after ensuring that you have identified the construct correctly (eg, via factor analysis), IMO. Nov 13, 2015 at 20:38
• Thank you very much for your input, I highly appreciate it! @gung: I was considering an EFA test and checking my data with the KMO and Bartlett's test. Considering normality test, I was thinking about applying a simple Kolmogorov-Smirnov or Shapiro-Wilk tests. My sample size is not too large or little so I though this might be a good fit? Nov 15, 2015 at 9:51

Several points:

I wouldn't check normality on likert items, since they are not normal.

Factor analysis methods consider the relationship between the independent variables you have (light, air) and have nothing to say about their relationship to the response (purchasing).

For the sort of data that you seem to have, I would try a regression tree as a useful exploratory method. Regression methods look for relationship that are linear across the full range of values, but trees could model that, say:

1. men purchase differently from women
2. men are affected by light
3. women are affected by freshness of air

I also recommend plotting the data. You could binarize the likert items and do boxplots of the response against "high" or "low" ... or simply do a boxplots against all five likert categories.

• Hello Placidia, thank you for your response! Unfortunately my study course (Business & Management) never provided me with a proper statistic class, I'm just trying to teach myself by reading papers and publications on that topic. So right now I'm not even sure what an regression tree is but I will definitely take a look at it! Nov 15, 2015 at 10:00