Analysing data on importance ratings I had following question in my questionnaire:
Rate the following factors: price, quality, advertisement, brand, reference from 1 (very important) to 5 (least important) that may have influenced your buying decision process.
Which approaches may be used in order to measure the most important factors?
I think cluster analysis would fit more but then i would have more problems by defining clusters. So, i am wondering is there any alternative approach to analyze it?
 A: My first stab at this would be to fit a logit model for the buy-or-not outcome with price-brand rankings entered as continuous regressors. To learn which factors are important, I would look at the exponentiated coefficients, which give you the multiplicative effect on the odds ratio. If the exponentiated coefficient on price is .5, then the odds of the purchase event halve as price ranking increases by 1. To group customers, you can use the predicted probabilities of purchase.  
Both of these should be pretty straight forward with R and SPSS. I would leave some fraction of your sample out of the estimation, and use them to get a sense of how well the model fits out of sample.
A: Conventional ("stated") importance ratings have been discredited in the literature on survey methods.  For example, Richard Nisbett writes:

The most important thing that social psychologists have discovered over the last 50 years is that people are very unreliable informants about why they behaved as they did, made the judgment they did, or liked or disliked something.
  The Edge

Instances such as the following abound:


*

*Based on stated importance ratings, a factor such as "price" has the highest mean rating and is therefore assumed to be the most important.

*Data also allow the researcher to see a) what purchasing decision each person made and b) what was the price that person was faced with.  The researcher then statistically tests the relationship between the decision and the price (e.g., using correlation or a t-test).  It turns out price has a much weaker connection to the decision than the importance rating indicated - or, that price failed to strongly differentiate between buyers and non-buyers.
Instead of relying on stated importance ratings, there are many better ways to assess the importance of different factors in decision-making.  "Derived importance" methods are varied and, in addition to those mentioned above, include conjoint analysis, vignette research, the Gabor-Granger and Van Westendorp methods (where price is concerned), and market basket or shopping cart analysis.  (Maximum differential scaling pretty much falls into the stated importance category).
Also see this page.
A: You can also try principal component analysis (PCA) to see if buy_decision is closely linked to any of the predictor variables. Using iris data set as an example (and converting Species variable to numeric), following is the PCA plot of variables: 

It shows that Species variable is closely linked to Petal.length and Petal.width. It is also correlated with Sepal.Length but not with Sepal.width. The first 2 components used in this plot account for 95% of variability of data. The plot has been drawn using FactoMineR package in R.
