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What are some interesting techniques that can be used to analyze Likert data?
As a frame of reference, I have constructed a survey with about 50 items which are intended to assess the attitudes of the survey participants towards two very broad categories. Each item is on a 5 point scale.
The survey will be offered multiple times, thus pre and post testing is possible, although not necessarily the aim of the survey.
It looks like you want to do something like principal component analysis and find out two components from these 50 items. A very good technique for Likert data will be conducting Non-linear Principal Component Analysis or Categorical PCA instead of usual PCA. Papers have shown that it works better than usual PCA for ordinal data.
Key papers are from Jacqueline J. Meulman, see e.g. Nonlinear principal components analysis: Introduction and application (Psychol Methods. 2007 12(3):336-58) or PCA with nonlinear optimal scaling transformations for ordinal and nominal data (SAGE Handbook of Quantitative Methodology for the Social Sciences, 2004).
Tests involving the multinomial will be useful for you if you want to examine the distribution of Likert scores. From what I recall, Likert data are ordinal, not interval/ratio. Therefore, many nonparametric tests will be helpful, for example:
Likert questions can be analyzed individually or simultaneously. When analyzed individually, one can use a non-parametric test (Mann-Whitney U) to compare the proportions of two groups. One can use Kruskal-Wallis to test for more than two groups.
However, more commonly likert questions can be combined into multiple ranking questions, like:
The questions can be analyzed simultaneously with a non-parametric paired test, such as the Wilcoxon signed-rank test. The data is paired because a respondent be an Asian and might not like any kind of fast-food restaurant, whereas a US respondent would be morel likely to pick "High" for Burger King and McDondal's.
We can use the signed-rank test to answer question such as: Is McDonald more favourable than Burger King. This is like comparing proportions.
