Analyzing relationship between two Likert-items (is it possible?) I am a student and am new to statistical market research.
Is it possible to analyze the dependence of answers to one Likert-type item on answers to another Likert item (predictor)? If so, what test can I use?
I am doing an analysis of how much attachment/affinity (dependent Likert item) of consumers to a certain brand can be affected by their perception of how much a new brand extension of that certain brand fits the current brand image they have in mind (independent/predictor Likert item).
I am thinking a linear regression can be applicable here. But please suggest other ways if it is not. I am very open to any suggestion and advice. Thank you very much. :)
 A: In terms of context, it is important that you first think about the distribution & type of your independent and dependent (or explanatory and response) variables before selecting a method.
What is a Likert-type item? There is disagreement on specifically what type of measurement a Likert answer is. Some schools believe that it should be classified as interval-level data, while others believe that it should be treated as ordered-categorical data. Regardless of which school you come from, it is important to realize that a Likert-type answer is not continuous. Regression, linear regression, is used when you have a continuous response variable. This is not the case here, since you cannot choose affinity or attachment level 1.36471284. Unfortunately, you can only choose level 1 or 2 as an example. Since you have a categorical response, immediately, you should be thinking about techniques that could handle categorical responses. 
Going down this path, the first place you might start is logistic regression. This assumes that we have a categorical response variable with really 2 outcomes. A great resources that you can consult if you want to put these into action in R can be found here.
Now, this doesn't seem to fit our case, because, I would assume that you have many different levels of your response or dependent variable. Thus, we might look to extend the logit model, and use a multinomial logit model. Conveniently, UCLA also has an excellent set of resources that you can refer to if you were to use R to solve these problems, which I would recommend.
Finally, these models, can be more broadly classified into a category of generalized linear models, or GLM's. I won't go into detail here. That said, Princeton has an excellent resource page here that can help provide you with more context on GLM's and how to use them in R.
A: Once you identify your explanatory and dependent variables, you may want to use ordinal regression if your dependent variable is ordered and has few categories (e.g., 4 or 5 points scale). And for the explanatory variables measured by a likert scale you can test whether it makes sense to include them as continuous variables by first including dummy variables for each answer category and seeing whether the coefficients of these dummy variables show a linear pattern. If not, maybe you can recode these variables and include as dummies. 
If you are just interested in associations you can use polychoric correlation to see if these measures are related at all. 
