I would like to determine whether the relationship between variable X and Y depends on the value of a third variable M. It's a psychological topic and unfortunately I've got a sample size of 30 persons only (survey consisting of Likert-scaled items). A colleague told me, instead of doing a moderator analysis, I shoud prefer a multiple regression. Is a multiple regression indeed a better choice? Why is that? Are there other models?
EDIT (the nature of my data in detail): The research is about the relationship between the level of engagement (predictor) of family caregivers of patients with mental disorders and the burden these caregivers experience (outcome). In general, higher levels of engagement are associated with higher experienced levels of burden. My hypothesis states, that caregivers, who are recognized and get actively involved by psychiatrists and therapists, experience relatively less burden than caregivers who are not allowed to participate by the professionals. So "participation" is seen as moderator here.
participation (moderator) v engagement(predictor) -------> burden(outcome)
Nature of variables: engagement: 4-point Likert scale, 5 items participation: 5-point Likert scale, 9 items burden: 4-point Likert scale, 7 items
All scales are considered to be continuous.