I have a dependent/response variable that is categorized into 7 different levels with 1 being least significant and 7 being most significant. I have 20 plus independent/predictor variables that are nominal, ordinal, interval and ratio data that I want to utilize. I know I cannot use regular logistic regression because my dependent/response variable is not binary. I am pretty sure I need to use multinomial logistic regression but am unsure. Any ideas?
In your situation, beyond each method's assumptions, there are several considerations that could affect a choice between one of the logistic regression techniques (ordinal or multinomial) and a simpler, probably more familiar ordinary least squares or linear regression.
Suppose you have very few cases scored 1 or 7; linear regression would handle those data better, and with logistic you might not be able to obtain estimates for certain groups for certain main effects, let alone interaction effects.
Also, consider your audience: will they require a particular level of rigor (will they be aware of or care about the differences in underlying assumptions), and will they be able to easily interpret a given technique's typical sort of results.
Then there is the matter of analytical flexibility: there are some diagnostic procedures that can be done only with, or more informatively with, linear regression.
One solution you might find appealing is to create a linear model for the R-squared, coefficients, and diagnostics it offers, and then an ordinal logistic model for the probabilities of being in certain groups, as well as for p-values--if you use them. (Drawback: variable selection might turn out quite differently between the two.)