Hi everyone,

I have a data set with a very specific structure and I am looking for a suitable way to analyze it. To be more precise, I am considering cross-classified multilevel modeling or multiple membership modeling. However, I am facing great difficulties understanding the exact structure in my data. That's where I am stuck. If anyone can help me to get this a little bit clearer, I can return to library and continue reading.

Here we go:

This is what my data looks like:

First data source:
Consumer data, obtained via a survey (N=250). Consumers do have individual characteristics that vary with each consumer (gender, age, psychographics).

Second data source:
Financials from 20 companies (marketing expense, revenue, number of employees).

Dependent variable:
Each consumer from the survey answered a question regarding his/her perception of the firm image of those 20 different firms ("Firm (1-20) has a positive image." -> disagree ... agree). To stress this point once again: Every single consumer rated all 20 firms by answering this question. The dependent variable "firm image" therefore is present twenty times within each individual consumer.

Here comes what I want to do:

The perception of the firm image does not only depend on the individual properties of the consumer (gender, age, psychographics). It also depends on the properties of the perceived firm (marketing expense, revenue, size, etc.). I therefore want to explain the perception of the firm image as an interplay of (1) the consumer's characteristics and (2) the properties of the firm.

Problem:

The dependent variable "firm image" now should come along with errors from two different sources. It has an error term resulting from the individual consumer and it also has an error term from the firm sample. How can I model this?

Modeling ideas:

One part of the solution might look a bit like this: My dependent variable might represent a level on its own. "Firm image" might be the lowest level. The dependent variable "firm image" is nested in the indivual consumer. It further more is nested in the firm. However, there is no hierachy between consumers and firms, because consumers are not nested in firms (only the "firm image" variable is).

I have read about cross-classified multilevel models. I also came across multiple membership models. But everytime I try to find a representation for my structure, I get lost at the point that there is no clear hierachy between my data sets. Are there non-hierachical ways of modeling multilevel data that might suit to my problem?

Thank you very much in advance! I really appreciate every hint.

Cheers,
numerator