Multinomial mediator model interpretations

[seanharrigan]

Hello @BS1125,

My team and I are currently working on a research question involving a multinomial meditator with 4 levels. Our exposure is categorical and the outcome is binary (this is depicted by the equation below from the overview section on the website). In this model, we are not considering an exposure-mediator interaction.

In our example above, we are interested in the interpretation of the TNIE. By looking at the above equation, it looks like it sums the indirect effect across all non-reference mediator strata. Therefore, how would we interpret the mediator effect?

Also, we are wondering about one particular part of the formula (see below). Could you explain why the a* is on the numerator and a is on the denominator. This is on the risk scale and usually the effect is the exposed divided the the unexposed.

Thanks very much

Sean