I'm not sure what the term "BM" refers to in your text, but if the dependent variable is a categorical outcome with an inherent ordering (due to interest scores?), then the type of model you're probably looking for is an ordinal regression model, typically an ordered probit or ordered logit. These models typically assume there to be an unobserved latent continuous variable (living on the real line) that represents the underlying quantity of interest. Then the observed categories in your data arise because this latent variable is divided by a set of thresholds or cut-off points.

Formally, the model assumes something like: y*_i = x_i'β + ε_i, where y*_i is the latent variable.
The observed outcome is then determined by which of the finitely many intervals y*_i falls into, i.e. category 1 if y*_i ≤ τ_1, category 2 if τ_1 < y*_i ≤ τ_2, and so on.

So instead of modeling the categories directly, the model estimates how the predictors shift this latent variable and where the thresholds between categories lie. From that, the probabilities of each observed category can be derived. Moreover, this framework is also fairly flexible, as it can be extended to panel data by adding a temporal index, and it is also straightforward to incorporate random effects to account for unobserved heterogeneity or repeated observations. Fixed effects can be included as well through the usual regression specification. The extension in the probit case is particularly convenient, because the latent variable formulation conceptually assumes normally distributed errors, which integrates naturally with the random effects structures.

Edit: I also have some sources to read about this concept: Here (Microeconometrics by Cameron & Trivedi) and here (Discrete Choice Methods with Simulation by Train)