Generalised Ordered Logit Model

I've taken interest in the generalised ordered logit model (the gologit2 command in stata)

I'm trying to convert this linear equation: Ηij = β0 + β1Χij + β2μj + ∑q γqΖqij + εij
into a generalised ordered logit regression equation. Where H = happiness, X = absolute income, u = relative income, γ = effect of control variables, Z = control variables.

Therefore I'm wondering if it would be possible to receive help on how to convert this above equation as after trying numerous approaches I've made next to no progress. Thank you very much.