Multinomial mixed model equation

library(mclogit)
multinom_model <- mblogit(Spawn_ID2 ~ average_Ca + average_Mn + average_Zn, data = train, random = ~1 | ID)

To obtain the parameters of the mixed multinomial model

coefs <- summary(multinom_model)$coefficients
LLs <- coefs[,1] + qnorm(.025)*coefs[,2]
ULs <- coefs[,1] + qnorm(.975)*coefs[,2]
OR <- exp(coefs[,1])
ORLL <- exp(LLs)
ORUL <- exp(ULs)
HHES <- coefs[,1]/1.81 # Hasselblad and Hedges Effect Size

To obtain the coefficients of the mixed multinomial model

round(cbind(coefs, LLs, ULs), 3)

To obtain the odds ratio of the mixed multinomial model

round(cbind(OR, ORLL, ORUL, HHES), 3)