What Is A Logit Coefficient. In this section I will describe an extension of the multinomial logit model that is particularly appropriate in models of choice behavior where the explanatory variables may include attributes of the choice alternatives for example cost as well as characteristics of the individuals making the choices such as income. Therefore to interpret them expcoef is taken and yields OR the odds ratio.
But these make the math work out nicely so lets stick with them. If beta_1 0012 the interpretation is as follows. For one unit increase in the covariate X_1 the log odds ratio is 0012 - which does not provide meaningful information as it is.
Ln is the natural logarithm log exp where exp271828 p is the probability that the event Y occurs pY1 p1-p is the odds ratio.
This model is also called the random coefficient logit model since is a random variable. It allows the slopes of utility ie the marginal utility to be random which is an extension of the random effects model where only the intercept was stochastic. The logit function is the natural log of the odds that Y equals one of the categories. More explicitly we can say that for male students a one-unit increase in math score yields a change in log odds of 013.
