Multinomial Logistic Regression - Interpretation Method

Announcement. Multinomial Logistic Regression - Interpretation Method. That is indeed correct in the context of a multinomial logit. Intuitively, if you have three possible options (let's just say A, B, and C), and A is the reference group, then when calculating marginal effects, the change in probability associated with B is dependent on the change in probability associated with C. In other words, if the coefficient on some variable, X, is positive for both option B and C, then the probability of picking one of the two cannot be considered independently of the other! After taking derivatives, the actual 'formula' for the marginal effects of coefficient B in option C is: (BC)(PC)[1-(BB)(PB)], where BC is the coefficient for variable X in option C, PC is the starting probability for option C, BB is the coefficient for variable X in option B, and PB is the starting probability for option B. (This is easily extended to more than two choices, but it is easiest to explain with just the two.) Hope this helps. Join Date: May 2015 Posts: 57. Join Date: May 2015 Posts: 57. Join Date: Jun 2015 Posts: 86. In your second post just above (with the quote from Cameron and Trivedi), note that they are talking about a comparison between alternative j and alternative 1. This interpretation is correct. The same goes for the website you linked: they are talking about the relative odds of " being in general program vs. academic program", where academic program is the base outcome. Have a look at some of the graphs using the "margins" on the UCLA webpage, specifically the very first graph below the line " Sometimes, a couple of plots can convey a good deal amount of information. Below, we plot the predicted probabilities against the writing score by the level of ses for different levels of the outcome variable." You will notice that the marginal effect of writing score on the probability of being in the general group is positive and then negative! (The marginal effect is the slope of the line, not the value of the line itself.) For SES=1, increasing writing scores increase the probability of being in the general group until a score of about 45. 47, then increasing writing scores decrease the probability of being in the general group. And also note that the coefficient on writing score is positive. Hope this helps, Join Date: May 2015 Posts: 57. For my research I have three category in the dependent variable, female_occupation male_occupation and mix_occupation where mix_occupation is the reference category where I have 3 categorical independent variable and 1 continuous (income; maybe the continuous would be changed with an interaction with age (also continuous)). So what exactly do I say if I use the mlogit command (log odds) if I am only interested if these variables have an effect. For example female occupation and mix occupation(reference category): If the independent variable x1 (categorical variable with category a b c; focus on c ) has a positive sign and x2 (continuous variable) has a positive sign. Sorry for asking again, I didn't get it really. Join Date: Apr 2014 Posts: 13265. Join Date: Apr 2014 Posts: 3562. Join Date: Apr 2014 Posts: 13265. Join Date: Jun 2015 Posts: 86. When comparing some category to the base outcome, a positive coefficient always means you are more likely to be in the comparison category than in the base category. However, when talking about the probability of being in a given category, the marginal effect (that is, the effect on the probability of being in a specific group by increasing the independent variable by one) does not have to be positive. This is because, in the former example, we are only comparing the two categories to one another. On the other hand, in the latter example, we are talking about comparing the probability of being in the comparison category not just to the base outcome (which will always be higher if the coefficient is positive) but also to the probability of being in all the other comparison groups. Let's assume we have gropus A, B, and C. A is the base outcome. If a coefficient on variable X is positive for group B, then increasing X will always make you more likely to be in B than A. However, increasing X does not necessarily make you more likely to be in group B, because the effect on the probability of being in group C may be even greater than the probability of being in group B, which means the marginal effect of X may actually be negative for group B (because you are more likely at this point to be in group C), but you are still more likely to be in group B than group A.