 We're at a point where things are going to get very complicated, at least they could get very complicated. Multinomial logistic regression is potentially a very sophisticated analysis. What you're trying to do is use several predictor variables in a regression equation to predict not two categories, but several categories. And although it may not sound like a big change, the processing behind it becomes exponentially more complicated. Fortunately, Jmovi makes it possible to do a relatively simple multinomial logistic regression. I'm going to demonstrate this with the state data. And I'm going to look at this one category here, which actually has to do with psychology profiles for the various states in the United States. Let's start by doing this, let's do a quick exploration and get descriptives for psych regions. I'm going to put that over here. And I want to get the frequency table and I want to get the bar plot. And this is based on an analysis of people's online behavior and other characteristics. And the researchers ended up with three categories, what they called friendly and conventional, which is half the states in the sample, relaxed and creative. That's 10 states were about 21% and temperamental and uninhibited, that's 14 of these states in this sample. And here's a bar chart, you can see them. And unfortunately, the labels don't automatically adjust in Jmovi at this point, but that'll happen eventually. But let's see how we can use other variables to predict which states go into which categories. And what I'm going to do for that is I'm going to come back up here to regression and go to n outcomes that's multinomial logistic regression. And when I click on that, the first thing I have to do is pick what my dependent variable is, what's the thing that I'm trying to predict. In this case, it's the psych regions. So I'm going to put that right there. Now I've chosen one with just three categories, that's going to be the simplest. If we had only two we do binomial. And if we had more than that, it just gets so complicated, it's hard to deal with. In terms of covariates, what I'm going to do is I'm going to pick the five elements of the big five personality factors. So that's extraversion, agreeableness, conscientiousness, neuroticism, and openness. Mind you, this is not a person by person level, it's a state by state level. I'm going to slide that over into covariates. And then from there, we can start looking at the model that it creates. It takes a moment, sometimes for it to run through this, because there's a lot of calculating that goes on behind it. Let me close this so I can slide this over for a second. We have a pretty big table here. The first one is the fit measures. So we have deviants, we have the AIC, and you'll see that a lot of this is very similar to what we had in the binomial logistic regression. We also have the model coefficients where it's comparing the different groups, the relax and creative minus the friendly and conventional. And it's looking at these various elements, the personality factors, and we have the p values over here. And we see that, for instance, when distinguishing between relax and creative, none of these seem to make a big difference. When we look at temperamental and uninhibited versus friendly and conventional, we do get one to conscientiousness is appears to be an important one and neuroticism is nearly there. Now let's take a look at some of the options we have. Click back on this. And it comes down to model builder, I can put the variables in in blocks if I want. And there may be situations in which I want to do that. But with just these five personality ones, I'm not going to do blocks. But I did demonstrate that in linear regression. So you could take a look at that reference level is what's the one I want to compare it all to. I actually think I'm going to take the temperamental and uninhibited and make that the reference level. And you can see how the order just switches around over here. So this is friendly and conventional minus temperamental and uninhibited. And it just changes the sign of some of the comparisons. Although you see down here, neuroticism becomes an extremely big thing for distinguishing between the relax and creative and the temperamental and uninhibited. We're going to follow up with that. We'll come down to model fit. These are the standard choices here, we'll keep those as they are. And model coefficients. Now, this is where we have the estimates, those are coefficients, but it's nice to have odds ratios and confidence intervals for those as well. And when I do that, I just get a few more columns over here. Now you can ignore this one because it's for the intercept, we don't expect anything particular there. It's the rest of the ones that we're interested in. And you can see, for instance, here, this second to bottom one, this is relaxing, creative, minus temperamental and uninhibited, we're looking at neuroticism, which has to do with kind of having a lot of mood swings or also getting irritable. And we have a significant association here, the odds ratio 0.731. Remember, the null value for an odds ratio is one, if it's either below one or above one, then you have something going on. And especially if both sides of the confidence interval are on the same side of one, as we see here. But this is all going to be a lot easier to interpret if we get the graphs. And so I'm going to come down here to the estimated marginal means. And now it's going to take a moment because I'm going to put all of them in here and I have to do them one at a time. I'm going to take extra version, put that over here. I'll add a new term, do agreeableness, add a new term to conscientiousness, add a new term to neuroticism, and add a new term and do openness. And then I'm going to close this for right now. And what we're waiting for are all the graphs that are come at the bottom, really pretty graphs, what they are, are lines that show the probability. So we have our three regions, each of which is shown by a different color. So this gray line right here is the friendly and conventional. And by the way, this shows this extra version where the mean is about 50 and it goes down to about 30 up to 70. And so as extra version goes up, there's a much higher probability that that state is in the friendly and conventional, you can see that when extra version is low, it's probably relaxing creative. And the temperamental and uninhibited is just kind of low all the way through on that one. agreeableness, friendly and conventional is really high all the way through, you can see that the temperamental and uninhibited low agreeableness, so they're a little cranky there. As it comes down, it comes less likely that they are one of the temperamental and uninhibited because they're more agreeable. Conscientiousness has this amazing crossover where friendly and conventional as conscientiousness increases friendly and conventional, the probability of a state being friendly and conventional increases dramatically. And we have the exact opposite for temperamental and uninhibited, much lower levels of conscientiousness and it doesn't seem to really figure into the relaxing creative states. And then neuroticism with this really peculiar huge crossover. This is temperamental and uninhibited as neuroticism levels get higher, relax gets low, and then we have a funny little peak here for friendly and conventional. And then openness. We see that the friendly and conventional as openness increases, they start out on the low end and then it drops off and the other two pick up. So there's a trade off there. And so this is a really neat way of seeing a visualization of the probabilities and how each factor goes into determining whether a state falls into one of these three different categories. And this is probably how you're going to get the most information and the most insight into your data is through these marginal mean graphs. But you also get an idea for which ones really matter overall by looking at the calculations and the numerical summaries in the multinomial logistic regression.