 Another surprising but useful option in Jmovi for analyzing frequency data and associations between them is log linear regression. Now what this is, is a form of regression where instead of trying to predict a person's score on a quantitative or continuous outcome variable, you're trying to predict the number of observations, the frequencies within cells of a contingency table. It's actually, now it's a powerful method, although it can be confusing to read the output. My goal here is simply to show you that it's easy to put these together in Jmovi. If you decide that this is something you need, then you're going to want to consult your other resources on how to design and how to interpret a log linear regression. But calculating it in Jmovi is very simple. Let's do this. Let's look at the association between two of the categorical variables in the state data. Let's look at psych regions where the 48 contiguous states of the United States are classified according to their personality characteristics, whether they're friendly and conventional, temperamental and uninhibited or relaxed and creative. And then let's also look at whether that state currently has a Republican or Democrat governor. It's not the most compelling, but it's a useful comparison. What I'll do is I'll come here to frequencies and come down to this last option, which is log linear regression. When I get that, it asks me for what the factors are. Now please note it's not saying which one is the predictor and which one is the outcome because the model really is kind of symmetrical. It doesn't matter. It's just trying to put together the entire table without necessarily saying this one causes that one. So what I'm going to do is I'm going to come here and get psych regions. I'll move that over. And then I'll also get governor and I'll put that over because I have a table that gives one rope or observation. I don't need to do the counts, but this is my initial result. Let me scroll this over a little bit. It's kind of a big table, but you can see, for instance, that we have an intercept at the top. I'll close this so we can look at the whole thing at once. You can see that what we have here are a collection of coefficients. This is like a regular regression, and we have the estimate the actual predicted value for that coefficient. The standard error, the z score, which is this one divided by that one, and the p value that goes along with it. Now, we aren't surprised that the intercept is significantly different from zero. The two for psych regions are not significant. Democrat versus Republican, we have a major effect there. And then we have a nearly significant interaction for these two regions, relaxed and creative versus friendly and conventional, by Republican versus Democrat, in terms of trying to reconstitute the frequencies within the table. Now let me click on this and let's look at a couple of our other options. By default, it gives us the one factor for psych regions, the other factor for governor and the interaction, which is what we want. That gets us a more nuanced model, even when we're dealing with a really kind of small three by two table. In terms of the other options, we get to pick our reference levels. So let's say we can pick instead, temperamental and uninhibited, and that's going to switch the way the table over here is displayed. And if we want to put Republican as the default value for governor, we can do that as well. And that's going to change the way that some of these values are calculated over here. So now you can see, for instance, we have this value up here, friendly and conventional versus temperamental and uninhibited, that's now statistically significant. And this value here that compares the two with Democrat and Republican, it's changed a little bit. So overall, it's going to give you the same values, it's just going to parse it out differently. You have several choices on the how you evaluate model of it, we'll just leave it with the standard deviance and AIC, as well as McFadden's R squared, those show up here in the table at the top. Actually, I am going to add the overall model test, that's going to give us a few more columns here, that gives us a chi squared test and allows us to do an inferential test for the entire model. And here we have a chi squared value, and we can see that there is a significant deviation between the observed and the expected frequencies or predicted values. We can also come down and get some of these other values, say, for instance, a confidence interval for the estimates. And that's going to add another two columns over here, in case you want a little richer picture for the values you have. And then we can come down and we can get estimated marginal means. Now I find it handy to do these, this goes as charts, I'm going to add a new term and I'll do governor right here, just click that in. And then that's going to give us marginal means plots, and this is probably the single best way to look at the results of the log linear regression is to come down and see these in terms of the counts that we get for psych regions, along with their confidence intervals, and the confidence intervals for the governor. And so there's more that you can do with this, there are some important distinctions to be made when conducting a log linear regression. But the amazing thing is that to movie includes this that it's an option for a free open source and user friendly program. And so depending on the nature of your data, you could do either the chi squared test of association or independence, or you could do something a little more sophisticated with the log linear regression. And the great thing is that the job of gives you the choice of one or the other.