 One of the most amazing things about Jmovi is that this free, simple, friendly, open source analysis package includes some incredibly high end analyses. In fact, the most surprising one for me is the inclusion of confirmatory factor analysis, something that for instance not even possible to do in SPSS if you're on a Macintosh. And if you're doing it in other programs, it gets really, really complicated, really fast. And this is by far the easiest and fastest and cheapest way to do a very sophisticated procedure. What confirmatory factor analysis or CFA is, is an attempt to take data and say we know how the data is supposed to combine. We know that these 10 variables should go to this factor. These 10 should go to this other factor. It allows you to specify those factors and see how well your data fit your hypothesized factor structure. It also allows you, by the way, to compare the fit of factor structures across two different samples. That's a different thing. But let's go and take a look at how to set up a confirmatory factor analysis in Jmovi. We come to factor, and we come down here to confirmatory factor analysis. Now I am working with the big five data set that you can download from the sample files on data lab dot CC. And what I have are 50 different variables with 10 each for the five different big five personality factors, extraversion, agreeableness, openness, and so on. And what we have to do is we have to tell Jmovi which variables go together and what the name of that factor should be. So for instance, E1 through 10 come first, I need to come here and say that that is extraversion. So I just click on it and type that. Then I come and select these 10 and you can see the names of highlighted over here. And I put them in right there. After that, N1 through 10, which is for neuroticism. So I'm now going to add a new factor. We scroll down a little. We'll see if I can spell neuroticism correctly. And we select the 10 variables and put them into neuroticism. There they go. We're going to add another factor because there's five total. And this one is agreeableness. I'll select those variables. Put them in. After that is C, which is for conscientiousness. Scroll down here. Conscientiousness. Think I got that right. C1 through 10, feed those over. And then the last factor is O for openness. Come down to the bottom and type in openness. And put those 10 in. And now we've specified the important part of our confirmatory factor analysis. We've told Jmovi we've got five different factors. We said what the names are and we said which variables go with which. What's interesting is we don't even have to tell it which ones are positively associated, which ones are negative. We don't have to look at the reverse-scaled items. We're going to be crunching away on this for a little while because this is a pretty mathematics-intensive option. But let's take a look at a few other things we can do. Now, if we had specific other variables that contain what are called residual covariances, things that don't necessarily go into the factor but help explain some of the leftovers, we could specify those. And what you do is you would say you take this one variable and then you specify another one for the residual covariance. We don't have that, so I'm going to ignore that. Under options, we can change how we deal with missing values. We only have a very small number of missing values. I'm just going to leave it like this. We can do constraint factor variances equal one. That sounds good. Under estimates, we can look at a few different ways of calculating results. I'm going to do a standardized estimate right here. I'll close that. Under model fit, we have several choices. CFI stands for comparative fit index. TLIs for the Tucker-Lewis index. RMSEA is for root mean square error of approximation. And this over here is a chi-squared test. We've seen that in several other places. I'm going to leave those defaults right there. And then the additional output, we've got a couple of really nice things. One is the residual observed correlation matrix and what Jamovie's going to do is it's trying to reconstitute a correlation matrix based on what I said how the variables went together. And so I'm going to ask for that. And it's also going to highlight any residual values that are greater than 0.1. It's going to say this is where the model is off more than in other places. And then finally, I'm going to ask for a path diagram. And then we'll just wait a minute for Jamovie to finish crunching all the data and see what it has for us. I actually paused the recording for a minute because it takes a while to get through all this calculation. But here's what we have. We have our factor loadings where we said extraversion is the first factor and the indicator is the name of the variable that we say goes into that factor. The estimates are like regression coefficients and they say multiply this number against the variable to get the factor loading. We have standard error z-scores, the p-value, and by the way you can see that everything here is highly significant. And then finally the standardized estimate, again like a z-score and that's a good way of assessing the relative contribution of the variables. We have the same thing for neuroticism, agreeableness, conscientiousness, openness and we've got a lot of numbers there. We come down to the factor estimates. It parses it up a little bit differently where it's looking at the connection between the factors in terms of extraversion as a function of these other things. The model fits an important one. This is where we have things, again the comparative fit index and so on. But I like these two things at the end. I'm going to close this so I can make a little more space on the screen and open this up. I'm not going to be able to get the whole thing. This is a really, really big correlation matrix. These are correlations, again from negative one which means a perfect negative linear association to zero which means no linear association to plus one which is a perfect positive association. And this correlation matrix is reconstituted based on the way that we said the variables went together. And these are residuals which means compared to the actual correlations which it computed in the background this is how far off our reconstituted matrix is. The important things here are the ones in red and that says we're off a little bit on that combination of variables and I can scroll down and you can see this thing's really kind of huge. And so you can take that as an indication of how close or how far away you are. If you want to go back to the fit indices I can tell you that these numbers indicate that our fit is adequate. It's kind of okay. It's nothing spectacular but it looks like we're not too far off. Maybe we would want to see which variables are loading best which ones seem to be contributing the most to the fit but we may have a go ahead here in terms of confirming the structure that we think we have. And then the last thing is the path diagram and it's not putting the coefficients on this but it simply says these are the associations. We say that we have five major factors extraversion, neuroticism, agreeableness, conscientiousness and openness to experience. And it says that we have all of them associated with each other and that each of them feeds into its own 10 variables and so that is in a nutshell. This is the basic functionality of confirmatory factor analysis again a very sophisticated procedure that a lot of programs don't let you do at all and it's one of the really a special present from Jamobi that it makes it possible to do this. You're going to have to do more research on how it all works and how to interpret the results but the fact that you have a tool that can do it and that does it so easily is a huge boon to researchers everywhere.