 Tämä video explained the basic idea of structural recursion models that are sometimes referred to as structural equation models in the literature. What is a structural recursion model? This technique is used in, for example, the MESQUIR & LASERINI paper. They explain the technique that it's a combination of a factor analysis and a path analysis. A path analysis is basically a recursion analysis where there are multiple equations. For example, when you do a mediation model using the simultaneous equations approach, Tämä al from the path analysis. The path analysis is just regression with observed variables except that they are more than one dependent variables. And factor analysis is the analysis where we check what different indicators have in common and perhaps whether we can group those indicators and consider them as measures of the same concept. So SCM or structural regression combines these two analysis approaches. että mitä SCM on ja mitä se tapahtuu, voimme esittää basic recursion analysis modelin. The basic recursion analysis model makes the important assumption that the X1 and X2 here are measured without any measurement error. The X1 and X2 are the quantities of interest instead of being measures of the quantities of interest. X1 is of direct interest instead of being a measure with possibly some error in there of some concept that we can't measure observed directly. So recursion analysis makes that assumption if the assumption of no measurement error fails, these recursion coefficients beta1 and beta2 will be inconsistent and biased. Then we have the factor analysis model. The idea of the factor analysis model was that we have a set of indicators and then we ask what these indicators have in common and what they have in common is one factor. In converter factor analysis we ask, do these indicators represent one factor or not, the computer gives us an answer in an exploratory analysis, which is not part of structural recursion model, the computer finds the factor. So we define a factor structure here and then we estimate it. So that's part of structural recursion model. The idea of structural recursion model is that we take these variables, these analysis approaches and we combine them. So we have a recursion analysis model here, where instead of having the indicators that are possibly contaminated with measurement error, we model a regression between latent variables x1, x2 and y and then we add the factor analysis directly to the model. So we have a combination of factor analysis and a regression analysis between the factors in the factor analysis. This is a clearly more complicated concept than simply applying regression analysis on scale scores. This model has two parts. This inner part here with the latent variables is referred to as the latent variable model. Some people call this part of the model as the structural model, but that's a bit misleading because these measurement relationships here are also equally structural in terms that they have theoretical causal interpretations. Then the outer part linking the measures to the factors is called measurement model and this is uniformly accepted definition. So whenever anyone speaks about or talks about measurement model it means the part that links the latent variables to their indicators. So that's a big model and it's a complicated model. This is clearly more complicated than taking a sum of indicators and using regression analysis. So why would you want to use a more complicated analysis approach? The structural regression model approach has a couple of advantages over regression analysis with scale scores. Let's take a look at this example. So we have these concepts A and B represented by these two latent variables and then we have indicators here. The indicators variances here consist of variance due to the concept A and variance due to the concept B plus all these different sources of measurement error variance. So we have random noise E and then we have some item uniqueness here that is not related to the concepts B or A that these indicators are supposed to measure. When we take a sum of these indicators of A, sum of these indicators of B, then all the sources of variation including the measurement errors will be in the sum. So we just take everything together, we take a sum and we have this combination of mostly variation of interest but also some variation that is not of interest. When we estimate this regression coefficient beta here, then the estimate will be too small, it will be attenuated and it's going to be inconsistent and biased. So what can SCM bring us that will help with this problem? The idea of SCM or structural regression model is that instead of taking a sum of the indicators, we estimate the factor model and a regression analysis between the factors. So the idea of a concrete factor analysis was that we take the variation of these indicators apart. So for example the B1, B2 and B3 indicators variation is modeled as being due to the factor here and also due to these measurement error components here. Because we have now these factors that are presumed to be free of measurement error, the correlation between the factors, the beta, is going to be correct. The advantage is that structural equation or structural equation model corrects for measurement error. This correction comes with certain assumptions that I will explain a bit later in this video, but this is the basic idea. If your model is correct, then measurement error is controlled for. The practical outcome is presented here. So this is a paper from a paper that I have written and we simulated a data set from two concepts that we are measuring each with three indicators. So we have six indicators together. Total, we take a sum of the first three indicators, we take a sum of the indicators 4, 5 and 6 and we calculate the correlation between those two sums. We vary how much the concepts correlate in the population. We vary it between 0.0 to 0.6 and then we replicate this analysis 300 times. We estimate the correlation between the, they are using SCM or using our sum scales, sum of the indicators and recursion analysis. We can see here clearly that when we take a sum of the indicators and when we apply recursion analysis, regardless of whether we take a sum of indicators or we use weights that are maximized, the reliability of the indicators, there is not much difference. These correlations here will be too small because there is any way measurement error ending up in the sum of those scale items. In SCM, because we model not a sum correlation between two sums, but a correlation between two factors, this effect is unbiased. We can see that the effect here, the estimates here, or whether it's correct, so that's the true value here and it's roughly equally, roughly normally distributed around the true value. SCM provides you this small advantage in precision and that's a good thing if you can apply it well. There's also another advantage in SCM that I have demonstrated in earlier videos and it's testing the model. So we had the confronter factor analysis example model. We have the chi-square test that tells whether the factor model fits the data. If it doesn't, you have to do diagnostics and then we have the mediation example where we also have the chi-square test that tells whether the full mediation model fits the data well or not. The idea of the chi-square test again is to test if the constraints implied by the model are close enough to the correlations in the data so that we can say that these differences here are only due to chance only. And we want it here to not reject the null hypothesis because rejecting the null hypothesis that these are discrepancies in the implied correlation and opposite correlations are due to chance only means that we have to declare or we have to conclude that the model is not correctly specified and we need to do some diagnostics to understand why. So this is the second advantage in structural regression models. It allows you to test whether the model fits the data. Regression analysis doesn't allow you to test the model. It only allows you to assess how much the model explains the data. It doesn't allow you testing whether the model is correct. So that's the second big advantage. There are also other advantages in SCM such as we can model relationships that go in the both ways. So recent provocation for example but that's more advanced and these are the reasons why people typically apply structural regression models or SCMs instead of regression with some scales. There is this slippery slope to SCM. So whenever you have a scale with multiple items you should apply a factor analysis. So every time you have a survey instrument for example you get data, then you run a factor analysis. You must do that to, for example, calculate coefficient alpha to assess reliability. Then if you do an exploratory factor analysis then in most cases actually the confirmatory factor analysis would be better because it's a bit more rigorous. It allows you to test whether the model is correct and also in cases where exploratory factor analysis cannot find your solution then it's possible that confirmatory factor analysis still works because you give the solution and you don't require the computer to find it for you. But then if you apply confirmatory factor analysis then instead of taking the sums of indicators and using those as regression analysis you really should be using structural regression model for rigorous and it allows you to control for measurement error and it allows you to do overall model testing. So every time when you do a survey or any other multiplied measurement you must do a factor analysis. If you do a factor analysis then it's better to apply CFA. If you do CFA then it's better to apply structural regression model than to do regression analysis with some scales. So this is all good. But there are reasons why you probably shouldn't apply structural regression models as your first analysis technique. So if structural regression models are so much better than regression with some scales why would I not use it? So that's the question. There are good reasons. There are reasons not to use structural regression models. The first reason is that it's more complicated to apply. So that has two implications. The first implication is that if you are a beginner and you want to get your first paper for a first conference publication out then doing that with regression and some scales it's easier and you can get more done with regression analysis than SCM. In SCM it's possible that when you give the computer data the computer doesn't give you any results at all. That doesn't happen with regression analysis. If it happens with SCM then you need some expertise to be able to get the model to work. There is also another reason related to the complication of application. It is that it's better that if you know a tool well like a regression analysis that is slightly suboptimal so regression analysis can deal with measurement in the same way that structural regression models can. It's nevertheless better to use that technique than a more complicated technique that you may not understand very well. So it's better to have results that you know are done correctly using a slightly suboptimal techniques than having results that are done with the state of the art technique but you are not sure whether they are done correctly. So I would encourage you to first do regression analysis really well and only after you know that then move to the more complicated models. SCM also has some statistical issues. So SCM requires that the model is correctly specified. The idea of correct model specification is that if your model is not correct, the SCM results can be highly misleading. Motor correctness means that the measurement model must be correctly specified so each indicator must belong to those factors that they say that they do and then all this causal relationship between the factors must be correctly specified. Otherwise, the results can be very misleading. Then what helps you here is the chi-square test. If your chi-square test rejects the model, then that means that something is incorrect. The model is incorrect for the data in some way you have to understand why and you have to do diagnostics. That requires some expertise to do and unless you do that, then the results could be widely misleading. It's probably easier to get misleading results than structural recursion models than recursion analysis with some scores. My personal take is that if you know how to use structural recursion models well, you probably always use that as your own the main analysis technique instead of recursion analysis. Then again, I have the impression that most people who apply structural recursion models or structural recursion models probably don't understand these techniques well enough to use them in a way that we can rely on the results to be correct. That's a big problem and for that reason I recommend that people start with recursion analysis instead. Finally, if you want to get started with recursion analysis, study a good book. There are so many different ways that can go incorrect and my favorite SCM book is Klein's book Principles and Practices in Structural recursion modeling. He concludes his book with this nice chapter of how to fool yourself with SCM and then he had at least 52 different things that can go wrong and you need to know these things really before you apply this technique because otherwise you will have problems with the technique and your results may not be trustworthy. But it is a technique worth learning in the long run because it allows you to do things that you cannot do with recursion analysis.