Welcome to our third workshop and this time we will be talking about multi level analysis. This is the session one, in which we will be introducing you to multi level analysis. And we'll have the session two in which we'll actually get our hands in the data and run multilevel models. This should be really fun and you'll see that's not that complicated. Once you get the concept of multilevel analysis, then you can play around with your dataset, run different models. And keep in mind that you can have mediation models with multilevel analysis. You can have conditional interaction effect models with multilevel analysis. For simplicity and the purpose of this workshop, we are keeping it to the direct effect. So we are looking at the direct effect of our independent variable to our dependent variable at multilevel of observations, okay? So we can have different levels. And this will become more clear to you as we move through our sessions. So this is the agenda for today. We will start off with this question: what are multilevel models? And then we address the second question, why is multilevel analysis important for management scholars? And then we'll start talking about some more technical things, like Rwgs, ICC1, ICC2, and then we will also dive into the equations. And some people are more visual. They like graphs. Other people like numbers. So in this particular session in which we are introducing multilevel analysis, we will be doing both the visual and also the equations. And another terminology that you may hear about to refer to multilevel analysis is HLM, Hierarchical Linear Modeling. Usually, they are used to mean the same thing. In general, my understanding is that HLM Is a tool that you can apply to read multilevel analysis models. So let's start talking about multilevel analysis. Let's try understanding what is this thing. So usually when we refer to multilevel analysis, we are implying that parameters can vary at different levels. Just to give an example, okay, so schools would be our level 2 variables in the model and the teachers level 1. So the teachers are embedded in the school and the students are embedded in classes. So there is this dependance in the higher level that you are talking about. Remember, when we are running regressions, one of the assumptions is this independence of the observations. But now because the students are embedded in the classes, that independence has been violated. If we bring this concept to organizations, we have departments embedded in firms, we have employees embedded in departments. And we have days embedded in employees. So for example, you may have one leader managing for 5, 10 followers. So those followers are embedded in that particular leader. The observations of the followers are not independent. So you needed to take that into consideration, when running models. It could be that the leader is extremely extroverted, and that has an effect on how these followers behave. It could be that the leader is more introverted, and that could also have an impact on this other followers would behave. Another thing that's important is that we can actually run models. And to take into consideration daily observations. And those daily observations would be embedded in the individual. For example, you can measure mood. We can have positive mood on Monday, negative mood on Tuesday. Perhaps Friday you are more in a positive mood because the weekend is just over there but all those observations are embedded in the individual. And that individual has his or her own personal characteristics. In general he is a more positive person. In general, he is a more negative person. So, all of those characteristics also influence the daily observation. So it's important to take into consideration this nesting, this embeddedness of the observations. We can have models that go from level 1 to level 2 to level 3 to level 4. So there is no problem at all with having multiple levels. The problem, if you will, becomes from in a statistical standpoint because we have low power as we move up, because the number of observations then is what we have at the highest level of the data set possible. And we can run models in which the independent variable is at level 2 and that influences our dependent variable at level 1. For example what I mentioned, the leader influencing how followers behave. You can have independent variables at level 1, independent variables at level 2, influencing the dependent variable. In this case, usually you'll have a level 2 variable that you can use as a control. So we are not interested in the effect of the leader or the employee performance, but we are interested in the job satisfaction of the employee influencing the performance. But because these employees are embedded in the leader, we need to take that into consideration. And also, we can test for interactions at different levels of analysis. In this case, let's say that's the leader interacts with the follower job satisfaction to predict follower performance. Notice here that we don't have level 1 variable predicting level 2 variable. We don't have follower satisfaction predicting leader behavior. And the reason is because we don't have, we think individual variance to be explained if our dependent variable is at level 2, okay? This is more technical, we can address that later in one of our sessions. So, why is multilevel analysis important? The reason here, is that, we can theorize about cross level effects. As I describe it, the effects of the department culture, or the leader on employee performance, or the effect of leadership on creativity. We can also theorize about longitudinal effects. Do you remember the example I gave? Employees are measuring mood on a daily basis? So that's a longitudinal design. We can model that as well. And statistically what's important is that we are partialling out our clustering effects, our nesting effects. That fact that is unique to that particular group of people. And if we don't do that, we may have mistakenly small standard errors. Because how we are violating this assumption of independence of the observations. I added here a few equations. So if you want to go through those equations by yourself, you can do that. This is just a piece of information for you to run some models or to use this variables or equations, to get to this conclusion that, well, yes, we are getting is more standard errors. If we don't adopt multilevel analysis. There is this, I mean, in 1998 Chan put together this idea of different models for multilevel analysis. We have the additive model in which we just add the observations of the employees. Let's say the followers of that particular leader. So, we add those observations and then that's another additive model. The direct consensus model, we need it to show that there is some agreement among those followers. So that is the direct consensus model. And then we have the reference-shift consensus model. So think about the reference shift when we are changing from the individual level to the team level. And that happens for example, with let's say performance. Are you looking at the individual performance or are you looking at the team performance? You can report on my performance or you can report on the team performance. You are changing the reference. And you have also the dispersion model, and there is a lot of opportunities here with the dispersion model. With the dispersion model, we are looking at the variance in that particular group, okay. It could be that the mean is important, but also the variance can provide you information about how individuals behave in that particular group. In the process model, in which we are theorizing here, that the process at different levels of analysis, are exactly the same.