 Multi-level-modellinen terminologia on yksinkertaisesti yksinkertaiset. Niin, että se on yksi pari kertaa uusia kertaa, joita on käytössä multi-level-modellista. Onneksi, että pitää myös yksinkertaisuudesta, mitä on randominen effekt ja mitä on kertaa. koska nämä yksinkertaiset olisivat yksinkertaiset, joilla olisivat yksinkertaiset, mitä kirjoittavat nämä modelissa. Ja myös, että randomipäivät ja fiksipäivät ovat käyttäneet yksinkertaiset erilaiset jälkeen, kuten on, mitä literatuurissa olisivat yksinkertaiset. Tämä videossa järjestelmät yksinkertaiset erilaiset erilaiset randomipäivät ja fiksipäivät yksinkertaiset. Let's start with the random effect and fixed effects. What are those? And let's take a look at the basic recursion model. So we have a y, the dependent variable, that is a linear function of the explanatory variables x, multiplied by recursion coefficients b. And then we have the error term u here that presents variation that is not explained by these predictor variables x. This model has a fixed part and a random part. The fixed part is the data and the recursion coefficients and the random part is just the random variation around the recursion line. So let's take a look at what this fixed part and random part are. The fixed part gives us the expected value and can be used to predict. So using the fixed part we can calculate a specific value for each observation. So the key here is that the fixed part, we have specific values for the recursion coefficients, we have specific values for the x's and we can calculate a specific predicted value for each of our observations. Then the random part on the right is uncorrelated with the fixed part. So that's an assumption and explains the variation around the recursion expected value. So whereas in the fixed part we can predict a specific value here in the random part, we can just say that the observations vary around the predicted value but we can't give any specific value for any observation based on this model. So that is just variation that we estimate. To be more precise, the random part, we don't estimate the specific value but we estimate the distribution. So normally we assume that the u, the error term in the Rikason model is normally distributed in which case this estimating, the u simplifies to estimating the error variance of the model. We could use other distributions as well with more parameters but normally we just use the normal distribution in which case we estimate this distribution by estimating its mean. So the random part is variation that we estimate, the fixed part specific values that we estimate. Let's take a look at how this relates to multi-level modeling because this really, the difference really becomes relevant only when we add more levels to the data. So here is the basic setup from multi-level model. See we have these indices so i is an individual, j is a cluster for example, i could be an observation, j is a person and we are repeated observation of its people or i could be a person and j could be a team so we have individuals nested in teams or i could be a company and j could be an industry so we have companies nested in industries. The level one equation is a normal regression equation with a catch. So we have the y that depends on the x's and we have betas that are regression coefficients. In the multi-level model this level one equation is like a normal regression model. What makes it multi-level is that we also have this level two equation here and we say that these level one coefficients are functions of level two variables. In this model we don't have any level two predictors that would predict the beta zero j and beta one j but we just have these gamma zero zero gamma one zero which are fixed effects and then we have these random effects u zero j and u y j. So we have three random effects in the model. We have the variation around the regression line, the level one error term. We have random intercept and we have random slope and this same kind of modeling approach is used also in panel data where we often have at least a random intercept model. If you read about random effects regression analysis then that could refer to having a random intercept in the model for example. So these are random effects. They are variance components. We estimate variances. We don't estimate specific values. The reason why we estimate variances is that we assume that these are normally distributed. Also other distributions could be used. This same model can be expressed in a single equation format. So we just write the equation for y as a function of these gammas from the level two equations and the absurd values and the error term from level one equation. It's called a mixed model because it has a fixed part and a non-trivial random part. So normally we don't refer to a regression model as a mixed model because there's just one error term but here we have a random part. We have three random effects that we estimate from the data and it's called a mixed model because it has this fixed part and a random part. So important things, fixed effects belong to fixed part. Random effects belong to random parts. Fixed effects are specific values that we can use to calculate predicted values for each observation and the random part is just variance components. We don't estimate specific values. We just estimate how much the case is vary. The fixed part and the random part are almost always assumed to be uncorrelated and that's called the random effects assumption and that will be explained in another video.