It's got a fixed part (which is the intercept and the coefficient of the explanatory variable times the explanatory variable) and it's got a random part, so that's this u j + e ij at the end. The random intercept model has two parts. But like the single level regression model, we've included the explanatory variable so we are controlling for that. So we are going to be able to see how much variance is at each level. So the random intercept model has got 2 random terms, just like the variance components model so we've got a variance of the level 1 random term here …a variance of the level 2 random term here ![]() So what we do is we combine the variance components and the single level regression model and we get a random intercept model. And so if we fit that model, we won't actually find out how much of an effect school has on exam score after controlling for intake score and since that's what we're interested in, that's a problem. The second problem, is that that model doesn't actually show us how much variation is at the school level, and how much is at the pupil level. And we saw that a bit in the first presentation about different analysis strategies. So the first problem, of using this model with clustered data, is that we'll actually get the wrong answers, so for the standard errors, our estimates will actually be wrong. And clustered data are data where observations in the same group are related, so, for example, exam results for pupils within schools, or heights of children within families. Well usually, if we want to control for something, we do that by fitting a regression model, like this, but when we have clustered data, using this single level model causes problems, as we've seen. So we'd actually like to control for the previous exam score so that we can try and look at just the variance that's due to things that have happened whilst those pupils are at that school. ![]() So this 20% variance at the school level could actually be caused, partly or wholly, by the fact that the pupils were actually different before they entered the school. But can we really interpret that as meaning "20% of the variance in exam scores is caused by schools"? Because schools differ in their intake policy and in the pupils who apply. So for example, suppose that we have data on exam results of pupils within schools and we fit a variance components model, and find that 20% of the variance is at the school level. But what if we want to look at the effects of explanatory variables? We've seen how to fit a variance components model and that lets us see how much of the variance in our response is at each level. ![]() Covariance matrix for a random intercepts modelġ) Random intercept models: What are they and why use them? Explanatory variables.Covariance matrix for a single level model.Random intercept models: the correlation matrix.Random intercept models: Variance partitioning coefficients.Random intercept models: Hypothesis Testing.Random intercept models: Adding more explanatory variables.Random intercept models: Research questions and interpretation.To watch the presentation go to Random intercepts models - listen to voice-over with slides and subtitles (If you experience problems accessing any videos, please email Random intercept models: What are they and why use them?.Random intercept models A transcript of random intercept models presentation, by Rebecca Pillinger
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |