Richard Erickson explains hierarchical models in R, showing why standard regression fails when data is nested (students in classrooms in schools) and how mixed-effects models pool information across groups instead. The course covers fitting these models with lme4, interpreting results, and extending to repeated-measures data.
Chapters
Hi, I'm Richard Erickson. I'm a data scientist and I'll be teaching you about mixed effect models. Data can have several types of structure, including being nested within itself, thus making the data hierarchical. During this course, you will learn how to analyze this Data using the LME4 package. We will also go over how to plot this data and describe the results. First, we will go over the basic parts of a mixed effects model and see how it may be applied to student test scores. Second, we will learn how to apply and interpret the results of a linear mixed effects regression or model. Third, we will learn how to use a generalized linear mixed effects model. Lastly, we will apply mixed effect models to time series analysis as part of a repeated measures analysis. Why do we use a hierarchical model? Sometimes we have data that can be nested within itself and our observations are not truly independent. For example, we might have a set of student test scores where each student has her or his own test score. But student performance can vary because of classroom level factors such as teacher quality or school level factors such as building condition. Hence, one might ask, are students really independent from other students in the same classroom or school? The answer is probably not. Additionally, what if each classroom has a different number of students? For example, maybe the fifth grade has 30 students while the third grade only has five. By chance alone, the third grade test scores are more likely to have high or low outliers because of the law of large numbers. By treating classrooms as a random effect within the model, we can pool shared information about the means across the classrooms within the same school. Lastly, what if we revisit the same group of students year after year? In this scenario, our observations are not independent across years. A repeated measures analysis, another example of a hierarchical model, allows us to correct for this. We'll revisit this in Chapter four. In fact, all three of the problems I just described occur somewhat often in statistics. These models go by different names nested models like the classrooms nested within schools in our example, hierarchical models because the data has, not surprisingly, a hierarchy and multilevel models because we have two or more levels of interest. Also, in a regression framework, the multilevel covariate can sometimes be called a random effect that pools information across groups. A model with both a fixed effect, such as the standard linear regression and a random effect is called a mixed effect model. Last, some models can account for resampling the same individuals or groups over time. These models are called repeated measures or paired tests. In the following exercise, we'll explore a data set of test scores collected from elementary school children between kindergarten and first grade to assess how their math knowledge improved. The data is a subset of a national level exam given across the United States and is from a book by west and collaborators. The data set contains several variables at different levels this individual student level, the classroom teacher level, and the school level. At the end of this chapter, we will fit a multilevel model to the data, but first, let's explore the data set. The purpose of the next coding exercise is to show you that linear models do not always produce intuitive results and that it is necessary to add a new technique to your modeling toolbox. As you can see on this slide, the data contains two levels of data, classroom and student level data. Now let's go look at the school data.
