ABSTRACT
Multilevel Linear Modeling/Hierarchical Linear Modeling In this chapter, we introduce multilevel linear modeling, which is often called Hierarchical Linear Modeling (HLM). Although these two terms can be used interchangeably in most cases, we will use the term “multilevel linear modeling” or “multilevel modeling” in this chapter, because we are not using the HLM software program. Multilevel modeling is a complex statistic in which several levels of nested data are considered in relation to one another. By nesting, we mean that several observations are not independent of one another. For example, there may be multiple observations on the same individuals, such that these observations are not independent of one another (observations nested in individuals). Or there may be a set of particular individuals who are found in particular groups or settings (such as schools) so that the individuals are not independent of one another (individuals nested in groups/settings). An example of the first type of nesting is found in Problems 11.1 and 11.2. In these problems, we will examine data from a longitudinal study of physical growth, in which data at four different ages are measured on the same individuals. This illustrates multiple observations nested in the same individuals. Although this problem could be analyzed using other methods (see Chapter 9), we will explain why you might want to use multilevel modeling. In Problems 11.3 and 11.4, we will analyze a slightly different HSB dataset, in which students were nested in particular schools and tested on their math achievement. In multilevel models, differences between the entities in which observations are nested (e.g., individuals or schools) often are not the focus of the study but are seen as random differences within a population of individuals or schools. Yet one cannot ignore the fact that the data are nested within those individuals or schools. In other cases, the variability among schools or persons is of interest, in that the researchers believe they can explain this variability using meaningful variables. Even if you are not interested in the systematic variability between individuals or schools, you might want to explain that variability first before you use predictors to explain the variability in which you are truly interested, much as one covaries out “extraneous” variables in regression or ANCOVA (see Chapters 6 and 8). In many applications in education and the behavioral sciences you need to deal with nested data. For example, you may have a quasi-experimental design, in which different interventions or curricula must be assigned to different sets of existing schools or classrooms, even though students are not assigned randomly to those schools or classrooms. In addition to the effects of the manipulation, you may need to determine whether preexisting characteristics of the classrooms or schools impact the outcome. Multilevel linear modeling enables you to appropriately treat students as nested within particular schools or classrooms and to examine the role of school or classroom-level data, such as class size, gender of teacher, average socioeconomic status of school, or type of school (e.g., Core Knowledge, International Baccalaureate, or traditional) as predictors of the student-level outcome variables. Another common situation is to have many observations on each participant (e.g., in a longitudinal study) and to want to use participant-level data to explain a pattern or growth curve shown in those many observations. It is possible to examine many of these models using the SPSS program Linear Mixed Models. The term Mixed Models refers to the fact that some variables are viewed as fixed variables, and some are viewed as random. Typically, the variables that one is construing as predictors are considered fixed, meaning that the levels of the variable that you measured are the levels in which you are interested. In contrast, random variables are viewed as providing a random sample of the levels of the variable to which one wants to generalize. In multilevel or hierarchical linear models, the levels of the nesting variable (e.g., schools or individuals) are viewed as being random. The various schools or individuals are considered to represent a larger population of schools or individuals. As a result, the Level 1 intercepts (means of the different levels of the nesting variable) are viewed as random as well.
