Suppose that a researcher wants to conduct Hierarchical Linear Modeling on educational data. Hierarchical linear modeling is a kind of regression technique that is designed to take the hierarchical structure of educational data into account.
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Hierarchical Linear Modeling is generally used to monitor the determination of the relationship among a dependent variable (like test scores) and one or more independent variables (like a student’s background, his previous academic record, etc).
In Hierarchical Linear Modeling, the assumption of the classical regression theory that the observations of any one individual are not systematically related to the observations related to any other individual is violated. This assumption is violated in Hierarchical Linear Modeling because this yields biased estimates by applying this assumption in classical regression theory.
Hierarchical Linear Modeling is also called the method of multi level modeling. Hierarchical Linear Modeling allows the researcher working on educational data to systematically ask questions about how policies can affect a student’s test scores.
The advantage of Hierarchical Linear Modeling is that Hierarchical Linear Modeling allows the researcher to openly examine the effects on student test scores when the policy relevant variables are used on it (like the class size, or the introduction of a particular reform etc.).
Hierarchical Linear Modeling is conducted by the researcher in two steps.
In the first step of Hierarchical Linear Modeling, the researcher must conduct the analyses individually for every school (in the case of educational data) or some other unit in the system.
The first step of Hierarchical Linear Modeling can be very well explained with the help of the following example. In the first step of Hierarchical Linear Modeling, the student’s academic scores in science are regressed on a set of student level predictor variables like a student’s background and a binary variable representing the student’s sex.
In the first step of Hierarchical Linear Modeling, the equation would be expressed mathematically as the following:
(Science)ij=β0j+β1j(SBG)ij+β2j(Male)ij+eij. In this first step of Hierarchical Linear Modeling, β0 would signify the level of performance for each school under consideration after controlling the SBG (student’s background) and sex. In this first step of Hierarchical Linear Modeling, β1 and β2 indicate the extent to which inequalities exist among the student with respect to the two different variables taken under consideration.
In the second step of Hierarchical Linear Modeling, the regression parameters that are obtained from the first step of Hierarchical Linear Modeling become the outcome variables of interest.
The second step of Hierarchical Linear Modeling can be very well explained with the help of the following example. In the second step of Hierarchical Linear Modeling, the outcome variables mean the estimate of the magnitude of consequence of the policy variable. In the second step of Hierarchical Linear Modeling, the β0j is given by the following formula:
β0j = Y00 + Y01(class size)j + Y02 (Discipline)j + U01.
In the second step of Hierarchical Linear Modeling, Y01 indicates the expected gain (or loss) in the test score of science due to an average reduction in the size of the class. In the second step of Hierarchical Linear Modeling, Y02 signifies the effect of the policy of the discipline implemented in the school.
According to Goldstein in 1995 and Raudenbush and Bryk in 1986, Hierarchical Linear Modeling’s statistical and computing techniques involve the incorporation of a multi level model into a single one. This is where regression analyses is performed (it has been already explained in the above two steps of Hierarchical Linear Modeling). Hierarchical Linear Modeling estimates the parameters specified in the model with the help of iterative procedures.
