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  • The history of hierarchical linear models generally traces its roots back to the work of Robinson (1950) in recognizing contextual effects. The discovery that Robinson made is sometimes thought of as the “frog pond” theory and is fairly simple to relate. Suppose that a researcher was conducting an analysis on environmental factors affecting the weight of frogs. And also suppose that two of the frogs being analyzed both weighed 500 grams. However, the first frog that weighed 500 grams was drawn from a pond where it was the largest frog in the pond. The second frog that weighed 500 grams was drawn from a lake where 500 grams was the weight of the average frog for that pond. In a typical ordinary least squares (OLS) analysis, the researcher would have no way of honoring the pond nesting structure for these two frogs and would then erroneously assume that the environmental factors affecting frog growth were the same regardless of which pond was home to the frog. This same problem often presents itself when researchers are analyzing data obtained from school research. For example, suppose that a researcher were to try to run a regression analysis in which student grade point average (GPA) scores were used to predict performance on the Stanford Achievement Test (SAT). It stands to reason that, within a given school, GPAs might be good predictors of SAT scores where higher GPAs correlate with higher scores on the SAT. However, across schools, the relationship between GPA and SAT may be dramatically different. Whereas in a low-performing school, a student with a 4.0 GPA might score only a 1,000 on the SAT, a student with a 4.0 GPA in an elite, high-performing private school might score a 1,600 on the SAT. This happens because GPA scores are not independent of the school from which they are drawn. This problem of independence of observations is often a factor when collecting data in schools, yet until the development of hierarchical linear modeling (HLM), no methods for dealing appropriately with such data existed. (PsycInfo Database Record (c) 2024 APA, all rights reserved) (Source: chapter)

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