Kaz's SAS, HLM, and Rasch Model HLM brief description
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Survey data in the social sciences are often structured hierarchically. In the case of PISA, for example,students are nested within schools, which are nested within countries. Hierarchical linear modeling (HLM) is a specialised regression technique designed to analyse hierarchically structured data (Goldstein, 1995; Bryk and Raudenbush, 2002). With traditional regression approaches, such as multiple regression and logistic regression, an underlying assumption is that the observations are independent. This means that the observations of any one individual are not in any way systematically related to the observations of any other individual. The assumption is violated, however, when some of the children sampled are from the same family, or the same classroom or school. When the assumption of independence is violated, the regression coefficients can be biased, and the estimates of standard errors are smaller than they should be. Consequently, there is a risk of inferring that a

relationship is statistically significant when it may have occurred by chance alone.

In addition, the interest from a policy perspective is usually in the relationships within schools,whether these relationships vary among schools, and if so, whether the variation is related to school characteristics. For example, the average level of students’ engagement (either sense of belonging or participation), and the relationship between engagement and socio-economic status, may vary among schools within a given country. The policy analyst may be interested in whether schools with high average engagement and more equitable engagement have smaller class sizes, different kinds of instructional techniques, or differing forms of school organisation (Lee et al., 1990; Raudenbush and Willms, 1995).

The basic idea underlying HLM is that there are separate analyses for each school (or the unit at the lowest level of a hierarchical structure), and the results of these analyses – usually regression coefficients– become the ependent variables for analyses at the school level (or at the next level of the hierarchy). Willms (1999b) provides an introduction to HLM for the non-statistical reader, with a general discussion of its applications to educational policy issues. Goldstein (1995), and Bryk and Raudenbush (2002) provide comprehensive texts on HLM that can be understood fairly easily by those familiar with basic regression analyses.

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