Hierarchical Modeling form Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

Hierarchical models, also commonly called multilevel models, hierarchical linear modeling, nested models, and multilevel analyses, are structures that consist of multiple units of analysis, one “nested” within the other. This type of model is useful in political science because often the effect of an independent variable on the dependent variable, observed at one level, is influenced by variables observed at another level. For example, household income might affect the amount one donates to a campaign. However, the degree to which politicians practice clientelism across nations, such as giving privatized benefits to certain constituents, may also influence the effect of income on campaign donations. A hierarchical model, in this case, affords the researcher the opportunity to account for variance in individual campaign donations by considering information at all levels of analysis.

Traditional methods of statistical analysis, such as ordinary least squares (OLS), ignore the nested structure of hierarchical models by assuming observations are independent when they are not. That is, OLS assumes residuals to be independently distributed and, to the extent that observations in groups (e.g., voters in nations) share common characteristics, their residuals correlate. Violating this assumption causes the underestimation of standard errors, thus placing the researcher at risk for committing Type I errors. Adding dummy variables to flag a voter’s citizenship mitigates the problem. This allows the calculation of differences in the intercepts between voters of different nations, but it does not allow the explanation of these differences with information in the set of data. Using robust standard errors, which allow residuals within groups to covary, also provides a fix for standard errors, but again, the robust standard errors do not allow one to model differences between groups.

Hierarchical models allow the information in the data set to model the phenomenon of interest as well as differences between groups on intercepts and slope coefficients. Using the example above, campaign donations can be modeled as

where individual i is contained within nation j and is affected by explanatory variable xij (household income). The second level effects of the nation can then be modeled by the coefficients b0j and b1j as follows:

Here the γ-coefficients are fixed parameters, zj is a second-level predictor (the degree to which politicians practice clientelism in the example above), and the δs are the disturbances. The coefficient g00 is referred to as the grand mean and represents the level-2 intercept. This specification allows the researcher to explore the phenomenon in question along with differences in the intercept or slope coefficients, by nation. The model expands to include more independent variables or, if necessary, to account for variables measured at higher levels of aggregation.

Hierarchical models provide several advantages to researchers, but there are weaknesses worth noting. First, the stability of any given hierarchical model decreases as more predictors are added. Second, multicollinearity is a more acute concern in a hierarchical model relative to an OLS model. Last, hierarchical models are typically estimated using either restricted maximum likelihood or empirical Bayes/ maximum likelihood; both are computationally intensive.

Bibliography:

Gelman, Andrew, and Jennifer Hill. Data Analysis Using Regression and Multilevel/Hierarchical Models. New York: Cambridge University Press, 2007.
Kreft, Ita, and Jan De Leeuw. Introducing Multilevel Modeling. Newbury Park, Calif.: Sage Publications, 1998.
Raudenbush, Stephen W., and Anthony S. Bryk. Hierarchical Linear Models: Applications and Data Analysis Methods. Thousand Oaks, Calif.: Sage Publications, 2002.
Steenbergen, Marco R., and Bradford S. Jones. “Modeling Multilevel Data Structures.” American Journal of Political Science 46 (2002): 218–237.

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