Alternative Ways of Analyzing Hierarchical Data
There are several alternative ways of analyzing hierarchical data, although most of them have some problems. First, traditional statistical techniques can be used. One could disaggregate higher-order variables to the individual level, and thus conduct an analysis on this individual level (for example, assign class variables to the individual level). The problem with this approach is that it would violate the assumption of independence, and thus could bias our results. This is known as atomistic fallacy. Another way to analyze the data using traditional statistical approaches is to aggregate individual level variables to higher-order variables and then to conduct an analysis on this higher level. The problem with this approach is that it discards all within-group information (because it takes the average of the individual level variables). As much as 80-90% of the variance could be wasted, and the relationship between aggregated variables is inflated, and thus distorted. This is known as ecological fallacy, and statistically, this type of analysis results in decreased power in addition to the loss of information.
Another way to analyze hierarchical data would be through a random-coefficients model. This model assumes that each group has a different regression model - with its own intercept and slope. Because groups are sampled, the model assumes that the intercepts and slopes are also randomly sampled from a population of group intercepts and slopes. This allows for an analysis in which one can assume that slopes are fixed but intercepts are allowed to vary. However this presents a problem, as individual components are independent but group components are independent between groups, but dependent within groups. This also allows for an analysis in which the slopes are random; however, the corrrelations of the error terms (disturbances) are dependent on the values of the individual-level variables. Thus, the problem with using a random-coefficients model in order to analyze hierarchical data is that is still not possible to incorporate higher order variables.
Read more about this topic: Multilevel Model
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