statisticalrethinkin..

13 Multilevel ModelsIntro idea: Case of Clive Wearing, as described by his wife Deborah in book ForeverToday. Wearing is a conductor and pianist who acquired anterograde amnesia aer a caseof Herpes simplex encephalitis. He can still play the piano and conduct, but he cannot formnew long-term memories. He is always forgetting recent events.Statistical models that are not multilevel are similar, in the sense that as they move fromone cluster (individual, group) in the data to another, trying to estimate parameters for eachcluster, they forget everything about the previous clusters. ey behave this way, becausethe model assumptions force them to, assuming that cluster intercepts and slopes containno joint information. is would be like forgetting you had ever been in a coffee shop, eachtime you go to the coffee shop. Coffee shops do vary, but information about one does helpyour expectations about the others. As it is in life, it is in statistics: anterograde amnesia isbad for learning about the world. We want models that instead use all of the information insavvy ways. Multilevel models do that.13.1. What are multilevel models good for?e basic reason to use a multilevel model is that your data are clustered somehow. Byclustered, I mean observations (cases) within different groups differ in their averages, resultingin correlations within groups. As a result, describing these differences can improveprediction and inference. ere are two common forms of clustering: (1) repeat observationsof the same entities and (2) observations of separate entities that are associated temporally,spatial or causally. In my mind, these are really the same thing, but it’s worth providingexamples of each.Repeat observations arise when we observe the same individual (person, tadpole, chimpanzee)multiple times. is may arise because we use the same individuals in multiple treatmentsof an experiment (within subjects design). Or it may arise because some individualssimply appear more oen by chance. Another common way to realize repeat observationsis with a time series, in which each individual appears once at each time step, but manytimes within the data. In all of these contexts, heterogeneity among individuals will lead toa particular pattern of variation between observations: variation will tend to cluster, if onlya little, by individual.e entities that exhibit clustering could just as easily be days of the week, cities, orstreams. We might observe individuals only once, but many individuals on common daysand in common places. Observations of all individuals on Monday, for example, may cluster,because of unobserved causal influences on that day. Likewise, observations of all individualsfrom a common stream or other location may also cluster. In this way, we actually have337