Multilevel Models

Examples of Multilevel Models in the following topics:

• Social Epidemiology and Health

  • Use of such multilevel models is also known as hierarchical and mixed effects models.

• Intorduction to qualitative analysis

  • An alternative approach is block modeling.
  • In principle, one could fit any sort of block model to actor-by-event incidence data.
  • We will examine two models that ask meaningful (alternative) questions about the patterns of linkage between actors and events.
  • Both of these models can be directly calculated in UCINET.
  • Alternative block models, of course, could be fit to incidence data using more general block-modeling algorithms.

• Introduction to explaining the relations among actors in a network

  • Models like these are very useful for examining the relationships among relational and non-relational attributes of individuals.
  • Several of the models below explore homophily and closeness to predict whether actors have ties, or are close to one another.
  • The last model that we will look at the "P1" model also seeks to explain relations.
  • The P1 model tries to predict whether there exists no relation, an asymmetrical relation, or a reciprocated tie between pairs of actors.
  • This type of model -- a probability model for the presence/absence of each possible relation in a graph as a function of network structures -- is one of the major continuing areas of development in social network methods.

• Homophily models

  • The routine Tools>Testing Hypotheses>Mixed Dyadic/Nodal>Categorical Attributes>ANOVA Density Models provides specific tests of some quite specific homophily models.
  • Next, a regression model is fit to the data.
  • The results of fitting this model to the data is shown in figure 18.19.
  • This model fits the data much better (R-square = .269, with p < .000) than the constant homophily model.
  • The fit of this model is better (R-square = .037) but still very poor.

• Integration Theory

  • Numerous models could be presented in this vein.
  • George Ritzer's Integration Model is a good example.
  • If used for understanding a specific cultural phenomenon, like the displaying of abstract art in one's home, the integration model depicts the different influences on the decision.
  • For instance, the model depicts that cultural norms can influence individual behavior.
  • The model also shows that individual level values, beliefs, and behaviors influence macro-level culture.

• The Structure of Cities

  • Urban structure is the arrangement of land use, explained using different models.
  • In grid models, land is divided by streets intersect at right angles, forming a grid.
  • This model's general applicability has been challenged.
  • Like the concentric ring model, Hoyt's sectoral model has been criticized for ignoring physical features and new transportation patterns that restrict or direct growth.
  • Analyze, using human ecology theory, the similarities and differences between the various urban structure models, such as grid model, sectoral model and concentric ring model, among others

• Two-mode factions analysis

  • An alternative block model is that of "factions."
  • Networks>Subgroups>Factions fits this block model to one-mode data (for any user-specified number of factions).
  • Network>2-Mode>2-Mode Factions fits the same type of model to two-mode data (but for only two factions).
  • The fit of the two factions model is not as impressive as the fit of the core-periphery model.
  • Two mode factions model of California $1M donors and ballot initiatives (truncated)

• The probability of a dyadic tie: Leinhardt's P1

  • The P1 model (and its newer successor the P* model), seek to predict the dyadic relations among actor pairs using key relational attributes of each actor, and of the graph as a whole.
  • Figure 18.27 shows the results of fitting the P1 model to the Knoke binary information network.
  • Using the equations, it is possible to predict the probability of each directed tie based on the model's parameters.
  • For example, the model predicts a 93% chance of a tie from actor 1 to actor 2.
  • Here we see that, for example, that actors 3 and 6 are much more likely to have ties than the P1 model predicts.

• Activity Theory

  • The disengagement model suggests that it is natural for the elderly to disengage from society as they realize that they are ever nearer to death.
  • Five decades of gerontological research, however, suggest that the activity model is more accurate than the disengagement model .
  • Compare the activity model and disengagement model of aging, in terms of activity level and level of life satisfaction

• CONCOR

  • The goodness of fit of a block model can be assessed by correlating the permuted matrix (the block model) against a "perfect" model with the same blocks (i.e. one in which all elements of one blocks are ones, and all elements of zero blocks are zeros).
  • For the CONCOR two-split (four group) model, this r-squared is .451.
  • That is, about 1/2 of the variance in the ties in the CONCOR model can be accounted for by a "perfect" structural block model.
  • The block model and its image also provide a description of what it means when we say "the actors in block one are approximately structurally equivalent."