September 29, 2009 Session 5Slide 1 PSC 5940: Interactions as Multi- Level Models Session 5 Fall, 2009

September 29, 2009 Session 5Slide 2 Theoretical Considerations Hierarchy implies groups Groups behave systematically differently Intercepts, slopes and variance (error) Group-level variables may be predictable Example: Group: state-level party split f(electoral institutions) Individual: partisanship f(state split, other x’s) Accounting for group differences may reduce group error When are the differences sufficient to treat groups as theoretically distinct?

September 29, 2009 Session 5Slide 3 Flip the Orientation When is it appropriate to treat a population as a “population” with no group distinctions? This is what we do in classical regressions Our estimated coefficients are means over the entire population Our variances (hence errors) are assumed to be constant Are we masking and misrepresenting the important dynamics in our models?

September 29, 2009 Session 5Slide 4 Two Extremes in Model Structure Complete Pooling There is no group indicator Any grouping variation in slope and intercepts will be masked in the overall “pool” average “Underfits” the data – variance will be inflated No Pooling Data are modeled separately for each group There is no sharing of variance (estimated variance will tend to be larger) “Overfits” the data – ignores the overall pattern of variation evident in the larger dataset (especially for groups with small n’s)

September 29, 2009 Session 5Slide 5 Hierarchical Models are a Partial- Pooling Compromise Uses information from both groups and the entire population Weights the information such that For groups with smaller samples, gives greater weight to the full sample values For groups with larger samples, gives greater weight to the group values Biker study implications Amounts to a weighted compromise between the full-pooling and no-pooling model strategies

September 29, 2009 Session 5Slide 6 EE and NS Data Extension EE09 & NS09 Data: cross-sectional –Individual level variables –Group indicators (some implied) What kinds of groups can be identified? –Time? (length depends on series of interest) –Region? (region, state, zip) –Organized “group”? Partisanship Religious affiliation

September 29, 2009 Session 5Slide 7 Types and Sources of Data: States Republican/Democrat “gap” in 2008 as measured by Gallup tracking poll (n=350,000+) – affiliation.aspxhttp:// affiliation.aspx Type of primary system (open, closed, etc). Coded in many places – here’s one: – Level of income inequality by state –Gini coefficients for each state (most recent may be 1999) Others?

September 29, 2009 Session 5Slide 8 Data Structure By individual –Individual-level variables and grouping indicators, by individual (i * X) for i individuals By groups –Group-level variables, by group (j * U) for j groups

September 29, 2009 Session 5Slide 9 BREAK

September 29, 2009 Session 5Slide 10 Literature Reviews Research Questions and Hypotheses? Applicability to hierarchical models? Often involves weaving together quite different literatures Data Development What are your groups? What group dependent variables will be of importance?

September 29, 2009 Session 5Slide 11 For Next Week Data presentations Sources, characteristics Preliminary group-level models Running hierarchical models in R Readings: Gellman & Hill, Chs