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

September 29, 2009 Session 5 Slide 1

PSC 5940: Interactions as Multi-Level Models

Session 5

Fall, 2009


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?


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?


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)


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


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


Types and Sources of Data: States• Republican/Democrat “gap” in 2008 as measured by Gallup tracking poll (n=350,000+)

– http://www.gallup.com/poll/114016/state-states-political-party-affiliation.aspx

• Type of primary system (open, closed, etc). Coded in many places – here’s one:– http://en.wikipedia.org/wiki/Primary_election

• Level of income inequality by state– Gini coefficients for each state (most recent may be 1999)

• Others?


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


BREAK


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?


For Next Week• Data presentations

• Sources, characteristics• Preliminary group-level models

• Running hierarchical models in R

• Readings: Gellman & Hill, Chs. 11-12

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

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