1. Following are positions taken by twelve Senators on a half dozen key issues. The issues are scaled from 1 to 5, with lower numbers indicating stronger support. Place the senators in a two-dimensional MDS (multidimensional scaling) space, showing similarities and differences between them across the issues. Interpret the value of the stress index and name at least one dimension along with the clusters. To what extent do these results suggest that the Senate is (or is not) polarized?
Issues
Senators Health care Troops Tax relief Education Immigration Jobs
Barbara Boxer (CA) 1 5 4 1 1 1
Jim Bunning (KY) 5 1 1 5 5 5
Robert Byrd (WV) 3 3 3 3 2 2
Benjamin Cardin (MD) 1 5 5 1 1 1
Susan Collins (ME) 4 2 3 4 3 3
Jim DeMint (SC) 4 1 1 5 5 5
Christopher Dodd (CT) 2 4 4 2 2 2
Richard Durban (IL) 1 4 5 1 1 1
Kay Baily Hutchison (TX) 5 1 1 4 4 4
Richard Lugar (IN) 3 3 3 3 3 3
John Kerry (MA) 1 5 5 1 1 1
Mitch McConnell (KY) 5 1 1 5 5 4
Health care: lower score, more support for the public option
Troops: lower score, more support for increasing the troop levels in Afghanistan
Tax relief: lower score, less taxes on the wealthiest Americans
Education: lower score, more federal support for education
Immigration: lower score, more benefits for legal immigrants
Jobs: lower score, more support for federal stimulus for job creation
2. Can you infer causation from the following familiar data set? What kind of correlation analysis would facilitate a causal inference? Perform the analysis and state conclusions about the key factor causing cooperation.
Time Period Mediation Policy shifts Cooperation
1 1 4 1
2 1 4 1
3 1 3 2
4 2 1 1
5 3 2 2
6 4 3 3
7 2 3 2
8 1 4 2
9 3 5 2
10 2 5 3
11 1 4 2
12 4 4 3
13 5 3 4
14 4 4 5
15 3 5 4
3. Add the following new variable (change in external events; higher scores indicate more change). Based on a correlational analysis, what do you conclude about the effect of this variable on cooperation? Is the effect on cooperation stronger or weaker than the effects of mediation and policy shifts?
Time Period External events
1 3
2 3
3 3
4 2
5 4
6 1
7 3
8 4
9 3
10 2
11 4
12 1
13 3
14 2
15 3
4. Perform a factor analysis on the three variables shown in question 2 above. What do conclude about the factors? Perform another factor analysis that includes the new variable, change in external events. What do you conclude?
5. Students faced with a decision about which Virginia university to attend would be helped by information about differences and similarities among them. The data below shows profiles for three universities. How well do these 10 features discriminate among the three schools below? If the discrimination is good (above 60% correct classification), then what are the key differences between the schools? If the discrimination is weak (below 60% correct), then what accounts for this? Are there differences among the universities in discrimination accuracy? If so, what does this suggest?
GMU UVA JMU
Features
Size 1 3 4
Tuition 1 5 2
Location 1 4 5
On-campus living 2 5 4
Faculty ratings 2 1 3
Diversity 1 4 5
Teaching emphasis 2 4 3
Social life 3 1 4
Sports 3 1 5
Campus life 2 5 3