Multivariate Analysis

1
Multivariate Analysis

• Reading JR Chapter 13 (skip section on Two-Way
  Analysis of Variance and section on Logistic
  Regression)
• MC Chapters 12 13 (Due Friday)

2
Multivariate Analysis

• Problem with bivariate analysis in
  nonexperimental designs spuriousness
• Need for techniques that allow the research to
  control for other independent variables

3
Controlling for Other Independent Variables

• Crosstabulation evaluate bivariate relationship
  within subsets of sample defined by different
  categories of third variable (control by
  grouping)

4
Multiple Regression

• Now working with a new model
• Yi a b1X1i b2X2i ... bkXki
  ei

5
Slope Coefficients

• Slope coefficients are now partial slope
  coefficients, although we still refer to them
  generally as slope coefficients. They have a new
  interpretation
• "the expected change in Y given a one-unit
  increase in X1, holding all other variables
  constant"

6
The Intercept

• Intercept value is now the expected
• value of Y when ALL the independent
• variables are set to 0.

7
Multiple Regression

• By holding constant all other Xs, we are
  therefore controlling for all other Xs, and
  thus isolating the independent effect of the
  variable of interest.

8
Multiple Regression

• The change in Y associated with an increase in X1
  (i.e. the partial slope coefficient for X1) is
  assumed to be exactly the same for every unique
  combination of all the other Xs.

9
Testing for Statistical Significance

• Proceeds as before a probability value
  (p-value) is generated for each sample slope
  coefficient

10
Fit of the Regression

• R-squared value the proportion of variation in
  the dependent variables explained by ALL of the
  independent variables combined

11
Comparing the Strength of Effects

• b1 "beta coefficients," "beta weights" or
  standardized slope coefficients
• b1 the expected standard deviation change in Y
  associated with a one standard deviation increase
  in X1, holding other variables constant

12
Hill, Leighley and Hinton-Anderson, Lower Class
Mobilization and Policy Linkage in the United
States (AJPS 1995)

• Research Question Given that the lower class is
  generally unorganized politically, what
  consequences does this have for public policy?
• Dependent variable State welfare benefit
• Independent variable Lower class mobilization
• Control for several other causes of state welfare
  benefits

13
Hill, Leighley and Hinton-Anderson, Lower Class
Mobilization and Policy Linkage in the United
States (AJPS 1995)