GRA 5917: Input Politics and Public Opinion

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GRA 5917 Input Politics and Public
Opinion Logistic regression in political economy
Lars C. Monkerud, Department of Public
Governance, BI Norwegian School of Management
GRA 5917 Public Opinion and Input Politics.
Lecture, September 9th 2010
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First, though Interaction effects in basic
regression analysis (from last week)

• Given the model

simple rearrangment yields
that is
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Interaction effects in basic regression analysis

• Model with interaction terms

entails symmetry Effect of one variable
contingent on the other and vice versa
terms are mostly not to be interpreted in
isolation bA effect of XA when XB0 (but,
consider centering of variables to rescale an
interesting value of XB to 0) bAB tells whether
effect of XA (XB) on Y depends on XB (XA) for
some values of XB (XA)
additive terms are not to be seen as
unconditional effects little sense in asking of
effect of Xk in general
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Interaction effects in basic regression analysis

• In model with interaction terms both the effect
  and

the significance of the effect of one varaible
varies with value of other variable
that is
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Interaction effects in basic regression analysis

• Need estimated variances and covariances. In
  SPSS

Click statistics
Request variance-covariance matrix
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Interaction effects in basic regression analysis

• Variance-covariance matrix

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Interaction effects an example Government
duration

• govdur Average duration of governments in
  parliamentary systems after WWII (in months),

• PS Average parliamentary support as a
  percentage of seats held in the assembly,

• NP Average number of parties in the government
  coalition,

• PD A measure of party discipline in the
  following model

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Interaction effects an example Government
duration

1. in SPSS dataset gvmnt_duration.sav (downloaded
   from Its Learning) create interaction variable
   NPPS (Transform gt Compute Variable). Output
   descriptive statistics (max., min., mean) for the
   variables in the dataset

1. run a regression (Analyze gt Regression gt Linear)
   with the model and request Covariance matrix
   under Statistics

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Interaction effects an example Government
duration
Estimates of bk
Estimates of variances and covariances
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Interaction effects an example Government
duration

• in a spreadsheet (Excel) use estimates (B) to
  map expected marginal effects of increasing the
  number of parties (NP) as it depends on
  reasonable (i.e. observed) values for
  parliamentary support (PS)
• and covariances and an appropriate t-value to
  find confidence intervals for the effect at
  different values of PS

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Excercise (I)

• Download the social_welfare.sav file for Its
  Learning (under todays lecture). To see whether
  gender and partisanship are substitutes or
  (complements) when it comes to explaining factors
  influencing views on the social welfare-state you
  run the following regression
• What is the difference in attitudes between
  females and males within the Democratic party?
  And within the Republican party? Are diffrences
  significantly greater in the one party as
  compared to the other? Use the results from the
  regression to map expected gender differences and
  their (95) confidence intervals.

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Excercise (II)

1. Under todays lecture on Its Learning download
   the lr_md2.sav data that combines the left-right
   self placement median etsimate from the 1990s
   with Persson and Tabellinis economic and
   institutional data (the 85crosssav). Construct
   interaction terms between the LR estimate
   (md_est) and the institutional indicators
   (propres2, majpar2 etc.) and perform a regression
   where you include these intarction terms. Analyze
   the effect of changing from a proportional
   parliamentary system to a majoritarian
   parliamentary system as the electorates
   ideological position changes (a la Gable and Hix
   (2005 figure2)). Compare the results to GHs
   original result.

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Logistic regression

• Appropriate for categorical dependent variables,
  e.g. yes vs. no responses, voting for party X
  or not, acheiving an MSc degree or not, etc.

• A popular model for the simple binary response
  (1sucess vs. 0failure) is the binary Logit
  model

where P is the probability of y1 (success
or yes, say)
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Logistic regression

• Wheras L may vary between 8 and - 8, it is
  easily seen that P (reasonably) stays within the
  0-1 range

i.e. the odds of success vs. failure eb is
the odds-ratio (OR)
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Logistic regression

• Intuitively appealing since Pf(Xk) increases in
  L as factor Xk changes, but slowly initially and
  as P approaches 1

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Logistic regression in SPSS
Choose Analyze gt Generalized Linear Models
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Logistic regression in SPSS
Choose Binary logistic
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Logistic regression in SPSS
Choose dependent variable
Choose reference category, i.e. to model P(not in
ref. category)
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Logistic regression in SPSS
Choose predictors class variables (factors) or
contiuous variables (covariates)
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Logistic regression in SPSS
Build model
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Presenting changes in P(y1) from logistic
regression results
Have estimated L0.41.2X for X ranging from -4
to 10
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Presenting changes in P(y1) from logistic
regression results
Have estimated L0.41.2X for X ranging from -4
to 10