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
First, though: Interaction effects in basic regression analysis
(from last week)…
• Given the model…
y   0   A X A   B X B   AB X A X B  e
…simple rearrangment yields
y   0  ( A   AB X B ) X A   B X B  e or y   0  ( B   AB X A ) X B   A X A  e
that is…
y / X A   A   AB X B
or
y / X B   B   AB X A
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: A
effect of XA when XB=0 (but, consider centering of variables
to rescale an interesting value of XB to 0); AB 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
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:
var(y / X A )  var( A )  var( AB ) X B2  cov( A ,  AB )  2 X B
that is…
se(y / X A )  var(y / X A ) , with CI  y / X A

t  se(y / X A )
Interaction effects in basic regression analysis
• Need estimated variances and covariances. In SPSS:
Click statistics
Request
variancecovariance
matrix
Interaction effects in basic regression analysis
• Variance-covariance matrix:
XA
XB
XC
XA
XB
XC
var(X A )
cov(X B , X A ) cov(X C , X A )
cov(X A , X B )
var(X B )
cov(X C , X B )
cov(X A , X C ) cov(X B , X C )
var(X C )
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:
govdur  0   NP NP   PS PS   NPPS NP  PS   PD PD  e
Interaction effects… an example: Government duration
govdur  0   NP NP   PS PS   NPPS NP  PS   PD PD  e
1) in SPSS dataset gvmnt_duration.sav (downloaded from
It’s Learning) create interaction variable NPPS
(Transform > Compute Variable). Output descriptive
statistics (max., min., mean) for the variables in the dataset
2) run a regression (Analyze > Regression > Linear) with
the model and request Covariance matrix under
Statistics
Interaction effects… an example: Government duration
Estimates
of k
Estimates of
variances and
covariances
Interaction effects… an example: Government duration
3) 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):
govdur/ NP   NP   NPPS PS
and covariances and an appropriate t-value to find
confidence intervals for the effect at different values of
PS:
 t  var( NP )  var( NPPS ) PS 2  cov( NP ,  NPPS )  2 PS
20
15
10
5
marginal effect of
0
NP on gvmnt.
duration (solid
-5
line), 95% CI
-10
(broken lines)
-15
-20
-25
40
50
60
PS
70
80
Excercise (I)
1)
Download the social_welfare.sav file for It’s Learning (under today’s 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:
socwel   0   R Republican  F Female  RF Republican Female e
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.
Excercise (II)
1)
Under today’s lecture on It’s Learning download the lr_md2.sav data that combines
the left-right self placement median etsimate from the 1990s with Persson and
Tabellini’s economic and institutional data (the 85cross…sav). 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 electorate’s ideological position changes (a
la Gable and Hix (2005; figure2)). Compare the results to G&H’s original result.
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
(1=sucess vs. 0=failure) is the binary Logit model:
 P 
Logit  L  log
  0   k X k  
1

P


… where P is the probability of y=1 (”success” or
”yes”, say)
Logistic regression
• Wheras L may vary between ∞ and - ∞, it is
easily seen that P (reasonably) stays within the 0-1
range:
eL  e
 P 
log

 1 P 
P

1 P

eL
P
1  eL
i.e. the odds of
”success” vs.
”failure”; e is the
odds-ratio (OR)
Logistic regression
• Intuitively appealing since P=f(Xk) increases in L
as factor Xk changes, but slowly initially and as P
approaches 1:
1
0.9
0.8
0.7
0.6
P
0.5
0.4
0.3
0.2
0.1
0
L(X)
Logistic regression in SPSS
Choose Analyze >
Generalized Linear
Models
Logistic regression in SPSS
Choose Binary
logistic
Logistic regression in SPSS
Choose dependent
variable
Choose reference
category, i.e. to
model P(not in ref.
category)
Logistic regression in SPSS
Choose predictors:
class variables
(factors) or
contiuous variables
(covariates)
Logistic regression in SPSS
Build model
Presenting changes in P(y=1) from logistic regression
results
Have estimated L=0.4+1.2·X for X ranging from -4 to 10
Presenting changes in P(y=1) from logistic regression
results
Have estimated L=0.4+1.2·X for X ranging from -4 to 10