GRA 5917: Input Politics and Public Opinion Logistic regression in political economy GRA 5917 Public Opinion and Input Politics. Lecture, September 9th

GRA 5917: Input Politics and Public Opinion

Logistic regression in political economy

GRA 5917 Public Opinion and Input Politics. Lecture, September 9th 2010

Lars C. Monkerud, Department of Public Governance,

BI Norwegian School of Management

First, though: Interaction effects in basic regression analysis (from last week)…

• Given the model…

…simple rearrangment yields

eXXXXy BAABBBAA 0

that is…

AABBBBABAA XXyXXy /or /

eXXXyeXXXy AABAABBBBABABA )(or )( 00

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


• 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…

)/(se /CI with ,)/var()/(se AAAA XytXyXyXy

BABABABAA XXXy 2),cov()var()var()/var( 2


• Need estimated variances and covariances. In SPSS:

Click statistics

Request variance-covariance matrix


• Variance-covariance matrix:

)var(),cov(),cov(

),cov()var(),cov(

),cov(),cov()var(

CCBCAC

BCBBAB

ACABAA

CBA

XXXXXX

XXXXXX

XXXXXX

XXX

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:

ePDPSNPPSNPgovdur PDNPPSPSNP 0


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

ePDPSNPPSNPgovdur PDNPPSPSNP 0


Estimates of k

Estimates of variances and covariances


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):

and covariances and an appropriate t-value to find confidence intervals for the effect at different values of PS:

PSNPgovdur NPPSNP /

S2),cov()var()var( 2 PPSt NPPSNPNPPSNP

-25

-20

-15

-10

-5

0

5

10

15

20

40 50 60 70 80

PS

marginal effect of NP on gvmnt. duration (solid line), 95% CI (broken lines)

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:

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.

eFemaleRepublicanFemaleRepublicansocwel RFFR 0

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:

… where P is the probability of y=1 (”success” or ”yes”, say)

kk X

P

P01

logLLogit

Logistic regression

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

L

L

1log

L

1

1

e

eP

P

Pee P

P

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:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

L(X)

P

Logistic regression in SPSS

Choose Analyze > Generalized Linear Models


Choose Binary logistic


Choose dependent variable

Choose reference category, i.e. to model P(not in ref. category)


Choose predictors: class variables (factors) or contiuous variables (covariates)


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

Documents

GRA 5917: Input Politics and Public Opinion Logistic regression in political economy GRA 5917 Public Opinion and Input Politics. Lecture, September 9th