GRA 5917: Input Politics and Public Opinion

Panel data 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 16h 2010

First, though: A short note on logistic regression (from last week)…

• L (the log-odds, the

logit

) theoretically varies between ∞ and ∞, but

P

(reasonably) stays within the 0-1 range:

e

L 

e

log  

P

1 

P

   1 

P P



P



e

L 1 

e

L i.e. the odds of ”success” vs. ”failure”; e b is the odds-ratio (OR)

Logistic regression

• Intuitively appealing since

P

=f(

X k

) increases in L as factor

X k

changes, but slowly initially and as

P

approaches 1:

P

1 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 L(X)

Logistic regression

Logit

i

 L

i

• Extensions and special variants of the logit model:  log  

P i

 n

P i

 n    b 0

i

  b

ki X k

  the

multinomial logit model

, which models responses in

i

=1 to n categories (with

i

=n the reference category) Logit

c

 L

c

 log     1 

i c

  n  1

c



i

 n  1

P i P i

     b 0

c

  b

k X k

  the

ordinal logit model

, which models responses in

i

=1 to n

ordered

categories (with

i

=n the reference category), assuming that the odds ratio effect on the odds of a lower ordered event (i.e. numerator events vs. denominator events) is independent of the observed category response (aka the

proportional odds model

)

Logistic regression in SPSS

Choose Analyze > Generalized Linear Models

Logistic regression in SPSS

A flexible tool with many possible model specifications 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

Excercises (I)

a) You are interested in how people’s age influences their general feeling of happiness. Use the

XWVSEVS_1981_2000_v20060423.sav

data set supplied under the PolEc Dataset folder on

It’s Learning

. a) Create a new variable

happy

that takes on the value 1 if the individual in question reports to be happy (’very’ or ’quite’) and 0 otherwise. Run a simple binary logistic regression with

happy

as dependent variable and (continous) age (

x003

) and the indivual’s houshold income (

being happy and age

mean).

(

Tip:

x047

) as independent variables.

Comment on the results and graph the realtionship between the probability of

Use descriptive analysis to find the minimum and maximum of age, i.e. the range for which reasonable predictions of happiness can be made, and graph the relationship holding income level constant at the b) Redo the analysis with year of birth (

their respective means).

x003

) added to the model.

Comment on the results in the SPSS output and again graph the relationship between age and the probability of being happy (holding both year of birth and income cosntant at

Analysis of panel data

A time-invariant covariate…

• Given the correct model…

y it

 b 0  b

A X Ait

 b

B X Bi



e it

…estimating the model

y it

 b 0  b

A X Ait



N k

  1  1 

k D i k



e it

will give unbiased estimates of b

A

: the

D k

exhaust varaiation between cross–section units (

i

); i.e. influence from all

observable

and

unobservable time-invariant

variables are accounted for

Analysis of panel data in SPSS (I)

OLS regression with country specific (and time specific) dummy variables added to the equation (as independent variables) with

Analyze > Regression > Linear…

problem: How create a large set of dummy variables?

1) Recode group variable

Auto-recode the variable indexing the groups (e.g. individuals, countries by proper names) into a running numeric code (

Transform > Automatic Recode…

)

2) Create dummies with syntax, e.g.:

DO REPEAT d=c1 to c60 /i=1 to 60.

* here, d defines the array of dummy variables that will be generated (c1, c2 to c60); The i controls the number of repeats.

COMPUTE d=(cc=i).

* computes the ith element in d (conveniently named ci) as 1 if cc=i, as 0 otherwise.

END REPEAT.

EXECUTE.

Analysis of panel data in SPSS (II)

Or use the mixed models feature: variables automatically

Analyze > Mixed Models > Linear…

(Maximum Likelihood estimation); creates group dummies from class

Analysis of panel data in SPSS (II)

Click Continue

Analysis of panel data in SPSS (II)

Move the dependent variable into

Dependent

frame and class independents into

Factor(s)

and continuous independents into

Covariate(s)

; choose

REML estimation

under

Estimation…

and

Parameter Estimates

under

Statistics…

Analysis of panel data in SPSS (II)

Click

Fixed…

Analysis of panel data in SPSS (II)

Mark variables that will appear in the

Factors and Covariates

frame and

Add

them to the

Model

frame. Click

Continue

Analysis of panel data in SPSS (II)

Click

OK

to start analysis

A note on within R 2

In the output from the mixed… procedure we get estimates of residuals: The often reported measure of within R 2 is simply: (Residual Model with group effects only – Residual Full Model ) / Residual Model with group effects only i.e. the proprortion of explainable variance (after group effects have been taken into account) that is explained by variables varying within groups

Analysis of panel data (II)…

• Instead of the model…

y it

 b 0  b

A X Ait



N k

  1  1 

k D i k



e it

…one could estimate the random effects model

y it

 b 0  b

A X Ait

 b

B X Bi

 

i e it

Valid if the group effect

v i

(viewed as a disturbance term) is uncorrelated with other regressors… (and RE estimator of b

A

more efficient than the FE estimator) will be

Analysis of panel data in SPSS (II)

Click

Random

and build random terms in same way as you would build fixed terms

Excercises (II)

a) Use the

60panel…sav

set supplied under today’s lecture. a) b) Redo the P&T’s analysis in model (1) in table 3.2 (Persson and Tabellini 2005:44).

Compare the results with those presented in the book.

Redo the P&T’s analysis in model (2) and (3) in table 3.2 (Persson and Tabellini 2005:44). (

Tip:

Before analysis, use select cases using the criteria discussed on pp. 76-77 in P&T).