Cairo, May 2015 Irina Vartanova (Institute for Futures Studies) Training on " Measurements And Analysis of Opinion Poll Data"

1. Categorical dependent variables:
Application using WVS data from selected Arab countries
Irina Vartanova
Institute for Futures Studies, Stockholm
ERF Workshop – May 11, 2015
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2. Example: Income and Happiness
• Positive but diminishing association between income and
happiness (see Clark, et al., 2007 for a review)
• The association can be partially explained by reverse
causation and by unobserved individual characteristics, such
as personality traits.
• Relative income is more important than actual income, besides
comparisons of relative position are made across nations.
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3. Variables
Taking all things together, would you say you are
• Very happy
• Rather happy
• Not very happy
• Not at all happy
1
0
On this card is an income scale on which 1 indicates the lowest
income group and 10 the highest income group in your country.
We would like to know in what group your household is.
1 - Lowest group 10 - Highest group
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4. Data
• WVS, 6th wave
• 12 MENA countries: Algeria, Egypt, Iraq, Jordan, Kuwait,
Lebanon, Libya, Morocco, Palestine, Qatar, Yemen
• Bahrain excluded
• Pool sample: 9928 after listwize deletion of missing cases
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5. Raw Probabilities
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6. Logit Model
logΩ(X) = 0.525 + 0.047β
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7. Income Distribution
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8. Model Summary
Model 1 Model 2
s.income 0.267∗∗∗
(0.010) 0.252∗∗∗
(0.011)
Palestine −0.308∗∗∗
(0.106)
Iraq −0.786∗∗∗
(0.100)
Jordan 0.367∗∗∗
(0.113)
Kuwait 0.825∗∗∗
(0.135)
Lebanon −0.353∗∗∗
(0.105)
Libya 0.507∗∗∗
(0.103)
Morocco 0.014 (0.106)
Qatar 2.084∗∗∗
(0.231)
Tunisia 0.011 (0.106)
Egypt −2.482∗∗∗
(0.097)
Yemen −0.132 (0.106)
Constant −0.102∗∗
(0.047) 0.260∗∗∗
(0.089)
N 14617 14617
Log Likelihood −7558.220 −6399.145
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9. Maximum Likelihood Estimation (recap)
L(β0, β) =
n
i=1
p(xi )yi
(1 − p(xi )1−yi
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10. (Relatively) full model of happiness
Based on the extensive review of existing factors of subjective
well-being (Dolan et. all, 2008), we control for:
• Gender - women tend to report higher happiness.
• Age squared - younger and older generations are happier.
• Marital status, being married is associated with the highest
happiness and being divorced with the lowest.
• Having children, the effect is mixed. Positive effect on life
satisfaction, but not on happiness. Negative consequences of
additional children, also culturally dependant.
• Health.
• Education has positive effect, especially in low income
countries.
• Unemployment is detrimental for happiness especially among
men.
• Religiosity have positive effect on happiness.
• General trust positively associated with happiness.
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11. (Relatively) full model of happiness - 2
Happiness
s.income 0.198∗∗∗
(0.013)
female 0.307∗∗∗
(0.054)
poly(age, 2)1 5.221 (3.915)
poly(age, 2)2 21.006∗∗∗
(3.252)
education Middle −0.057 (0.060)
education High −0.055 (0.081)
marital.st Divorced −0.661∗∗∗
(0.148)
marital.st Widowed −0.396∗∗∗
(0.125)
marital.st Single −0.366∗∗∗
(0.109)
children 1 child 0.278∗∗
(0.125)
children 2 or more 0.113 (0.100)
to be continued
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12. (Relatively) full model of happiness - 3
s.health Good −0.649∗∗∗
(0.069)
s.health Fair −1.765∗∗∗
(0.076)
s.health Poor −2.767∗∗∗
(0.112)
imp.religion Rather important −0.474∗∗∗
(0.089)
imp.religion Not very important −0.895∗∗∗
(0.166)
imp.religion Not at all important −1.164∗∗∗
(0.214)
general.trust 0.325∗∗∗
(0.065)
unemployed −0.494∗∗∗
(0.103)
Female:unemployed 0.158 (0.175)
Constant 1.712∗∗∗
(0.155)
N 13750
Log Likelihood −5302.329
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13. Country Effect: All Pairwise Comparisons
Palestine
Iraq
Jordan
Kuwait
Lebanon
Libya
Morocco
Qatar
Tunisia
Egypt
Yemen
Egypt
Tunisia
Qatar
Morocco
Libya
Lebanon
Kuwait
Jordan
Iraq
Palestine
Algeria 0.57
0.12
0.93
0.11
0.06
0.12
−0.60
0.16
0.04
0.13
−0.07
0.12
0.26
0.12
−1.66
0.24
0.14
0.12
2.85
0.11
0.54
0.12
0.36
0.11
−0.51
0.12
−1.16
0.16
−0.53
0.13
−0.64
0.12
−0.31
0.12
−2.23
0.24
−0.42
0.12
2.28
0.11
−0.02
0.12
−0.87
0.12
−1.52
0.15
−0.89
0.12
−1.00
0.11
−0.67
0.11
−2.59
0.24
−0.78
0.11
1.92
0.10
−0.39
0.11
−0.66
0.16
−0.02
0.13
−0.13
0.12
0.20
0.12
−1.72
0.25
0.08
0.12
2.79
0.11
0.48
0.13
0.63
0.16
0.53
0.15
0.85
0.16
−1.07
0.26
0.74
0.16
3.44
0.15
1.14
0.16
−0.11
0.13
0.22
0.13
−1.70
0.25
0.11
0.13
2.81
0.12
0.51
0.14
0.33
0.12
−1.59
0.24
0.21
0.11
2.92
0.10
0.61
0.12
−1.92
0.24
−0.11
0.12
2.59
0.11
0.29
0.12
1.81
0.24
4.51
0.24
2.21
0.25
2.70
0.11
0.40
0.12
−2.30
0.11
Significantly < 0
Not Significant
Significantly > 0
bold = brow − bcol
ital = SE(brow − bcol)
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14. Multiplicity Correction
• Since we test 66
hypothesis
simultaneously,
around 3 of them
could be significant
by chance
• There are several
ways to correct for
multiple testing. Here
I use the Holm
correction which sets
the α for the entire
set of tests equal to
α
n .
Palestine
Iraq
Jordan
Kuwait
Lebanon
Libya
Morocco
Qatar
Tunisia
Egypt
Yemen
Egypt
Tunisia
Qatar
Morocco
Libya
Lebanon
Kuwait
Jordan
Iraq
Palestine
Algeria 0.57
0.12
0.93
0.11
0.06
0.12
−0.60
0.16
0.04
0.13
−0.07
0.12
0.26
0.12
−1.66
0.24
0.14
0.12
2.85
0.11
0.54
0.12
0.36
0.11
−0.51
0.12
−1.16
0.16
−0.53
0.13
−0.64
0.12
−0.31
0.12
−2.23
0.24
−0.42
0.12
2.28
0.11
−0.02
0.12
−0.87
0.12
−1.52
0.15
−0.89
0.12
−1.00
0.11
−0.67
0.11
−2.59
0.24
−0.78
0.11
1.92
0.10
−0.39
0.11
−0.66
0.16
−0.02
0.13
−0.13
0.12
0.20
0.12
−1.72
0.25
0.08
0.12
2.79
0.11
0.48
0.13
0.63
0.16
0.53
0.15
0.85
0.16
−1.07
0.26
0.74
0.16
3.44
0.15
1.14
0.16
−0.11
0.13
0.22
0.13
−1.70
0.25
0.11
0.13
2.81
0.12
0.51
0.14
0.33
0.12
−1.59
0.24
0.21
0.11
2.92
0.10
0.61
0.12
−1.92
0.24
−0.11
0.12
2.59
0.11
0.29
0.12
1.81
0.24
4.51
0.24
2.21
0.25
2.70
0.11
0.40
0.12
−2.30
0.11
Significantly < 0
Not Significant
Significantly > 0
bold = brow − bcol
ital = SE(brow − bcol)
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15. Interpretation: Odds Ratios
• Odds ratios describe the factor by which odds change as one
variable changes holding other constant. They are easily
calculated:
ebs.income
= 1.22
• Interpretation: For all of the people who live in the same
MENA country, have the same gender, age, education and so
on and with 5 score on subjective income - for every 100 of
them we would expect to be happy, we would expect 122 of
the same types of people, but who had 6 score on subjective
income, be happy.
• Odds ratios remain only relative comparisons due to
unobserved heterogeneity (Mood, 2010).
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16. Alternatives: Types of Marginal Effects
• Average Marginal Effects - takes the average of the marginal
effect across all cases used to estimate the model.
• Marginal Effect at the Mean - takes the marginal effect of
each variable holding all other variables constant at their
mean values.
• Marginal Effect at Representative values - take the marginal
effect of each variable holding all others constant at
substantively/theoretically interesting values
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17. Predicted Probabilities
s.income effect plot
s.income
happy
0.70
0.75
0.80
0.85
0.90
2 4 6 8 10
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18. Model Fit, Evaluation and Comparison
• Specification tests: Wald test, Likelihood ratio test
• Pseudo-R2
• Information criteria: AIC, BIC
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19. Testing: Wald and Likelihood-Ratio Test
• A Wald test is base on the assumption that B N(β, V (B))
and tests whether β = 0
• A likelihood-ratio test compares two models, a full one (MF )
with coefficients BF and a nested model (MR) which places q
linear restrictions on the coefficients in BF :
LLR = −2(LL(MR) − (LL(MF ) χ2
q
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20. Hypothesis Test for Subjective Income
Wald test
Res.Df Df χ2 Pr(> χ2)
1 13718
2 13718 1 229.48 < 2.2e − 16 ∗ ∗∗
LR test
Df LogLik Df χ2 Pr(> χ2)
1 32 -5302.3
2 31 -5420.2 -1 235.69 < 2.2e − 16 ∗ ∗∗
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21. Pseudo-R2
• Pseudo-R2 rely on analogous to the linear model, but none of
them can be interpreted as the proportion of variation in the
dependent variable explained by the independent variables.
• Many different types, each of them produce different results
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22. Several Pseudo-R2
for the Happiness Model
OLS R2
= 1 − SSr esidual
SSt otal
Efron’s R2
= 1 − N (yi −πi )2
N (yi −y)2 .308
McFadden’s R2
= 1 − logL(MFull )
logL(MNull )
.291
Cox & Snell’s R2
= 1 − logL(MN ull)
logL(MF ull)
2
N
.273
Count R2
= Correct
Count
.824
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23. AIC and BIC
Akaike’s Information Criterion
AIC = −2log(L(Θ data)) + 2K
Bayesian Information Criterion
BIC = −2log(L) + Klog(n)
• Whether to use AIC or BIC depends on how much one wants
to penalize additional model parameters.
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24. AIC and BIC for the Happiness Model
Base model Without Gender*Unemployment
Log Likelihood −5302.329 −5302.867
AIC 10668.66 10667.73
BIC 10909.58 10901.13
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