Analysis of Cross-National Longitudinal Data Marc Callens (CBGS, Brussels

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Analysis of Cross-National Longitudinal
DataMarc Callens (CBGS, Brussels KULeuven,
Leuven)
EUROPEAN SCIENCE FOUNDATION Programme
Quantitative Methods in the Social Sciences
(QMSS) Seminar Theory and Practice in the
Analysis of Cross-National Cross-Sectional
Data 25 - 26 August 2005, University of Oxford,
United Kingdom
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Overview

• contextual regression
• multilevel logistic regression
• Models
• Estimation
• Retrospective data
• The Impact of Education on Third Births (FFS)
• Panel data
• Poverty Dynamics in Europe (ECHP)

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I. Contextual regression

• Callens, M. (2004), Regression Modelling of
  Cross-National Data, Brussels PSPC.

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Contextual regression - 1

• a nested data structure
• - j 1,, N countries
• - i 1,, nj individuals
• yij responses depend on
• - xij individual level explanatory variable
• - zj country level explanatory variable
• yij are correlated within each country
• ordinary multiple regression is not adequate
  here
• - independence assumption for yij violated
• - how to include country-level expl. var. zj ?

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Contextual regression - 2

• Key Methodological issues
• Small N
• technical problems (few degrees of freedom,
  )
• only simple models possible
• Galton problem
• nations are not independent (cultural
  diffusion, )
• Black box
• how to explain the impact of country-level
  variables?
• equivalence (See Harkness et al., 2003)
• how comparable are the data?

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• Contextual regression - 3
• 1. non-hierarchical models (e.g., separate
  regressions, pooled regression)
• - ignore hierarchical data structure
• 2. classical contextual models (e.g., ancova)
• - acknowledge hierarchical data structure
• - fixed intercepts aj and slopes ßj
• 3. modern multi-level models (e.g., multilevel
  analysis)
• - acknowledge hierarchical data structure
• - random intercepts aj and slopes ßj

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Separate regressions - 1

• N models (one for each country) yiC aC ßC
  xiC eiC
• parameters to estimate
• for each country a specific intercept aC
• for each country a specific slope ßC
• lack of parsimony, what if N large?
• how to introduce country-level covariates zj ?

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Pooled regression - 1

• one (global) model
• parameters to estimate
• one (global) intercept a
• one (global) slope ß
• country membership is ignored
• how to introduce country-level covariates zj ?

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Analysis of Covariance - 1

• one (global) model yij aj ß xij eij
• countries enter the model as N-1 dummies
• parameters to estimate
• for each country a specific intercept aj
• one global slope ß
• all countries have the same slope unrealistic
• how to introduce country-level covariates zj ?

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Multilevel Regression - 1

• one model yij aj ßj xij eij
• aj and ßj are random variables, following a
  normal distribution
• random intercept aj N (a , s0²)
• random slope ßj N (ß , s1²)
• parameters to estimate
• one average intercept a
• one average slope ß
• intercept variance s0²
• slope variance s1²
• intercept-slope covariance c01
• inclusion of country level covariates zj
  possible !!!!

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Multilevel Regression - 2

• - Empty model yij aj (eij )
  random intercept
• - Random intercept model yij aj ß xij
  (eij ) indiv. covar.
• - Random slope model yij aj ßj xij
  (eij )
• random slope
• - Extended random models yij aj ßj xij ?
  zj, dxij zj (eij )
  country covar.

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Contextual regression summary
Separate Pooled Ancova Multilevel
models countries 1 1 1
parms very large large large small
variances no no no yes
country vars? no 1 1 yes
complex? no no no yes
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II. Multilevel logistic regression

• Callens, M. and C. Croux (to appear), Performance
  of Likelihood-based Estimation Methods for
  Multilevel Binary Regression Models, Journal of
  Statistical Computation and Simulation.

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Multilevel Logistic Regression

• binary responses yij depend on
• - xij individual-level explicative variable
  - zj group-level explicative variable
• a nested data structure two levels
• - level 2 N groups (j 1, ..., N)
• - level 1 in each group nj individuals (i
  1, ..., nj)
• - in each group responses yij are correlated
• standard logistic regression model not adequate
• - independence assumption is violated here
• - inclusion of multiple group-level covariates?

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Models for

• standard logistic regression model
• random logistic regression models
• extended random logistic regression models

random intercepts
random slopes
cross-level interaction
group-level explicative variable
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multilevel discrete-time hazard models for event
data

• binary responses yijt are event data
• - yijt 1 event occurrence for individual i in
  group j at time t
• - yijt 0 event non-occurrence for individual
  i in group j at time t
• (a third birth in 1995?, in 1996?, .)
• event data analysis may be complicated by
  censoring
• - e.g., for some i, an event may occur after the
  survey
• - hazard models can take censoring into account
• recurrent events for i are possible
• (becoming poor)

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• maximum likelihood estimation
• - via equivalent model (Allison, 1982)
• - requires data in person-period format

pit Pr(yit) yit, indicator for event
occurrence in time-period t
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performance of estimation methods

• performance of
• generally available estimation methods?
• maximum likelihood estimation
• - step 1. compute likelihood L
• - step 2. maximise L with respect to model
  parameters
• difficulty likelihood intractable integral

random effects u Normal distribution
responses yij Bernouilli distribution
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• estimation ? three methods
• - penalised quasi-likelihood
• - non-adaptive gaussian quadrature
• - adaptive gaussian quadrature
• how good? ? four performance indicators
• - numerical convergence
• - bias
• - mean-squared error (mse)
• - computational efficiency
• simulation setting ? fractional factorial
  experiment
• - full experiment would take 6 months
• - fractional experiment only 1 month
• Key findings Penalised quasi-likelihood performs
  (surprisingly) well

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III. Application for retrospective data

• Callens, M. and C. Croux (to appear), The Impact
  of Education on Third Births, A Multilevel
  Discrete-Time Hazard Analysis, Models, Journal of
  Applied Statistics

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III. Application for Retrospective Data The
Impact of Education on Third Births. A
Multilevel Discrete-Time Hazard Analysis
Callens, M. and C. Croux, Journal of Applied
Statistics (to appear)
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• key findings for multilevel models
• - negative effect for education
• - positive effect for Nordic countries

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IV. Application for panel dataComparative
Poverty DynamicsA Multilevel Discrete-Time
Recurrent Hazard AnalysisCallens, M. and C.
Croux, (preprint)
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poverty theoretical perspectives

• general poverty theory?? (McKernan, 2002)
• individual structural perspectives (Iceland,
  2003)
• individual theories the poor create their
  poverty
• life cycle hypothesis (e.g., Rowntree, 1901)
• life cycle events (e.g., a divorce)
• human capital theory (Becker, 1975)
• education, age, gender,

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poverty theoretical perspectives

• structural theories econ., soc. policy systems
• skills mismatch hypothesis (Kasarda, 1990)
• deindustrialisation
• technological change
• - welfare state regimes (Esping-Andersen, 1999)
• - level and design of welfare benefits
• - relative role of state and market
• - four types social-democratic, conservative,
  liberal, southern

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individual hypothesis for poverty entry

• h1 demographic and labour market events
• h2 for women effect of demographic events is
  stronger

event Effect
marriage -
divorce
employment -
unemployment
event effect
marriage - -
divorce
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structural hypothesis for poverty entry

• ranking of welfare regimes dominant income
  changes
• h3 non-earned income changes dominate
• h4 earned income changes dominate
• 4 most dynamic

dominant income changes dominant income changes
regime non-earned earned
southern 4 1
liberal 3 2
conservative 2 3
social-democratic 1 4
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structural hypothesis for poverty entry

• h5 skills mismatch

mismatch effect
deindustrialisation
technological change
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two longitudinal EU databases (linked at nuts1
level)

• individual level panel data
• European Community Household Panel
• yearly individual and household panel (94-98)
• income, employment, housing, healthcare,
• regional level time series
• regio database, New Cronos
• regional time series
• demography, unemployment, education,

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poverty status in a year

• compare income with relative poverty line

country-specific poverty thresholds
equivalised individual income
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discrete-time hazard models

• binary responses y1ijt are discrete-time event
  data
• - y1ijt 1 poverty entry for individual i in
  region j in year t
• - y1ijt 0 no poverty entry for individual i
  in region j at year t
• (poverty entry in 1995?, in 1996?, .)
• event data analysis may be complicated by
  censoring
• - e.g., for some i, an event may occur after the
  survey
• - hazard models can take censoring into account

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• discrete-time hazard
• proportional odds model
• estimation via equivalent logistic regression
  model (Allison, 1982)

Tij is time of occurrence of event y1ijt for
individual i belonging to region j
conditional on being at risk
at set of t intercepts, one for each
discrete-time unit
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multilevel discrete-time recurrent hazard
analysis

• extension 1 poverty entry is a recurrent event
• here, an individual may experience two poverty
  entries in a row
• so, we simultaneously model k 2 discrete-time
  hazards
• extension 2 dependent individuals ? multilevel
  model

Extension 2 dependency of individuals in a
region is modelled by random intercepts
Extension 1 we allow for event-specificity
for the baseline hazard k 1, 2
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explicative variables at individual level i

• xijt demographic events (changes in a year)
• - marriage from never married to married
• - divorce from married to
  divorced/separated
• xijt labour market events (changes in a year) -
  employment from unemployed to employed
• - unemployment from employed to unemployed

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control variables at individual level i

• xij current status
• education ltsec, sec, third, at school
• xijt
• age 16-40, 41-50, 51-60, 60
• civil status married, sep./div, wid., unmarried
• cohabiting status no, yes
• activity status inactive, unemployed, working
  (15)
• health status bad, good
• household type single, singlechild,
  couplechild, oth.
• duration - 4, -3, -2, -1, 0, 1.

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explicative variables at regional level j

• zj
• - welfare regime
• southern es, it, gr, pt
• liberal uk, ie
• conservative be, fr, ge
• social-democratic dk (ref)
• - deindustrialisation
• employment service sector (relative to dk)
• zjt
• - technological change
• employment RD business sector (relative to
  dk)

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control variables at regional level j

• zj
• employment rate working in total pop (rel. to
  dk)
• zjt
• unemployment rate unemp. In active pop (rel.
  to dk)
• relative gdp of EU 15 average (rel. to dk)
• gdp growth log differences

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poverty entry results at individual level

• odds ratio
• p lt 0.05 p lt 0.01 p lt 0.001

women women women men men men
event effect OR p effect OR p
marriage (-) 0.75 () 1.30
divorce 5.28 () 1.27
employment 1.57 () 1.20
unemployment 1.34 1.77
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key results for individual level

• individual level strong impact
• for women
• demographic events gt labour market events
• for men
• labour market events gt demographic events

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poverty entry results at regional level

• Welfare regimes
• odds ratio
• p lt 0.05 p lt 0.01 p lt 0.001

women women women men men men
regime effect OR p effect OR p
southern - 0.61 - 0.55
liberal () 1.12 (-) 0.85
conservative -- 0.59 -- 0.53
social-democratic (ref) 1 (ref) 1
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poverty entry results at regional level

• skills mismatch

women women women men men men
skills mismatch effect OR p effect OR p
deindustrialisation () 1.00 () 1.01
technological change () 1.02 () 1.11
odds ratio p lt 0.05 p lt 0.01 p lt
0.001
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key results for regional level

• regional level variation small, but relevant
• welfare regimes have an impact
• but, theoretically ambiguous

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conclusion

• individual gt regional
• women demographic events
• men labour market events
• welfare regime important, but how??

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