MODELLING REPEATED MEASURES ON FAMILY MEMBERS IN GEOGRAPHICAL AREAS

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MODELLING REPEATED MEASURES ON FAMILY MEMBERS IN
GEOGRAPHICAL AREAS

• IAN PLEWIS
• UNIVERSITY OF MANCHESTER
• PRESENTATION TO RESEARCH METHODS FESTIVAL
• OXFORD, 2 JULY 2008

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• There are research questions in the social
  sciences that
• require descriptions and explanations of
  variability in one or
• more outcomes within and between families.

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• Some of these questions can be addressed by
  partitioning and
• modelling
• variation within individuals (when we have
  repeated measures)
• variation between individuals within families
  (with the appropriate design)
• variation between families within
  areas/neighbourhoods, schools, cross-classificatio
  ns etc. (with a clustered or spatial design).

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• The Millennium Cohort Study (MCS), for example,
  meets these
• three criteria because, as well as being
  longitudinal, data are
• collected from the main respondent (mothers),
  their partner (if in
• the household), the cohort child (or children if
  multiple birth) and
• older sibs. Also, MCS was originally clustered by
  ward (although
• residential mobility reduces the spatial
  clustering over time).

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• So we can model ytijk, assumed continuous, where
• t 1Tijk are measurement occasions (level 1)
• i 1Ijk are individual family members (level
  2)
• j 1..Jk are families (level 3)
• k 1..K are neighbourhoods (level 4).
• This is the usual nested or hierarchical
  structure.

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• For variables that change with age or time,
  educational
• attainment for example, we can use a polynomial
  growth
• curve formulation

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• Do growth rates vary systematically with
  individual, family and neighbourhood
  characteristics?
• We model variation in the random effects bqijk
  in terms of variables at
• the individual level, e.g. gender,
• the family level, e.g. family income,
• the neighbourhood level, e.g. Index of Multiple
  Deprivation.

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• We might prefer to model the variation in the
  time-varying outcome in
• terms of one or more time-varying explanatory
  variables. For example,
• we might be interested in how individuals
  smoking behaviour varies as
• their income changes.

This model raises the tricky issue of endogeneity
of individual (uijk) and family effects (v0jk)
generated by unobserved heterogeneity at these
two levels that is correlated with x, especially
if we are interested in the causal effect of
income on behaviour.
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• The growth curve and conditional models are
  compared in, for example
• Plewis, Multivariate Behavioral Research, 2001.

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• These two approaches both ignore the fact that
  family members have
• labels mother, father, oldest sibling etc.
• Often, we would like to know how the behaviour
  and characteristics of
• one family member are related to those of other
  family members.
• The influences of parents on children and
  children on parents mental health and behaviour.
• The influence of one parent (or, more generally,
  partner) on another quitting (or starting)
  smoking.
• The influence of one sibling on others risky
  behaviour.
• The association of parents/partners
  characteristics on each others behaviour
  educational qualifications and health behaviours.

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• In these cases, a multivariate approach (within
  a multilevel framework) can be more informative
  as Raudenbush, Brennan and Barnett, J. Family
  Psych. (1995) first pointed out.

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• Their model is based on repeated measures of men
  and women as members of intact
• couples

Correlations between males and females within
individuals - r(eMeF) - and at the family level -
r(u0u1) - can be estimated.
The equalities of within and between variances
for men and women can be tested.
Time varying variables can be introduced if
appropriate.
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• This basic model can be extended to
• Situations where growth isnt obviously
  applicable, as might be the case for binary and
  categorical variables (mover-stayer or mixture
  models).
• Couples plus children.
• Changing household structures (two parents to one
  parent for example).

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• Suppose we have repeated measures of whether (and
  how
• much) mothers, fathers and their adolescent
  children
• smoke and that we are interested in influences
  across
• family members over time, and of educational
  qualifications
• (and area of residence) on smoking behaviour.

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• t 2..Ti min(Ti 3) neighbourhood level
  omitted for ease of exposition.

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• The model allows for correlated random effects at
  the
• individual level (ui for M, F and A) and also
  correlated
• residuals at each occasion (eti also for M, F and
  A),
• multivariate Normal in each case.

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• Estimation and specification issues
• Simultaneity y2 is predicted by y1 but y2 is a
  predictor of y3 etc. so we need a FIML estimation
  method. Not a problem with continuous x and y but
  perhaps more problematic for non-linear models.
  MCMC needed?
• Autocorrelation structure for level one
  residuals? E(etet-1) lt 0?

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• Endogeneity of family residuals (ui) could use
  y1 as a control for this but then min(Ti) 4.
• Missing data essentially complete case analysis
  without imputation.
• Assumption of Normality for random effects. Clark
  and Etilé, J. Health Economics, 2006 use a
  similar model but estimate using a modified EM
  procedure with non-parametric individual random
  effects.

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Estimates from bivariate probit model MCS waves
1 and 2,intact couples
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• Effects of gaining, losing, changing partner
  previous
• research suggests that there are some for
  smoking but papers have not linked one family
  member to another.
• Focus here on women because men generally not
• followed up in cohort studies. Studies like BHPS
  might be more informative.

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Changes in household structure, MCS, waves 1 to 2
and 1 to 3.
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• Can accumulate data over time intervals.
• Can specify more complex models for women who
  change partners.
• Expect interactions between d and other
  explanatory variables.
• Single level but can be repeated for women
  gaining/losing partners more than once.

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• CONCLUDING REMARKS
• Multilevel modeling is a powerful technique for
  disentangling sources of variation.
• Using bivariate (or multivariate) multilevel
  models for repeated measures data extends the
  range of hypotheses about within household
  influences on behaviour that can be tested.
• It is important to model what actually happens
  to households over time and not always to rely on
  analyses of intact couples.
• What hypotheses might we consider for
  neighbourhood effects?

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• POSSIBLE EXTENSIONS
• The problem of limited dependent variables,
  especially for measures of amount smoked which is
  censored at zero. Multilevel extensions of Tobit,
  mixture or Heckman selection models might be
  useful here.
• Combining growth curve models with models for
  non-smokers. For example, Carlin et al.
  (Biostatistics, 2001) suggest a mixture model.