MODELLING REPEATED MEASURES ON FAMILY MEMBERS IN GEOGRAPHICAL AREAS. IAN PLEWIS UNIVERSITY OF MANCHESTER PRESENTATION TO RESEARCH METHODS FESTIVAL OXFORD, 2 JULY 2008. There are research questions in the social sciences that require descriptions and explanations of variability in one or
MODELLING REPEATED MEASURES ON FAMILY MEMBERS IN GEOGRAPHICAL AREAS
UNIVERSITY OF MANCHESTER
PRESENTATION TO RESEARCH METHODS FESTIVAL
OXFORD, 2 JULY 2008
There are research questions in the social sciences that
require descriptions and explanations of variability in one or
more outcomes within and between families.
Some of these questions can be addressed by partitioning and
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).
So we can model ytijk, assumed continuous, where:
t = 1…Tijk are measurement occasions (level 1);
i = 1…Ijk 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.
For variables that change with age or time, educational
attainment for example, we can use a polynomial growth
Do growth rates vary systematically with individual, family and neighbourhood characteristics?
We model variation in the random effects bqijk in terms of variables at:
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.
The growth curve and conditional models are compared in, for example:
Plewis, Multivariate Behavioral Research, 2001.
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.
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.
Their model is based on repeated measures of men and women as members of intact
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.
This basic model can be extended to:
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.
t = 2..Ti; min(Ti = 3); neighbourhood level omitted for ease of exposition.
The model allows for correlated random effects at the
individual level (ui for M, F and A) and also correlated
residuals at each occasion (etialso for M, F and A),
multivariate Normal in each case.
Estimation and specification issues:
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.
Can accumulate data over time intervals.
Can specify more complex models for women who change partners.
Expect interactions between δ and other explanatory variables.
Single level but can be repeated for women gaining/losing partners more than once.