The variation of migration propensity with age has been linked to life cycle factors, such as marriage, employment, career moves, and the presence of children in the family. Similarly year effects can be linked to economic factors, and employment and career moves are seen to represent underlying economic health. Do explanatory variables which measure these effects explain the variation of migration behaviour with age and year?
The large number of possible explanatory variables require a pragmatic strategy to model building.
|
| Model development |
We start with the parsimonious main effects model for the temporal variables,
| age+age2+age3+age4+age5 +age6+year+log(dur) |
and add explanatory variables which measure individual life cycle effects.
We choose explanatory variables suggested by substantive considerations
to include in our model. A number of such
explanatory variables are present in the data set, giving information on
education, occupation, marital status, employment,
the presence of children of different ages, etc.
Although empirical evidence is mixed, education is often considered to
increase the propensity to migrate, because it increases employment
opportunities and gives access to better information about other areas.
(Sandefur and Scott 1981, Goss 1985, Liaw 1990)
Marital status is an important feature of theories about migration
behaviour, with evidence that married individuals are less likely to
migrate. Getting married, marital break up and remarriage are expected
to increase the probability of migration. (Devis 1983, Grundy 1989)
School age children create important ties to an area, and the fear of
disrupting children's education may inhibit migration. (Long 1972,
Davies and Flowerdew 1992)
Employment and occupational status variables also important
in relation to migration (Warnes 1983, Greenwood 1985, Davies and Flowerdew
1992, Ellis et al. 1993, Herzog 1993).
Career progression is another important variable to affect migration
(Salt 1990). We consider three variables measuring changes in
employment or occupational status which, being "favourable to socio-economic
achievement" (Cote 1997) might encourage migration: obtaining a job,
promotion to manager and promotion to service class.
We fit a series of logistic models and use backward elimination
to assess which explanatory variables to retain.
As the parameter estimates, apart from that of the endogenous variable
ldur, are very similar for the simple logistic and random effects
models, and as the latter is much more computer intensive,
we use the simple logistic model for model development.
We start with the model for the temporal variables, and add
education (ed), occupational status (osb3), employment status
(esb2) and marital status (msb), each measured at the beginning
of the year, first marriage
(mfm), marital break-up (mbu), remarriage (mrm),
the presence of children of different ages (ch1, ch2, ch3, ch4),
obtaining a job (eoj), promotion to manager (epm) and
promotion to service class (ops).
For education and marital status we use the original 5 level
variables
to include in the model; for employment and occupational status we have
chosen for simplicity the collapsed variables esb2 and
osb3 with 3 and 2 levels respectively, instead of the original
8 and 12 levels. The other variables are all 2-level factors.
We note that some levels of the original employment and occupational
status variables are likely to be highly correlated (eg. employment
status: none, occupational status: none), and problems with aliasing
are likely to occur in models which include such variables. Cross
tabulation of the levels of these variables will help to identify
possible problems, but that is beyond the scope of the present
example.
We use a cut-off significance level of 0.1 rather than the conventional
0.05. This is very conservative, as the simple logistic model tends
to overestimate significance, as we noted earlier. However, as the model
may be misspecified due to our pragmatic approach, conservatism is
considered important to reduce the chance of rejecting a possibly
relevant explanatory variable.
At each step in the backward elimination we test if the removal of the
explanatory variable with the lowest t-ratio (ratio of a parameter
to its standard error) gives a significant deterioration
in model fit by comparing the change in deviance with the appropriate value
of c2.
At the 0.1 significance level the critical values of the chi-squared
distribution for various degrees of freedom are
c2
(1)=2.71, c2
(2)=4.61, c2
(3)=6.25, c2
(4)=7.78.
When the preferred main effects model is found, the same model is
refitted with random effects to allow for unobserved
heterogeneity.
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