Interpretation of results

The explanatory variables

Backward elimination using the simple logistic model has shown the following variables to be significant at the 10% level:

employment status: esb2=1 (self employed), esb2=2 (employed), esb2=3 (not working)

occupational status: osb3=1 (small proprietors, supervisors), osb3=0 (otherwise)

promotion to service class: ops=0 (no), ops=1 (yes)

first marriage: mfm=0 (no), mfm=1 (yes)

marital break-up: mbu=0 (no), mbu=1 (yes)

remarriage: mrm=0 (no), mrm=1 (yes)

presence of children age 15-16: ch3=0 (no), ch3=1 (yes)

marital status: msb2=0 (not married), msb2=1 (married)

Our preferred homogeneous main effects model is therefore:

Comparison of simple logistic and random effects models

When the same model is fitted with random effects, the deviance decreases by 27.4. Although it is not strictly correct to use the c² test to compare the simple logistic and random effects models, such a substantial reduction in deviance for three extra parameters estimated (scale and two endpoints) provides evidence that in addition to the time varying explanatory variables included in the model, there remains unobserved heterogeneity.

Comparison of the parameter estimates of the two models shows that, as before, only the estimate of the endogenous log(dur) has changed substantially (from -0.9995 to -0.6353): controlling for unobserved heterogeneity has decreased the observed negative duration of stay effect. (See Lancaster and Nickell 1980). The other parameter estimates for the two models are the same, within one standard error.

The parameter estimates of msb2 and ch3 are both negative, providing evidence that being married significantly reduces the probability of migration, as does the presence of children in the age group 15-16, presumably for fear of disrupting schooling close to public examinations. There is no evidence that younger or older secondary school-age children increase ties to an area.

The positive coefficient estimates for mfm, mbu, mrm and ops indicate that the events of first marriage, marital break-up, remarriage and promotion to service class all increase the probability of migration.

The positive coefficients for levels 2 and 3 of esb2 provides evidence that employed and unemployed individuals are more likely to migrate than the self-employed. Also the positive coefficient of osb3 indicates that small proprietors and supervisors are more likely to migrate than others.

The probability of 0.3276 estimated for the left hand endpoint again indicates a high proportion of stayers. The right endpoint is small and may be set to zero.

Variation with age

To illustrate the difference between the homogeneous and random effects models, we plot the probability of migration against age, with the year taken as 1985, duration of stay 10 years and all other explanatory variables set to zero (ie. to their reference levels). As there are no interaction terms, the patterns shown on the graphs are generally valid.

Simple logistic model

Random effects model

Both graphs show a peak just below age 50, where the data are sparse; the random effects model, although flatter over the earlier years, has a more accentuated first peak just above age 20. The three peaks are less pronounced than in the original analysis without explanatory variables, but it is clear that controlling for life cycle effects provides only a partial explanation of the three peaks.

We shall examine the contribution of some of the explanatory variables to the peaks. Because of the excessive computing requirements of the random effects model, we shall use the simple logistic model in this analysis.

Next:Contribution of life cycle events to the peaks

Home page

Contents

Previous