The models contain combinations of terms to capture the covariate and transition effects,
while three of the models also contain a random effects term to capture any between-subject
variability. Covariates shown to be significant terms in the model are gender, English-
speaking ability, pre-migration visit, age and mean-centred age-squared.
In complex hierarchical models such as these, the number of parameters associated with
a model is not usually obvious. We therefore use the DIC to compute the effective number
of parameters in each competing model and to assist with model selection. Model 5, which
contains fixed covariate effects and time-varying lagged response effects but no random effects
terms, was chosen to be the most favourable from the six models investigated.
For models containing a lagged response term, an additional random effects term in-
cluded to capture between-subject variability, led to an increased number of effective model
parameters but did not reduce the size of the DIC statistic at all. Here, the lagged response
term has been adequate in capturing the between-subject variation in employment status.
The inclusion of a time-varying transition effect has been useful in showing that the
probability of a PA remaining unemployed (relative to employed) is lower in Wave 3 than it
is in Wave 2. That is, the relative probability of a PA remaining unemployed diminishes over
three years from the first wave of interviews. However, the probability of transition from a
non-participant state does not alter significantly with time since arrival in Australia.
As is the case for most large social surveys, the data set is incomplete. The LSIA data
set has missing values in both the response (employment status) and one of the covariates
(English-speaking ability). An attractive feature of the Bayesian hierachical approach to this
type of analysis is that missing data may be routinely imputed according to some probability
distribution. This is clearly an advantage when prior information is available on the missing
data. In a subsequent analysis we have estimated and compared similar models for the full
data set which contains missing values. We have not reported the results in this paper,
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Convention