In Example 7.4 on employment histories, estimate model 2 using a lag in \(y\) rather than \(Z\), and also apply the random effects selection of Section 7.5, to assess whether there is exclusive true state dependence (and no spurious state dependence) for a subset of subjects.

Data from Example 7.4

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Consider data on monthly employment transitions of recently married women as (Skrondal and Rabe-Hesketh, 2004). There are n = 155 women with varying lengths of employment history, with N == 1580 observations. The response is y = 1 if a woman is in paid employment and y = 0 otherwise, though the models are framed in terms of latent normal augmented data Z (equivalent to a probit link). Predictors are husband unemployment status (x2 = 1 if unemployed, 0 otherwise), time in months from start of study (x3), whether parent to child under 1 (x4 = 1 if parent to child under 1, x4 = 0 otherwise), child under 5 (x5; = 1 if parent to child under 5, x5; = 0 otherwise), and age of woman (x6). Different dynamic specifications are considered, with the first (model 1) being the sepa- rate static model for period 1, as mentioned above. Thus priors p~ N(0, 1), 5~ N(0, 1), {b; ~ N(0,0%), i = 1,...,n}, ~ U(0, 100), and B; ~ N(0, 1000), ~ N(0, 1000) for covari- ates j, are adopted. Additionally it is assumed that residual variances e = $1 = 1. Conver- gence is obtained after 2500 iterations, and inferences are based on the second half of a run of 5000 iterations. Predictive assessment is based on sampling replicates Znew it without con- straint, so that the corresponding new,it is obtained according to whether Znew, it is positive or negative. A predictive assessment is based on the proportion of correctly identified transitions (Ynewy), denoted SPRD in the BUGS code. The and * estimates both show that a husband being unemployed also reduces the woman's chance of entering or retaining employment, perhaps reflecting local labour market conditions, while a child under 1 also reduces the probability of being employed. Specifically,