An ‘undeliberate determinacy’? The changing migration strategies of Polish migrants in the UK in times of Brexit

This paper reformulates classical questions regarding the plans and strategies of Polish migrants in the UK – such as decisions to leave or remain in the host country, or be ‘deliberately indeterminate’ about future plans – from a sociologically situated ‘rights-based’ perspective. This approach considers migrants’ attitudes towards specific ‘civic integration’ measures in a medium-term time frame, as well as in the new context created by the UK’s vote to leave the EU. Based on the quantitative analysis of original survey data, we investigate the factors behind Polish migrants’ migration strategies, and we argue that basic socio-economic and demographic factors are inadequate, on their own terms, to explain future migration and civic integration plans. Instead, we find that aspects such as interest in and awareness of one’s rights, as well as anxieties about the ability to maintain one’s rights in the future are stronger determinants.     

Ethnicity and Occupational Pension Membership in the UK

Reflecting a relatively low‐value Basic State Pension, occupational pensions have historically been a key aspect of pension protection within Britain. Existing research shows that minority ethnic groups are less likely to benefit from such pensions and are more likely to face poverty in later life, as a result of the interaction of their labour market participation and pension membership patterns. However, the lack of adequate data on ethnic minorities has so far prevented the direct comparison of different ethnic groups, as well as their comparison to the White British group. Using data from the UK Household Longitudinal Study, this article explores patterns of employment and the odds ratios of membership in an employer's pension scheme among working‐age individuals from minority ethnic groups and the White British population, taking into account factors not used by previous research, such as one's migration history and sector of employment (public/private). The analysis provides new empirical evidence confirming that ethnicity remains a strong determinant of one's pension protection prospects through being in paid work, being an employee and working for an employer who offers a pension scheme. However, once an individual is working for an employer offering a pension scheme, the effect of ethnicity on that person's odds of being a member of that scheme reduces, except among Pakistani and Bangladeshi individuals for whom the differentials remain. The article also provides evidence on the pension protection of Polish individuals, a relatively ‘new’ minority group in the UK.     

On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample

The power function distribution is often used to study the electrical component reliability. In this paper, we model a heterogeneous population using the two-component mixture of the power function distribution. A comprehensive simulation scheme including a large number of parameter points is followed to highlight the properties and behavior of the estimates in terms of sample size, censoring rate, parameters size and the proportion of the components of the mixture. The parameters of the power function mixture are estimated and compared using the Bayes estimates. A simulated mixture data with censored observations is generated by probabilistic mixing for the computational purposes. Elegant closed form expressions for the Bayes estimators and their variances are derived for the censored sample as well as for the complete sample. Some interesting comparison and properties of the estimates are observed and presented. The system of three non-linear equations, required to be solved iteratively for the computations of maximum likelihood (ML) estimates, is derived. The complete sample expressions for the ML estimates and for their variances are also given. The components of the information matrix are constructed as well. Uninformative as well as informative priors are assumed for the derivation of the Bayes estimators. A real-life mixture data example has also been discussed. The posterior predictive distribution with the informative Gamma prior is derived, and the equations required to find the lower and upper limits of the predictive intervals are constructed. The Bayes estimates are evaluated under the squared error loss function.     

Fitting parametric frailty and mixture models under biased sampling

Biased sampling from an underlying distribution with p.d.f. f(t), t>0, implies that observations follow the weighted distribution with p.d.f. f ^w (t)=w(t)f(t)/E[w(T)] for a known weight function w. In particular, the function w(t)=t ^α has important applications, including length-biased sampling (α=1) and area-biased sampling (α=2). We first consider here the maximum likelihood estimation of the parameters of a distribution f(t) under biased sampling from a censored population in a proportional hazards frailty model where a baseline distribution (e.g. Weibull) is mixed with a continuous frailty distribution (e.g. Gamma). A right-censored observation contributes a term proportional to w(t)S(t) to the likelihood; this is not the same as S ^w (t), so the problem of fitting the model does not simply reduce to fitting the weighted distribution. We present results on the distribution of frailty in the weighted distribution and develop an EM algorithm for estimating the parameters of the model in the important Weibull–Gamma case. We also give results for the case where f(t) is a finite mixture distribution. Results are presented for uncensored data and for Type I right censoring. Simulation results are presented, and the methods are illustrated on a set of lifetime data.     

Stakeholder identities in Britain's neoliberal ethical community: Polish narratives of earned citizenship in the context of the UK's EU referendum

This article examines the narrative strategies through which Polish migrants in the UK challenge the formal rights of political membership and attempt to redefine the boundaries of ‘citizenship’ along notions of deservedness. The analysed qualitative data originate from an online survey conducted in the months before the 2016 EU referendum, and the narratives emerge from the open‐text answers to two survey questions concerning attitudes towards the referendum and the exclusion of resident EU nationals from the electoral process. The analysis identifies and describes three narrative strategies in reaction to the public discourses surrounding the EU referendum – namely discursive complicity, intergroup hostility and defensive assertiveness – which attempt to redefine the conditions of membership in Britain's ‘ethical community’ in respect to welfare practices. Examining these processes simultaneously ‘from below’ and ‘from outside’ the national political community, the paper argues, can reveal more of the transformation taking place in conceptions of citizenship at the sociological level, and the article aims to identify the contours of a ‘neoliberal communitarian citizenship’ as internalized by mobile EU citizens.     

Parametric Proportional Odds Frailty Models

We define a parametric proportional odds frailty model to describe lifetime data incorporating heterogeneity between individuals. An unobserved individual random effect, called frailty, acts multiplicatively on the odds of failure by time t. We investigate fitting by maximum likelihood and by least squares. For the latter, the parametric survivor function is fitted to the nonparametric Kaplan–Meier estimate at the observed failure times. Bootstrap standard errors and confidence intervals are obtained for the least squares estimates. The models are applied successfully to simulated data and to two real data sets. Least squares estimates appear to have smaller bias than maximum likelihood.     

MCMC implementation for Bayesian hidden semi-Markov models with illustrative applications

Hidden Markov models (HMMs) are flexible, well-established models useful in a diverse range of applications. However, one potential limitation of such models lies in their inability to explicitly structure the holding times of each hidden state. Hidden semi-Markov models (HSMMs) are more useful in the latter respect as they incorporate additional temporal structure by explicit modelling of the holding times. However, HSMMs have generally received less attention in the literature, mainly due to their intensive computational requirements. Here a Bayesian implementation of HSMMs is presented. Recursive algorithms are proposed in conjunction with Metropolis-Hastings in such a way as to avoid sampling from the distribution of the hidden state sequence in the MCMC sampler. This provides a computationally tractable estimation framework for HSMMs avoiding the limitations associated with the conventional EM algorithm regarding model flexibility. Performance of the proposed implementation is demonstrated through simulation experiments as well as an illustrative application relating to recurrent failures in a network of underground water pipes where random effects are also included into the HSMM to allow for pipe heterogeneity.     

Graphical Tests for the Assumption of Gamma and Inverse Gaussian Frailty Distributions

The common choices of frailty distribution in lifetime data models include the Gamma and Inverse Gaussian distributions. We present diagnostic plots for these distributions when frailty operates in a proportional hazards framework. Firstly, we present plots based on the form of the unconditional survival function when the baseline hazard is assumed to be Weibull. Secondly, we base a plot on a closure property that applies for any baseline hazard, namely, that the frailty distribution among survivors at time t has the same form as the original distribution, with the same shape parameter but different scale parameter. We estimate the shape parameter at different values of t and examine whether it is constant, that is, whether plotted values form a straight line parallel to the time axis. We provide simulation results assuming Weibull baseline hazard and an example to illustrate the methods.