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The analysis of longitudinal data gives the chance to observe how unit behaviors change over time, but it also poses series of issues. These have been the focus of a huge literature in the context of linear and generalized linear regression moving also, in the last ten years or so, to the context of linear quantile regression for continuous responses. In this paper, we present lqmix, a novel R package that helps estimate a class of linear quantile regression models for longitudinal data, in the presence of time-constant and/or time-varying, unit-specific, random coefficients, with unspecified distribution. Model parameters are estimated in a maximum likelihood framework, via an extended EM algorithm, and parameters' standard errors are estimated via a block-bootstrap procedure. The analysis of a benchmark dataset is used to give details on the package functions., Comment: 25 pages, 2 figures

The financial and economic crisis recently experienced by many European countries has increased demand for timely, coherent and consistent distributional information for the household sector. In the Euro area, most of the NCBs collect such information through income and wealth surveys, which are often used to inform their decisions. These surveys, however, can often suffer from biases, usually caused by non-response and under-reporting behaviours, leading to a mismatch with macroeconomic aggregates. In this paper, we develop a novel allocation method which combines information from a power law (Pareto) model and imputation procedures so to address these issues simultaneously, when only limited external information is available. We provide two important contributions: first, we adjust the weights of observed survey households for non-response bias, then, we correct for measurement error. Finally, we produce distributional indicators for four Euro-Area countries.

The Italian National Institute for Statistics regularly provides estimates of unemployment indicators using data from the Labor Force Survey. However, direct estimates of unemployment incidence cannot be released for Local Labor Market Areas. These are unplanned domains defined as clusters of municipalities; many are out-of-sample areas and the majority is characterized by a small sample size, which render direct estimates inadequate. The Empirical Best Predictor represents an appropriate, model-based, alternative. However, for non-Gaussian responses, its computation and the computation of the analytic approximation to its Mean Squared Error require the solution of (possibly) multiple integrals that, generally, have not a closed form. To solve the issue, Monte Carlo methods and parametric bootstrap are common choices, even though the computational burden is a non trivial task. In this paper, we propose a Semi-Parametric Empirical Best Predictor for a (possibly) non-linear mixed effect model by leaving the distribution of the area-specific random effects unspecified and estimating it from the observed data. This approach is known to lead to a discrete mixing distribution which helps avoid unverifiable parametric assumptions and heavy integral approximations. We also derive a second-order, bias-corrected, analytic approximation to the corresponding Mean Squared Error. Finite sample properties of the proposed approach are tested via a large scale simulation study. Furthermore, the proposal is applied to unit-level data from the 2012 Italian Labor Force Survey to estimate unemployment incidence for 611 Local Labor Market Areas using auxiliary information from administrative registers and the 2011 Census.

We propose a M-quantile regression model for the analysis of multivariate, continuous, longitudinal data. M-quantile regression represents an appealing alternative to standard regression models, as it combines the robustness of quantile and the efficiency of expectile regression, providing a complete picture of the response variable distribution. Discrete, individual-specific, random parameters are used to account for both dependence within the same response recorded at different times and association between different responses observed on the same sample unit at a given time. A suitable parametrisation is also introduced in the linear predictor to account for possible dependence between the individual specific random parameters and the vector of observed covariates, that is to account for endogeneity of some covariates. An extended EM algorithm is proposed to derive model parameter estimates under a maximum likelihood approach. The model is applied to the analysis of the strengths and difficulties questionnaire scores from the Millennium Cohort Study in the UK.

This article considers the estimation of the number of severely disabled people using data from the Italian survey on Health Conditions and Appeal to Medicare. Disability is indirectly measured using a set of categorical items, which survey a set of functions concerning the ability of a person to accomplish everyday tasks. Latent Class Models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey, however, is designed to provide reliable estimates at the level of Administrative Regions (NUTS2 level), while local authorities are interested in quantifying the amount of population that belongs to each latent class at a sub-regional level. Therefore, small area estimation techniques should be used. The challenge of the present application is that the variable of interest is not directly observed. Adopting a full Bayesian approach, we base small area estimation on a Latent Class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data using penalized splines. Deimmler-Reisch bases are shown to improve speed and mixing of MCMC chains used to simulate posteriors.