Quantile regression provides a detailed and robust picture of the distribution of a response variable, conditional on a set of observed covariates. Recently, it has be been extended to the analysis of longitudinal continuous outcomes using either time-constant or time-varying random parameters.However, in real-life data, we frequently observe both temporal shocks in the overall trend and individual-specific heterogeneity in model parameters. A benchmark dataset on HIV progression gives a clear example. Here, the evolution of the CD4 log counts exhibits both sudden temporal changes in the overall trend and heterogeneity in the effect of the time since seroconversion on the response dynamics. To accommodate such situations, we propose a quantile regression model where time-varying and time-constant random coefficients are jointly considered. Since observed data may be incomplete due to early drop-out, we also extend the proposed model in a pattern mixture perspective. We assess the performance of the proposals via a large scale simulation study and the analysis of the CD4 count data.

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Motivated by the analysis of data from the UK Millennium Cohort Study on emotional and behavioural disorders, we develop an M‐quantile regression model for multivariate longitudinal responses. M‐quantile regression is an appealing alternative to standard regression models; it combines features of quantile and expectile regression and it may produce a detailed picture of the conditional response variable distribution, while ensuring robustness to outlying data. As we deal with multivariate data, we need to specify what it is meant by M‐quantile in this context, and how the structure of dependence between univariate profiles may be accounted for. Here, we consider univariate (conditional) M‐quantile regression models with outcome‐specific random effects for each outcome. Dependence between outcomes is introduced by assuming that the random effects in the univariate models are dependent. The multivariate distribution of the random effects is left unspecified and estimated from the observed data. Adopting this approach, we are able to model dependence both within and between outcomes. We further discuss a suitable model parameterisation to account for potential endogeneity of the observed covariates. An extended EM algorithm is defined to derive estimates under a maximum likelihood approach.

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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-ofsample 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.

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▶ Presents research and applications on the extraction of knowable aspects from many types of data ▶ Topics include structural, quantitative, or statistical approaches for the analysis of data; advances in classification, clustering, and pattern recognition methods; strategies for modeling complex data and mining large data sets ▶ Shows how new domain-specific knowledge can be made available from data by skillful use of data analysis methodsThe international journal Advances in Data Analysis and Classification (ADAC) is designed as a forum for high standard publications on research and applications concerning the extraction of knowable aspects from many types of data. It publishes articles on such topics as structural, quantitative, or statistical approaches for the analysis of data; advances in classification, clustering, and pattern recognition methods; strategies for modeling complex data and mining large data sets; methods for the extraction of knowledge from data, and applications of advanced methods in specific domains of practice. Articles illustrate how new domain-specific knowledge can be made available from data by skillful use of data analysis methods. The journal also publishes survey papers that outline, and illuminate the basic ideas and techniques of special approaches.

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