Nikos Tzavidis

Adverse life events, area socioeconomic disadvantage, and psychopathology and resilience in young children: the importance of risk factors’ accumulation and protective factors’ specificity

Few studies on resilience in young children model risk appropriately and test theory-led hypotheses about its moderation. This study addressed both issues. Our hypothesis was that for preschool children’s emotional/behavioral adjustment in the face of contextual risk protective factors should be located in the cognitive domain. Data were from the first two sweeps of the UK’s Millennium Cohort Study. The final study sample was 4,748 three-year-old children clustered in 1,549 Lower layer Super Output Areas in nine strata. Contextual risk was measured at both area (with the Index of Multiple Deprivation) and family (with proximal and distal adverse life events experienced) level. Moderator variables were parenting, verbal and non-verbal ability, developmental milestones, and temperament. Multivariate multilevel models—that allowed for correlated residuals at both individual and area level—and univariate multilevel models estimated risk effects on specific and broad psychopathology. At baseline, proximal family risk, distal family risk and area risk were all associated with broad psychopathology, although the most parsimonious was the proximal family risk model. The area risk/broad psychopathology association remained significant even after family risk was controlled but not after family level socioeconomic disadvantage was controlled. The cumulative family risk was more parsimonious than the specific family risks model. Non-verbal ability moderated the effect of proximal family risk on conduct and emotional problems, and developmental milestones moderated the effect of proximal family risk on conduct problems. The findings highlight the importance of modeling contextual risk appropriately and of locating in the cognitive domain factors that buffer its effect on young children’s adjustment.

M-quantile models with application to poverty mapping

Over the last decade there has been growing demand for estimates of population characteristics at small area level. Unfortunately, cost constraints in the design of sample surveys lead to small sample sizes within these areas and as a result direct estimation, using only the survey data, is inappropriate since it yields estimates with unacceptable levels of precision. Small area models are designed to tackle the small sample size problem. The most popular class of models for small area estimation is random effects models that include random area effects to account for between area variations. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier robust inference. An alternative approach to small area estimation that is based on the use of M-quantile models was recently proposed by Chambers and Tzavidis (Biometrika 93(2):255–268, 2006) and Tzavidis and Chambers (Robust prediction of small area means and distributions. Working paper, 2007). Unlike traditional random effects models, M-quantile models do not depend on strong distributional assumption and automatically provide outlier robust inference. In this paper we illustrate for the first time how M-quantile models can be practically employed for deriving small area estimates of poverty and inequality. The methodology we propose improves the traditional poverty mapping methods in the following ways: (a) it enables the estimation of the distribution function of the study variable within the small area of interest both under an M-quantile and a random effects model, (b) it provides analytical, instead of empirical, estimation of the mean squared error of the M-quantile small area mean estimates and (c) it employs a robust to outliers estimation method. The methodology is applied to data from the 2002 Living Standards Measurement Survey (LSMS) in Albania for estimating (a) district level estimates of the incidence of poverty in Albania, (b) district level inequality measures and (c) the distribution function of household per-capita consumption expenditure in each district. Small area estimates of poverty and inequality show that the poorest Albanian districts are in the mountainous regions (north and north east) with the wealthiest districts, which are also linked with high levels of inequality, in the coastal (south west) and southern part of country. We discuss the practical advantages of our methodology and note the consistency of our results with results from previous studies. We further demonstrate the usefulness of the M-quantile estimation framework through design-based simulations based on two realistic survey data sets containing small area information and show that the M-quantile approach may be preferable when the aim is to estimate the small area distribution function.

Area and family effects on the psychopathology of the Millennium Cohort Study children and their older siblings

BACKGROUND To model and compare contextual (area and family) effects on the psychopathology of children nested in families nested in areas. METHOD Data from the first two sweeps of the UKs Millennium Cohort Study were used. The final study sample was 9,630 children clustered in 6,052 families clustered in 1,681 Lower-layer Super Output Areas. The mean age of the children at Sweep 2 was 4.96 (SD = 2.76) years. Contextual risk was measured at area level with the Index of Multiple Deprivation (Sweep 1), and at family level with the number of proximal (Sweep 2) and distal (Sweep 1) adverse life events experienced. Psychopathology was measured at Sweep 2 with the Strengths and Difficulties Questionnaire. RESULTS At baseline, both proximal and distal family risk and area risk predicted broad psychopathology, although the most parsimonious was the proximal family risk model, and both the family-level and the area-level variability were significant. The area risk/broad psychopathology association remained significant even when family risk was controlled, but not when family socioeconomic status was controlled. The full model added parenting and paternal and maternal psychopathology. When parental qualifications were excluded from the family-level contextual controls the effect of area risk remained significant on both externalizing and internalizing psychopathology. CONCLUSIONS The effect of area on child psychopathology operated via the socioeconomic characteristics of the childs family, not just the adverse characteristics of the neighbors. Multiple family risk predicted child psychopathology directly and independently, and not because it was associated with family socioeconomic status. Family socioeconomic status explained the association between area risk and broad psychopathology.

Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators

Small area estimation is conventionally concerned with the estimation of small area averages and totals. More recently emphasis has been also placed on the estimation of poverty indicators and of key quantiles of the small area distribution function using robust models, for example, the M-quantile small area model. In parallel to point estimation, Mean Squared Error (MSE) estimation is an equally crucial and challenging task. However, while analytic MSE estimation for small area averages is possible, analytic MSE estimation for quantiles and poverty indicators is difficult. Moreover, one of the main criticisms of the analytic MSE estimator for M-quantile estimates of small area averages is that it can be unstable when the area-specific sample sizes are small. A non-parametric bootstrap framework for MSE estimation for small area averages, quantiles and poverty indicators estimated with the M-quantile small area model is proposed. Emphasis is placed on second order properties of MSE estimators with results suggesting that the bootstrap MSE estimator is more stable than corresponding analytic MSE estimators. The proposed bootstrap is evaluated in a series of simulation studies under different parametric assumptions for the model error terms and different scenarios for the area-specific sample and population sizes. Finally, results from the application of the proposed MSE estimator to real income data from the European Survey of Income and Living Conditions (EU-SILC) in Italy are presented and information on the availability of R functions that can be used for implementing the proposed estimation procedures in practice is provided.

Small area estimation under spatial nonstationarity

A geographical weighted empirical best linear unbiased predictor (GWEBLUP) for a small area average is proposed, and an estimator of its conditional mean squared error is developed. The popular empirical best linear unbiased predictor under the linear mixed model is obtained as a special case of the GWEBLUP. Empirical results using both model-based and design-based simulations, with the latter based on two real data sets, show that the GWEBLUP predictor can lead to efficiency gains when spatial nonstationarity is present in the data. A practical gain from using the GWEBLUP is in small area estimation for out of sample areas. In this case the efficient use of geographical information can potentially improve upon conventional synthetic estimation.

Robust small area prediction for counts

A new semiparametric approach to model-based small area prediction for counts is proposed and used for estimating the average number of visits to physicians for Health Districts in Central Italy. The proposed small area predictor can be viewed as an outlier robust alternative to the more commonly used empirical plug-in predictor that is based on a Poisson generalized linear mixed model with Gaussian random effects. Results from the real data application and from a simulation experiment confirm that the proposed small area predictor has good robustness properties and in some cases can be more efficient than alternative small area approaches.

Hierarchical modeling of indoor radon concentration: how much do geology and building factors matter?

Radon is a natural gas known to be the main contributor to natural background radiation exposure and only second to smoking as major leading cause of lung cancer. The main concern is in indoor environments where the gas tends to accumulate and can reach high concentrations. The primary contributor of this gas into the building is from the soil although architectonic characteristics, such as building materials, can largely affect concentration values. Understanding the factors affecting the concentration in dwellings and workplaces is important both in prevention, when the construction of a new building is being planned, and in mitigation when the amount of Radon detected inside a building is too high. In this paper we investigate how several factors, such as geologic typologies of the soil and a range of building characteristics, impact on indoor concentration focusing, in particular, on how concentration changes as a function of the floor level. Adopting a mixed effects model to account for the hierarchical nature of the data, we also quantify the extent to which such measurable factors manage to explain the variability of indoor radon concentration.

Outlier robust model-assisted small area estimation

Small area estimation with M-quantile models was proposed by Chambers and Tzavidis (). The key target of this approach to small area estimation is to obtain reliable and outlier robust estimates avoiding at the same time the need for strong parametric assumptions. This approach, however, does not allow for the use of unit level survey weights, making questionable the design consistency of the estimators unless the sampling design is self-weighting within small areas. In this paper, we adopt a model-assisted approach and construct design consistent small area estimators that are based on the M-quantile small area model. Analytic and bootstrap estimators of the design-based variance are discussed. The proposed estimators are empirically evaluated in the presence of complex sampling designs.

Resistance to outliers of M-quantile and robust random effects small area models

The presence of outliers is a common feature in real data applications. It has been well established that outliers can severely affect the parameter estimates of statistical models, for example, random effects models, which can in turn affect the small area estimates produced using these models. Two outlier robust methodologies have been recently proposed in the small area literature. These are the M-quantile approach and the robust random effects approach. The M-quantile and robust random effects approaches are two distinct outlier robust small area methods and a comparison between these two methodologies is required. The present paper sets to fulfill this goal. Using model-based simulations and showing an application to real income data we examine how the alternative small area methodologies compare.

Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences

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.