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This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random gradient and Hessian estimates. The derivative estimates are not required to satisfy suitable accuracy requirements at each iteration but with sufficiently high probability. Concerning the evaluation of the objective function we first assume that the noise in the objective function evaluations is bounded in absolute value. Then, we analyze the case where the error satisfies prescribed dynamic accuracy requirements. We provide for both cases a complexity analysis and derive expected iteration complexity bounds. We finally focus on the specific case of finite-sum minimization which is typical of machine learning applications.

Importance: Young adults with autism spectrum disorder (ASD) experience poor employment outcomes. Teaching soft skills and using peer-based interventions improve outcomes for people with ASD. Objective: To evaluate the preliminary efficacy of a soft skills intervention and the feasibility of delivery to a group of young adults with ASD by near-peer occupational therapy master’s-level students. Design: Pretest–posttest single-group design. Setting: College campus. Participants: Convenience sample of 14 young adults (M age = 21.57 yr) with ASD. Intervention: The Assistive Soft Skills and Employment Training (ASSET) program is a 12-session, manualized, soft skills group intervention previously validated with the ASD population. Topics include communication, attitude and enthusiasm, teamwork, networking, professionalism, and stress management. Outcomes and Measures: Social functioning, self-efficacy, and adaptive behavior were measured preintervention and immediately postintervention using standardized self-report rating scales. Participant satisfaction and experience were assessed using program-specific measures. Results: Participants made statistically significant improvements, with medium to large effect sizes in social functioning, self-efficacy, and adaptive behavior. They reported high levels of satisfaction and a positive experience with the program content and delivery. Conclusions and Relevance: This study provides evidence of participant satisfaction and perceived soft skills improvement and confidence, in addition to the preliminary efficacy of master’s-level students as near-peer facilitators of the ASSET program with an ASD population. What This Article Adds: The results suggest that trained and supervised master’s-level students can effectively deliver a manualized intervention as near-peer facilitators, elicit positive feedback and high levels of participant satisfaction, and replicate and extend previously reported participant gains.

Hypercoagulability is a common complication of the systemic inflammation related to coronavirus disease 2019 creating debate within the critical care community on the therapeutic utility of Low Molecular Weight Heparin (LMWH). We collected data on consecutive patients with COVID-19 admitted to the Emergency Department of Castel San Giovanni Hospital, between February 29th and April 7th, 2020. Exclusion criteria were age

Every year, 700 million twenty-foot (container) equivalent units pass through the container terminals of the harbours all over the world. Only a small percentage (34%) are scanned to inspect the presence of radioactive materials. The need for controls is hampered essentially by three factors: the amount of both time and personnel necessary to control each container and the use of scanning methods based on systems potentially harmful for the personnel itself. Muon tomography can become a strategy for fast and reliable inspection of containers without using ionizing radiation. This technology takes advantage of multiple Coulomb scattering of the muons (particle produced by cosmic rays) through media to understand the composition and the geometry of the scanned volume. The TECNOMUSE project has the purpose to realize a muon tomography scanner based on a novel geometry and, for the first time, using Resistive Plate Chambers detectors. In this work, the preliminary results from the TECNOMUSE scanner are evaluated via Monte Carlo simulations. Many different simulations have been made with the aim to assess the detection capabilities of the device, its spatial resolution and the time required to reconstruct and distinguish different materials.

In this work we study sensitivity to hyperprior specification of the dispersion parameter in a convolution model widely used in spatial disease mapping, that accounts for both structured (spatial) and unstructured heterogeneity. In the fully Bayesian approach to disease mapping, hyperprior choice sensibly affects inferences. In this work we critically review the most common hyperprior specifications. Moreover we propose a new hyperprior distribution, the Generalised Inverse Gaussian, starting from an idea explored in the estimation of the mean for iid log-Normal observations. In this context it is well known that hyperprior parameters have to be set accurately in order to avoid infinite moments of the posterior distribution. The performances of various hyperprior choices are compared via simulation studies. In particular we investigate the sensitivity of the relative risk estimates.

Accumulation of lead and zinc was studied in the moss Funaria hygrometrica Hedw. collected from mine tailings. Heavy metal accumulation in gametophytes and sporophytes was quantified by graphite furnace atomic absorption spectrometry (GFAAS) and inductively coupled plasma-atomic emission spectrometry (ICP-AES). Pb and Zn accumulation in the placental zone was analysed by x-ray scanning electron microscopy (SEM) and transmission electron microscopy (TEM) microanalysis. Spectrometry showed that while moss gametophytes accumulated considerable concentrations of heavy metals, sporophytes accumulated only small concentrations of metals. X-ray SEM and TEM showed that the two metals accumulated in placental transfer cells on both the gametophytic and sporophytic sides. To investigate the uptake pattern for both metals under controlled conditions, F. hygrometrica plants collected from a non-polluted site were treated in the laboratory with separate solutions of Pb and Zn at two concentrations (10−2and 10−4 M ) for 24 or 168 h. Metal accumulation was analysed separately in gametophytes and sporophytes using GFAAS and ICP–AES. Each generation had a different accumulation quotient for both metals, and gametophytes accumulated significantly more metal than sporophytes. Concentrations of Zn in sporophytes were always higher than concentrations of Pb. The findings are discussed in relation to the role performed by the gametophyte and the placenta in the accumulation and sequestration of Pb and Zn.

The European Community Household Panel (ECHP) is a panel survey covering a wide range of topics regarding economic, social and living conditions. In particular, it makes it possible to calculate disposable equivalized household income, which is a key variable in the study of economic inequity and poverty. To obtain reliable estimates of the average of this variable for regions within countries it is necessary to have recourse to small area estimation methods. In this paper, we focus on empirical best linear predictors of the average equivalized income based on “unit level models” borrowing strength across both areas and times. Using a simulation study based on ECHP data, we compare the suggested estimators with crosssectional modelbased and designbased estimators. In the case of these empirical predictors, we also compare three different MSE estimators. Results show that those estimators connected to models that take units’ autocorrelation into account lead to a significant gain in efficiency, even when there are no covariates available whose population mean is known.

Refusal of households in survey participation is becoming more frequent, and total nonresponse varies in subpopulations. Reweighting is performed in particular when information about nonrespondents is scarce. In survey practice, final sampling weights are defined in several stages: as the inverse of inclusion probabilities; then they are adjusted to reduce the bias in estimation due to unit nonresponse and undercoverage; eventually they are smoothed or trimmed, because the inflation of estimators' MSE is particularly severe at the domain level. In this paper, we deal with the design consistent estimation of domain parameters in surveys with massive nonresponse when the final sample is composed by two distinct parts drawn, with different designs, from two frames. We solve this problem of adapting a dual frame methodology by means of a simple model based on the Inverse Hypergeometric distribution. We also consider the smoothing of sampling weights. We propose a new trimming method, based on the Generalized Pareto distribution, which helps to improve the efficiency of estimators at the domain level.

The availability of reliable estimates of income distribution parameters at a sub-national level is essential for the study of regional disparities. For European Union, countries the estimation of income parameters can be obtained from the European Community Household Panel, that provides reliable estimates for large areas within countries. The aim of this work is to find a suitable small area estimator of the average income at a smaller geographical scale, based on data from this survey. Since it is a panel survey, we suggest some different specifications of unit level Linear Mixed Models leading to small area estimators that borrow strength across both areas and times. In the Small Area Estimation context, full time series and “time series and cross-sectional” aggregate models have been applied in the literature, while small area unit level models for panel data have not been studied extensively. We compare the estimators performance by a Monte Carlo simulation study. Results show a significant gain in efficiency of estimators connected to models that take into account units autocorrelation.

The aim of this paper is to assess the methodological problems of an unsuccessful randomized controlled trial (RCT) conducted to evaluate the effectiveness, in terms of survival and quality of life, of the early offer of home care (HC) to persons with AIDS (PWA). The study carried out was an intention-to-treat RCT. Persons in the treatment group (TG) received the offer of HC at the moment of AIDS diagnosis; those in the control group (CG) received it six months from diagnosis. Many problems have hindered the progress of the study: particularly, the low compliance to the offer and the failure to enroll the required sample size have made the results unreliable. Analogous problems have been reported within other trials evaluating HC in different fields. The present study thoroughly evaluates the specific ethical and methodological problems encountered in designing and conducting a RCT on HC for PWA. We conclude that, before designing and conducting a RCT in this field, it is advisable to examine some main issues carefully, such as the acceptability of the offer of treatment, the expected compliance and the required size of the study population. If one or more of these elements prove to be problematic, the results of the trial risk being seriously compromised, and alternative approaches should be considered.

Postural changes in 1-G environment induce well documented haemodynamic changes. On going from Earth's 1-G environment to the microgravity of space a marked cephalic blood volume shift occurs in humans with a subsequent loss of 2-3 L of fluid determined by diuresis and decreased fluid intake. Moreover, a number of transient changes in serum concentrations of sodium, potassium and calium have been observed in astronauts during spaceflight. It is conceivable that changes in the fluid status, and reduced muscle activities, which are changed by the microgravity environment, would also result in redistribution of some trace elements, such as zinc, copper and manganese. In particular, zinc metabolism, directly involved in many physiological processes, can be altered by a wide variety of factors including stress, rest, exercise, hormones and diet. Some of the microgravity-induced responses in space can be simulated in humans by using the posture of head-down tilt, and in rat by using the posture of hindlimb suspension. The aim of the present study was to investigate the effects of hindlimb suspension for 3-14 days on sodium, potassium and zinc content in various rat tissues including blood, muscle, brain, eye and nose's skin.

A multidisciplinary home care service for people with AIDS (PWAs) was started in Rome in September 1990. This paper describes the features of the home care service offered by the Associated Health Care Workers' Co-operative (OSA), an example of the integration of private and state systems. We detail the types and numbers of visits that PWAs have needed, and we explore the possible correlation between demographic and clinical variables and the care required. As of September 1994 service had been provided to 372 PWAs. During the 4-year period, 62,927 home care visits were made (an average of 4.3 visits/patient/week): 66% were made by psychologists, social workers and home helps, and 34% by health professionals. PWAs who, at the outset of their home care, suffered from AIDS-dementia complex (ADC), toxoplasmosis, wasting syndrome or cytomegalovirus retinitis required the highest number of visits. Psychologists, social workers and home care helps made more frequent visits than health professionals for all AIDS-defining conditions except retinitis (for which 63% of visits were for health care). Our study shows that careful assessment of patients receiving home care helps in planning visits and in organizing available resources. A controlled randomized multicentre study is under way with the aim of determining the effectiveness of home care in terms of survival, quality of life and care workload and related costs.

Seven patients, six suffering from amyotrophic lateral sclerosis (ALS) and one from Friedreich ataxia, were treated with a placebo i.v. infusion during the first day and with TRH-T i.v. infusion at a rate of 2 mg/h for 8 h daily (total daily dosage 16 mg) on the 2 consecutive days. Continuous blood pressure (BP) and EKG monitorings were performed during 3 days infusion. Blood samples were collected for endocrinological evaluations. The neurological evaluation after acute TRH-T treatment showed an objective improvement in 3 of the 8. We found significantly higher values of systolic (max. difference of 10.1 mm Hg) and diastolic (max. difference of 8.8 mm Hg) BP than during placebo, beginning from the 5th h of the infusion (p less than 0.05). A trend in progressive increase of the heart rate (HR) reached statistical significance (p less than 0.01) at the 8th h of the second TRH-T infusion. The cardiovascular changes during the i.v. continuous TRH-T infusions were clinically irrelevant and never required the interruption of the treatment.

The distribution of fixed anionic sites within glomerular capillary walls has been studied in man by applying two ultrastructural histochemical methods--the high iron diamine and dialysed colloidal iron methods--to tissue chopper sections and to isolated glomeruli obtained from surgical fragments of renal tissue. By using the high iron diamine method we have been able to demonstrate that in man, too, there are sulphate (possibly heparan sulphate proteoglycan) sites preferentially located in the lamina rara esterna of the basement membrane and in the cell coat of the urinary surface of podocytes. Non-sulphate (high iron diamine-negative, dialysed colloidal iron-positive) anionic sites have been identified not only in the glycocalyx of the epithelial and endothelial cells but also in the laminae rarae of the basement membranes, where they show a more extensive distribution pattern than sulphate sites. The proposed methods seem particularly suitable for the study of human renal tissue; they could, in fact, provide useful information about the behaviour of the various anionic components of the glomerular capillary wall in pathological conditions.

The antiarrhythmic activity of flecainide has been tested in seven old patients (mean age 71 years) suffering from recurrent episodes of ventricular tachycardia. A basal 24-hour dynamic electrocardiogram was recorded for each patient and was repeated on day 5 of oral flecainide treatment (200 mg). A significant reduction (p less than 0.0001) of premature ventricular beats, of bigeminism (p = 0.0025) and of the episodes of ventricular tachycardia (p = 0.017) was obtained with plasma flecainide levels between 322 and 614 ng/ml. In addition, sinus rhythm was restored in two patients with stable atrial fibrillation and in the others ectopic atrial beats were markedly reduced. Among the ECG parameters examined, only QRS was significantly increased (p = 0.034). No significant change of blood pressure and laboratory parameters was observed. Untoward side effects were not observed.

The aim of this work is validating the Monte Carlo Internal Dosimetry (MCID) tool for internal dosimetry, which allows personalized treatment planning starting from patient-specific images and direct Monte Carlo (MC) simulations. The absorbed dose for different computational phantoms, calculated with MC and with conventional MIRD methods at both organ and voxel level, were compared, obtaining differences of about 0.3% and within 3%, respectively, whereas differences increased (up to 14%) introducing tissue heterogeneities in phantoms. The absorbed dose of spheres with different radius (10 mm ≤ r ≤ 30 mm), calculated from MC code and from OLINDA/EXM was also compared, obtaining differences varying in the range 2–9% after correcting for partial volume effects (PVEs) from imaging. This work validated the MCID tool which allows the fast generation of input macros for MC simulations, starting from patient-specific images. It also shows the impact of tissue inhomogeneities on dosimetric results and their relevance for an accurate dosimetric plan.

Besides environment sensing, robot perception can be also aimed to interact with human users. To make comfortable this reciprocal action, usually the sensor system requires an intelligent interface. In particular, the paper describes an integrated guidance system for a low-cost wheelchair prototype to allow disabled people to move autonomously in the environment. The driving system consists of an obstacle avoidance module, a simple vocal command interpreter and a head position sensor to steer the wheelchair itself. After presenting the whole system, this paper deseribes in detail the head-activated device, the related signal processing and the methods used to reduce interactions between the wheelchair motion and the sensed values. Finally, integration with the overall driving system and experimental results will be presented.

We analyze the anti-poverty effect of social cash transfers using a micro-econometric approach. Aggregate analyses, based on comparing average poverty indicators before and after public transfers, fail to address who receives the transfers and how the transfers are distributed among the poor. We consider three dichotomous outcome variables: (i) poverty status before the receipt of transfers; (ii) the receipt of transfers; and (iii) poverty status after the receipt of transfers. We use a trivariate probit model with sample selection, connecting the outcome variables to the characteristics of the household and its head. Our empirical results highlight that the Italian social transfers system overprotects certain household typologies at the expense of others, as social transfers are primarily awarded to employees with permanent positions and the elderly, while the system is not generous enough to large households with dependant children, the self-employed, temporary contract workers, and the unemployed.

Nell’analisi statistica e abbastanza comune che i dati da analizzare siano costituiti da risposte yi (i = 1,2,…,n) che sappiamo essere dipendenti da un vettore xi di dimensione p×1 contenente valori di input osservati o fissati dal ricercatore. La situazione puo essere rappresentata dall’equazione: $$ y_i= f(x_i ,\beta ) + \varepsilon _i $$ (13.1) dove il termine ei e un residuo stocastico utilizzato per descrivere l’errore sperimentale nella misura di yi o l’effetto di variabili non osservabili. In termini statistici e comune assumere: $$ \varepsilon _i\sim NID(0,\sigma ^2 ) $$ (1) cioe che i residui siano distribuiti in modo normale, con valore atteso 0, varianza costante σ2 e siano inoltre a due a due indipendenti. Il termine f(xi,β @#@) esprime la componente sistematica della relazione tra yi e xi, nel senso che E(yi) = f(xi,β) ovvero, sfruttando le proprieta della distribuzione normale, che yi ∼ NID(f(xi,β), σ2). I parametri incogniti del modello sono dati dal vettore dei coefficienti di regressione β, nella maggior parte dei casi anch’esso di dimensione p×1, e dalla varianza dei residui σ2.

R e un ambiente statistico sviluppato da un team di ricercatori di fama mondiale per la gestione e l’analisi dei dati e per la costruzione di grafici. Si tratta di uno GNU software, distribuito gratuitamente sotto i vincoli della GPL (General Public Licence). R e inoltre open source, in quanto il suo codice sorgente e scaricabile liberamente. Il download del software e della relativa documentazione (compresi alcuni brevi manuali introduttivi in italiano) puo essere effettuato dal sito del CRAN (Comprehensive R Archive Network) all’indirizzo http://cran.r-project.org/.

The log-normal distribution is a popular model in biostatistics and other fields of statistics. Bayesian inference on the mean and median of the dis- tribution is problematic because, for many popular choices of the prior for the variance (on the log-scale) parameter, the posterior distribution has no finite mo- ments, leading to Bayes estimators with infinite expected loss for the most common choices of the loss function. We propose a generalized inverse Gaussian prior for the variance parameter, that leads to a log-generalized hyperbolic posterior, for which it is easy to calculate quantiles and moments, provided that they exist. We derive the constraints on the prior parameters that yield finite posterior moments of or- der r. We investigate the choice of prior parameters leading to Bayes estimators with optimal frequentist mean square error. For the estimation of the lognormal mean we show, using simulation, that the Bayes estimator under quadratic loss compares favorably in terms of frequentist mean square error to known estimators.

A model-based small area method for calculating estimates of poverty rates based on different thresholds for subsets of the Italian population is proposed. The subsets are obtained by cross-classifying by household type and administrative region. The suggested estimators satisfy the following coherence properties: (i) within a given area, rates associated with increasing thresholds are monotonically increasing; (ii) interval estimators have lower and upper bounds within the interval (0, 1); (iii) when a large domain-specific sample is available the small area estimate is close to the one obtained using standard design-based methods; (iv) estimates of poverty rates should also be produced for domains for which there is no sample or when no poor households are included in the sample. A hierarchical Bayesian approach to estimation is adopted. Posterior distributions are approximated by means of MCMC computation methods. Empirical analysis is based on data from the 2005 wave of the EU-SILC survey.

Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay–Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quantities are difficult to check. For a special case of the Fay–Herriot model, Sinharay and Stern [2003. Posterior predictive model checking in Hierarchical models. J. Statist. Plann. Inference 111, 209–221] showed that violations of the assumptions about the random effects are difficult to detect using posterior predictive checks. In this present paper we consider two extensions of the Fay–Herriot model in which the random effects are assumed to be distributed according to either an exponential power (EP) distribution or a skewed EP distribution. We aim to explore the robustness of the Fay–Herriot model for the estimation of individual area means as well as the empirical distribution function of their ‘ensemble’. Our findings, which are based on a simulation experiment, are largely consistent with those of Sinharay and Stern as far as the efficient estimation of individual small area parameters is concerned. However, when estimating the empirical distribution function of the ‘ensemble’ of small area parameters, results are more sensitive to the failure of distributional assumptions.

The present paper proposes a statistical strategy for the analysis of regional disparities in income poverty. For the EU countries, information on individual income has been collected until now by the European Community Household Panel survey, which only yields reliable estimates for very large regions within countries. In order to obtain reliable estimates for some of the poverty indicators suggested by the Laeken Council at the sub-national level, we suggest the adoption of a multivariate small area estimation approach which enables us to reduce estimate variability. We concentrate on Italy, the country with the lowest degree of regional cohesion within the EU. Results show that disparity cannot be reduced to the so-called “North–South divide,” with the “poor” South separated from the “affluent” North, as both these macro-regions display large internal differences in terms of both poverty level and income inequality. The strategy we propose could also be adopted in order to measure poverty in other European regions, using information produced by the new EU Survey on Income and Living Conditions, which is replacing the European Community Household Panel.

In recent years, the measure of regional disparities on household poverty and social exclusion has received increasing attention by policy makers and this has produced a growing demand of sub-national statistical information on income parameters. Many studies have shown a strong connection between poverty and some characteristics of the household such as its composition, highlighting the concentration of the greatest economic difficulties in particular household typologies. For this reason, the aim of the work is to provide estimates of some poverty indicators for domains defined by cross-classifying the population by household typology (9 categories) and administrative region (20 categories), on the basis of data collected for Italy by the “European Union – Statistics on Income and Living Conditions” survey (EU-SILC). The need of estimating simultaneously more than one parameter is due to the multidimensionality of the studied phenomenon. In particular, we focus on three poverty rates based on three different thresholds, so to distinguish between poor people (PR, standard poverty threshold defined as the 60% of median of personal equivalent income), very poor people (PR80, threshold defined as the 80% of the standard poverty threshold) and people who are at risk of becoming poor (PR120, threshold defined as the 120% of the standard poverty threshold). The considered source, EU-SILC, is a sample survey on households’ income and social conditions, coordinated by Eurostat (Eurostat, 2005), designed to provide reliable estimates of main parameters of interest for areas within countries that do not correspond to our target domains. The number of units sampled from those domains are too scarce, in many cases, to obtain reliable estimates of the parameters of interest, therefore some small area estimation strategies have to be considered.

Bayesian estimators of small area parameters may be very effective in improving the precision of “direct”, design-based estimates. By the way, the may be poor estimators of the actual Empirical Distribution Function of the ensemble of small area parameters. In this paper we review different adjusted estimators that correct or mitigate this problem in the context of Hierarchical Bayesian modelling, considering also extensions to the case of multivariate models that are widely used in Small Area estimation. In particular we consider constrained and linear constrained Hierarchical Bayes estimators, along with an estimation method recently by Zhang. The posterior Mean Square Errors are proposed as measures of uncertainty. Different methods are compared by means of a simulation exercise in which many situations occurring in small area estimation applied problems are artificially re-created. The main goals of the simulation is to assess the ability of various estimators to properly estimate the actual Empirical Distribution Function of area parameters and secondly to assess the frequentist properties of posterior MSEs. The method of Zhang emerges as best in both the univariate and the multivariate setting, although the picture in the latter case is less clear.

Classical rules for optimal one-way stratification, such as the Dalenius and Hodges rule, are applied under the assumption that a single stratification variable is to be used. In this paper, we consider an information setting in which a set of candidate stratification variables is available and a proxy of the target variable (or the target variable itself) is known for a random sample of units from the population. Under these assumptions, we propose various extensions of the Dalenius and Hodges rule based either on linear prediction and on non-parametric regression methods. The resulting stratification rules are compared by means of a Monte Carlo exercise based on a set of pseudo-populations covering a wide range of possible forms of relationship between the target and the stratification variables. The application of regression trees as stratification rules, an option that may be intuitively appealing in the considered information setting, is also discussed.

In recent years, the measure of regional disparities on poverty and social exclusion has received increasing attention by policy makers and this has produced a growing demand of sub-national statistical information on income parameters. Taking into account the multidimensionality of this phenomenon, in the Laeken European Council (Eurostat, 2003) a set of financial poverty indicators were suggested to monitor the progress in fighting inequality. In the European Union regional statistical information on income can be obtained from the European Community Household Panel, a survey designed to provide reliable estimates for large regions in the countries. The aim of this work is to estimate at sub-national level some of the income indicators suggested in the Laeken council. We propose Bayesian small area estimators based on multivariate area level models exploiting the correlation between different indicators. The tendency of model based estimates to over-shrink towards the synthetic component can be a draw-back for policy makers interested in capturing regional disparities in financial poverty. To preserve the relationship between different indicators and disparities over areas, we adopt a multivariate constrained Bayes estimator. The comparison between results based on different models allows us to select the estimator realizing the best compromise between gain in efficiency and reduction of the over-shrinkage.

Reactivity to workspace features and workspace changes is an essential capability for robotic systems performing motion tasks in unstructured environments [1,11,24]. A truly autonomous mobile robot should be able to discriminate between safe and dangerous areas, recognize free passages, as well as detect possibly moving obstacles. These goals can be achieved only if the robot is endowed with a fast, reliable, accurate sensory system.

Linear Mixed Models used in small area estimation usually rely on normality for the estimation of the variance components and the Mean Square Error of predictions. Nevertheless, normality is often inadequate when the target variable is income. For this reason, in this paper we consider Linear Mixed Models for the log-transformed income (which require back-transformation for prediction of means and totals on the variable’s original scale) and a Generalized Linear Mixed Model based on the Gamma distribution. Various prediction methods are compared by means of a simulation study based on the ECHP data. Standard predictors obtained from Linear Mixed Model for the untrasformed income are shown to be preferable to the considered alternatives, confirming their robustness with respect to the failure of the normality assumption.