Giorgio E. Montanari

Nonparametric Model Calibration Estimation in Survey Sampling

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on population means (totals) of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean (total). Implicitly, calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary information is available for all units in the population, more complex modeling can be handled by means of model calibration; auxiliary variables are used to obtain fitted values of the survey variable for all units in the population, and estimation weights are sought to satisfy calibration constraints on the fitted values population mean, rather than on the auxiliary variables one. In this work we extend model calibration considering more general superpopulation models and use nonparametric methods to obtain the fitted values on which to calibrate. More precisely, we adopt neural network learning and local polynomial smoothing to estimate the functional relationship between the survey variable and the auxiliary variables. Under suitable regularity conditions, the proposed estimators are proven to be design consistent. The moments of the asymptotic distribution are also derived, and a consistent estimator of the variance of each distribution is then proposed. The performance of the proposed estimators for finite-size samples is investigated by means of simulation studies. An application to the assessment of the ecological conditions of streams in the mid-Atlantic highlands in the United States is also carried out.

Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes

Performance evaluation of nursing homes is usually accomplished by the repeated administration of questionnaires aimed at measuring the health status of the patients during their period of residence in the nursing home. We illustrate how a latent Markov model with covariates may effectively be used for the analysis of data collected in this way. This model relies on a not directly observable Markov process, whose states represent different levels of the health status. For the maximum likelihood estimation of the model we apply an EM algorithm implemented by means of certain recursions taken from the literature on hidden Markov chains. Of particular interest is the estimation of the effect of each nursing home on the probability of transition between the latent states. We show how the estimates of these effects may be used to construct a set of scores which allows us to rank these facilities in terms of their efficacy in takingcare of the health conditions of their patients. The method is used within an application based on data concerning a set of nursing homes located in the Region of Umbria, Italy, which were followed for the period 2003–2005. 1. Introduction. Both in European countries and in the United States, elderly people with chronic conditions or functional limitations can access nursing homes whenever they are no longer able or choose not to remain in their own homes. These facilities provide a diverse array of services such as housing, support systems, nursing and medical care for a sustained period of time. These services range from minimal personal assistance to virtually total care for the patients. The challenge for the nursing homes is to provide the opportunity for elderly people to live with dignity even though they may be physically or cognitively impaired. The quality of the assistance and the

Three-step estimation of latent Markov models with covariates

A three-step approach is proposed to estimate latent Markov (LM) models for longitudinal data with and without covariates. The approach is based on a preliminary clustering of sample units on the basis of time-specific responses only, and is particularly useful when a large number of response variables are observed at each time occasion. In such a context, full maximum likelihood estimation, which is typically based on the Expectation-Maximization algorithm, may have some drawbacks, essentially due to the presence of many local maxima of the model likelihood. Moreover, this algorithm may be particularly slow to converge, and may become unstable with complex LM models. The properties of the proposed estimator are illustrated theoretically and by a simulation study in which this estimator is compared with the full likelihood estimator. How reliable standard errors for the three-step parameter estimates are obtained is also shown. The approach is applied to the analysis of a dataset about the health status of elderly people resident in certain Italian nursing homes.

Theory & Methods: Conditioning on Auxiliary Variable Means in Finite Population Inference

This paper reviews conditional properties of the mean and total estimators of a finite population when auxiliary information is available. An exact design-based conditional analysis for complex sampling designs is intractable, but an asymptotic conditional framework can be developed. Within such a framework the paper establishes sufficient conditions for conditional unbiasedness and explores conditional properties of various types of regression estimators. A sample statistic capable of indicating the presence of substantial conditional biases is proposed, and illustrated by a simulation study.

On estimating the variance of the systematic sample mean

We propose a new estimator of the variance of the systematic sample mean, which is based on a sum of two components: the first takes into account ofthe trend in the population list, the second takes into account of the stochastic component of a general superpopulation model. Such an estimator is compared with the simple random sampling variance estimator and the estimator based on overlapping differences, both theoretically and empirically. The comparison shows that for many superpopulation models, the proposed estimator outperforms the other two.

A Mixed Model-assisted Regression Estimator that Uses Variables Employed at the Design Stage

The Generalized regression estimator (GREG) of a finite population mean or total has been shown to be asymptotically optimal when the working linear regression model upon which it is based includes variables related to the sampling design. In this paper a regression estimator assisted by a linear mixed superpopulation model is proposed. It accounts for the extra information coming from the design in the random component of the model and saves degrees of freedom in finite sample estimation. This procedure combines the larger asymptotic efficiency of the optimal estimator and the greater finite sample stability of the GREG. Design based properties of the proposed estimator are discussed and a small simulation study is conducted to explore its finite sample performance.

Evaluation of long-term health care services through a latent Markov model with covariates

We focus on the evaluation of the long-term health care services provided to elderly patients by nursing homes of four different health districts in the Umbria region (Italy). To this end, we analyze data coming from a longitudinal survey aimed at assessing several aspects of patient health conditions and develop an extended version of the latent Markov model with covariates, which allows us to deal with dropout and intermittent missing data patterns that are common in longitudinal studies. Maximum likelihood estimates are obtained by a two-step approach that allows for fast estimation of model parameters and prevents some drawbacks of the standard maximum likelihood method encountered in the presence of many response variables and covariates. In the application to the observed data, we show how to obtain indicators of the effectiveness of the health care services delivered by each health district, by means of a resampling procedure.

A hierarchical latent class model for predicting disability small area counts from survey data

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.

Nonparametric Methods in Survey Sampling

Nonparametric techniques have only recently been employed in the estimation procedure of finite population parameters in a model-assisted framework. When complete auxiliary information is available, the use of more flexible methods to predict the value taken by the survey variable in non sampled units allows building more efficient estimators. Here we consider a general class of nonparametric regression estimators of a finite population mean. Four different nonparametric techniques that can handle multivariate auxiliary information are employed, their properties stated and their performance compared by means of a simulation study.

Item selection by latent class-based methods: an application to nursing home evaluation

The evaluation of nursing homes is usually based on the administration of questionnaires made of a large number of polytomous items to their patients. In such a context, the latent class model represents a useful tool for clustering subjects in homogenous groups corresponding to different degrees of impairment of the health conditions. It is known that the performance of model-based clustering and the accuracy of the choice of the number of latent classes may be affected by the presence of irrelevant or noise variables. In this paper, we show the application of an item selection algorithm to a dataset collected within a project, named ULISSE, on the quality-of-life of elderly patients hosted in Italian nursing homes. This algorithm, which is closely related to that proposed by Dean and Raftery in 2010, is aimed at finding the subset of items which provides the best clustering according to the Bayesian Information Criterion. At the same time, it allows us to select the optimal number of latent classes. Given the complexity of the ULISSE study, we perform a validation of the results by means of a sensitivity analysis, with respect to different specifications of the initial subset of items, and of a resampling procedure.