Missing Values

In this paper, a new approach based on multiple instance learning is proposed to predict student's performance and to improve the obtained results using a classical single instance learning. Multiple instance learning provides a more suitable and optimized representation that is adapted to available information of each student and course eliminating the missing values that make difficult to find efficient solutions when traditional supervised learning is used. To check the efficiency of the new proposed representation, the most popular techniques of traditional supervised learning based on single instances are compared to those based on multiple instance learning. Computational experiments show that when the problem is regarded as a multiple instance one, performance is significantly better and the weaknesses of singleinstance representation are overcome.

This article examined the relationships among race-related stress, quality of life indicators, and life satisfaction among elderly African Americans. A sample of 127 elderly African Americans, consisting of 87 women and 26 men (and 14 missing values), were administered the Index of Race-Related Stress, the Satisfaction With Life Scale, and the 36-item Short-Form Health Survey. Results indicated that elderly African American men and women differed significantly with regard to institutional and collective racism-related stress. In addition, the authors found that institutional racismrelated stress was a significant predictor of psychological health in this sample of elderly African Americans. • racism and health • African American elderly • quality of life indicators Several researchers have documented the stark disparities between African Americans and other racial groups with regard to quality of life indicators (Chatters,

Neutropenia and its complications, including febrile neutropenia, are major dose-limiting toxicities of systemic cancer chemotherapy. A number of studies have attempted to identify risk factors for neutropenia and its consequences to develop predictive models capable of identifying patients at greater risk for such complications and to guide more effective and costeffective applications of the colony-stimulating factors. A systematic review of the literature showed that age, performance status, nutritional status, chemotherapy dose intensity, and low baseline blood cell counts were associated with the risk of severe and febrile neutropenia or reduced chemotherapy dose intensity in multivariate analysis in two or more studies. Similarly, age, diagnosis of leukemia or lymphoma, high temperature or low blood pressure at admission, and i.v. site infection along with low blood cell counts and organ dysfunction were associated with serious medical complications of febrile neutropenia, including bacteremia and death. The available risk model studies, however, had several limitations, including retrospective analyses of small study populations lacking independent validation, frequent missing values, and differences in the predictive factors considered. To overcome the limitations of previous studies, efforts are under way to develop and validate risk models based on large prospective studies in representative populations of patients receiving systemic chemotherapy. The Oncologist 2005;10:427-437

A. Abraham el al.(Eels.) 251 Soft Computing Systems: Design, Management and Applications IOS Press. 2002 A Study of i^-Nearest Neighbour as an Imputation Method Gustavo EAPA Batista and Maria Carolina Monard University of Sao Paulo-USP Institute of Mathematics and ...

The objective of this research is to implement a method for estimating the real missing data in heart disease datasets and to show how it affects the resulting knowledge. Missing data is common problem in knowledge discovery from database (KDD) processes that can lead significant error in extracted knowledge. We use hybridization of artificial neural network and rough set theory (ANNRST) to estimate the real missing data on heart disease from UCI (University of California, Irvine) datasets. ANN with reduced input ...

Information related to land surface phenology is important for a variety of applications. For example, phenology is widely used as a diagnostic of ecosystem response to global change. In addition, phenology influences seasonal scale fluxes of water, energy, and carbon between the land surface and atmosphere. Increasingly, the importance of phenology for studies of habitat and biodiversity is also being recognized. While many data sets related to plant phenology have been collected at specific sites or in networks focused on individual plants or plant species, remote sensing provides the only way to observe and monitor phenology over large scales and at regular intervals. The MODIS Global Land Cover Dynamics Product was developed to support investigations that require regional to global scale information related to spatiotemporal dynamics in land surface phenology. Here we describe the Collection 5 version of this product, which represents a substantial refinement relative to the Collection 4 product. This new version provides information related to land surface phenology at higher spatial resolution than Collection 4 (500-m vs. 1-km), and is based on 8-day instead of 16-day input data. The paper presents a brief overview of the algorithm, followed by an assessment of the product. To this end, we present (1) a comparison of results from Collection 5 versus Collection 4 for selected MODIS tiles that span a range of climate and ecological conditions, (2) a characterization of interannual variation in Collections 4 and 5 data for North America from 2001 to 2006, and (3) a comparison of Collection 5 results against ground observations for two forest sites in the northeastern United States. Results show that the Collection 5 product is qualitatively similar to Collection 4. However, Collection 5 has fewer missing values outside of regions with persistent cloud cover and atmospheric aerosols. Interannual variability in Collection 5 is consistent with expected ranges of variance suggesting that the algorithm is reliable and robust, except in the tropics where some systematic differences are observed. Finally, comparisons with ground data suggest that the algorithm is performing well, but that end of season metrics associated with vegetation senescence and dormancy have higher uncertainties than start of season metrics.

Cloud cover usually denies the generation of land surface temperature (LST) time series over large areas from thermal infrared (TIR) data sensed by satellites. If cloud cover is brief ( < 4 h) and only partial on the scale of a METEOSAT pixel, the discontinuous time series of cloud-free measurements still approximates a cloud-free diurnal temperature cycle (DTC). In order to interpolate the missing values and to describe the thermal behaviour of the land surface as a whole, advantage is taken of METEOSAT's high temporal resolution of 30 min. A Levenberg ± Marquardt minimisation scheme is utilised to automatically fit a model of the DTC to the time series of cloud-screened brightness temperatures (BT). Out of physical considerations and in order to stabilise the fits, a priori knowledge from solar geometry is utilised and the model function is required to be smooth and continuous. A robust estimator of the error, which is based on the median rather than the arithmetic mean, is used to lessen the impact of outliers on the fits. The thermal behaviour of the land surface is then described by the determined model parameters, and the 48 METEOSAT BTs per pixel per day are reduced to five parameters per pixel per day. Monthly maximum and median composites of cloud-screened METEOSAT BTs yield synthetic DTCs, which are less influenced by synoptic effects. Fitting the model to monthly composites reduces the 17 520 METEOSAT BTs per pixel per year to 60 parameters per pixel per year. This data reduction is advantageous to climatological studies, which require the processing of long time series. The model parameters are shown to be related to physical properties of the land surface, particularly to the normalised difference vegetation index (NDVI) and thermal inertia. D

Modeling the activated sludge wastewater treatment plant plays an important role in improving its performance. However, there are many limitations of the available data for model identification, calibration, and verification, such as the presence of missing values and outliers. Because available data are generally short, these gaps and outliers in data cannot be discarded but must be replaced by more reasonable estimates. The aim of this study is to use the Kohonen self-organizing map ͑KSOM͒, unsupervised neural networks, to predict the missing values and replace outliers in time series data for an activated sludge wastewater treatment plant in Edinburgh, U.K. The method is simple, computationally efficient and highly accurate. The results demonstrated that the KSOM is an excellent tool for replacing outliers and missing values from a high-dimensional data set. A comparison of the KSOM with multiple regression analysis and back-propagation artificial neural networks showed that the KSOM is superior in performance to either of the two latter approaches.

Background and Objective: Epidemiologic studies commonly estimate associations between predictors (risk factors) and outcome. Most software automatically exclude subjects with missing values. This commonly causes bias because missing values seldom occur completely at random (MCAR) but rather selectively based on other (observed) variables, missing at random (MAR). Multiple imputation (MI) of missing predictor values using all observed information including outcome is advocated to deal with selective missing values. This seems a self-fulfilling prophecy. Methods: We tested this hypothesis using data from a study on diagnosis of pulmonary embolism. We selected five predictors of pulmonary embolism without missing values. Their regression coefficients and standard errors (SEs) estimated from the original sample were considered as ''true'' values. We assigned missing values to these predictorsdboth MCAR and MARdand repeated this 1,000 times using simulations. Per simulation we multiple imputed the missing values without and with the outcome, and compared the regression coefficients and SEs to the truth. Results: Regression coefficients based on MI including outcome were close to the truth. MI without outcome yielded very biasedd underestimateddcoefficients. SEs and coverage of the 90% confidence intervals were not different between MI with and without outcome. Results were the same for MCAR and MAR. Conclusion: For all types of missing values, imputation of missing predictor values using the outcome is preferred over imputation without outcome and is no self-fulfilling prophecy.

Copyright c 2002, 2004, 2008 by StataCorp LP All rights reserved. First edition 2002 Revised edition 2004 Second edition 2008 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in LATE X2ε Printed in the United States of America ...

Copyright c 2002, 2004, 2008 by StataCorp LP All rights reserved. First edition 2002 Revised edition 2004 Second edition 2008 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in LATE X2ε Printed in the United States of America ...

Cross-sectional data from a survey of Danish firms are used to examine branding behavior in 2002 and its change between 1997 and 2002+ Summary data from the survey are presented+ Branding behavior is defined and relevant literature is reviewed+ Based on hypotheses developed from this literature and supporting features of the Danish food marketing chain, six econometric models are specified+ Specification accounts for dependent variables' characteristics~count and fractional data, and truncated samples!+ Missing values are replaced using Griliches' method~Griliches, 1986!+ Large firms are found to own and introduce the most brands, although few associations with the commodity sector are identified+ Firms' use of retail brands is found to substitute for brand introduction in the long run and to increase with ownership by retail firms+ Conclusions are drawn regarding the strategic stance of retailers in the Danish food system and its employment of retailers' own-label brands+ @ECONLIT Classifications: Q120; Q130; L190#+

The increasing scientific and industrial interest towards metabonomics takes advantage from the high qualitative and quantitative information level of nuclear magnetic resonance (NMR) spectroscopy. However, several chemical and physical factors can affect the absolute and the relative position of an NMR signal and it is not always possible or desirable to eliminate these effects a priori. To remove misalignment of NMR signals a posteriori, several algorithms have been proposed in the literature. The icoshift program presented here is an open source and highly efficient program designed for solving signal alignment problems in metabonomic NMR data analysis. The icoshift algorithm is based on correlation shifting of spectral intervals and employs an FFT engine that aligns all spectra simultaneously. The algorithm is demonstrated to be faster than similar methods found in the literature making full-resolution alignment of large datasets feasible and thus avoiding down-sampling steps such as binning. The algorithm uses missing values as a filling alternative in order to avoid spectral artifacts at the segment boundaries. The algorithm is made open source and the Matlab code including documentation can be downloaded from www.models.life.ku.dk.

An Introduction to Survival Analysis Using Stata, Third Edition is the ideal tutorial for professional data analysts who want to learn survival analysis for the first time or who are well versed in survival analysis but are not as dexterous in using Stata to analyze survival data. This text also serves as a valuable reference to those readers who already have experience using Stata’s survival analysis routines. The third edition has been updated for Stata 11, and it includes a new chapter on competing-risks analysis. This chapter describes the problems posed by competing events (events that impede the failure event of interest), and covers estimation of cause-specific hazards and cumulative incidence functions. Other enhancements include the handling of missing values by multiple imputation in Cox regression, a new-to-Stata-11 system for specifying categorical (factor) variables and their interactions, three additional diagnostic measures for Cox regression, and a more efficient syn...

Classification and regression trees are prediction models constructed by recursively partitioning a data set and fitting a simple model to each partition. Their name derives from the usual practice of describing the partitioning process by a decision tree. This article reviews some widely available algorithms and compares their capabilities, strengths and weaknesses in two examples.

Environmental time series are often affected by the “presence” of missing data, but when dealing statistically with data, the need to fill in the gaps estimating the missing values must be considered. At present, a large number of statistical techniques are available to achieve this objective; they range from very simple methods, such as using the sample mean, to very sophisticated ones, such as multiple imputation. A brand new methodology for missing data estimation is proposed, which tries to merge the obvious advantages of the simplest techniques (e.g. their vocation to be easily implemented) with the strength of the newest techniques. The proposed method consists in the application of two consecutive stages: once it has been ascertained that a specific monitoring station is affected by missing data, the “most similar” monitoring stations are identified among neighbouring stations on the basis of a suitable similarity coefficient; in the second stage, a regressive method is applied in order to estimate the missing data. In this paper, four different regressive methods are applied and compared, in order to determine which is the most reliable for filling in the gaps, using rainfall data series measured in the Candelaro River Basin located in South Italy.

records with missing values. This work evaluates the performance of several statistical and machine learning imputation methods that were used to predict recurrence in patients in an extensive real breast cancer data set. Materials and methods: Imputation methods based on statistical techniques, e.g., mean, hot-deck and multiple imputation, and machine learning techniques, e.g., multi-layer perceptron (MLP), selforganisation maps (SOM) and k-nearest neighbour (KNN), were applied to data collected through the ''El Á lamo-I'' project, and the results were then compared to those obtained from the listwise deletion (LD) imputation method. The database includes demographic, therapeutic and recurrence-survival information from 3679 women with operable invasive breast cancer diagnosed in 32 different hospitals belonging to the Spanish Breast Cancer Research Group (GEICAM). The accuracies of predictions on early cancer relapse were measured using artificial neural networks (ANNs), in which different ANNs were estimated using the data sets with imputed missing values. Results: The imputation methods based on machine learning algorithms outperformed imputation statistical methods in the prediction of patient outcome. Friedman's test revealed a significant difference ð p ¼ 0:0091Þ in the observed area under the ROC curve (AUC) values, and the pairwise comparison test showed that the AUCs for MLP, KNN and SOM were significantly higher ( p ¼ 0:0053, p ¼ 0:0048 and p ¼ 0:0071, respectively) than the AUC from the LD-based prognosis model. Conclusion: The methods based on machine learning techniques were the most suited for the imputation of missing values and led to a significant enhancement of prognosis accuracy compared to imputation methods based on statistical procedures. ß

Hydrognomon is a software tool for the processing of hydrological data. It is an open source application running on standard Microsoft Windows platforms, and it is part of the openmeteo.org framework. Data are imported through standard text files, spreadsheets or by typing. Standard hydrological data processing techniques include time step aggregation and regularization, interpolation, regression analysis and infilling of missing values, consistency tests, data filtering, graphical and tabular visualisation of time series, etc. It supports several time steps, from the finest minute scales up to decades; specific cases of irregular time steps and offsets are also supported. The program also includes common hydrological applications, such as evapotranspiration modelling, stage-discharge analysis, homogeneity tests, areal integration of point data series, processing of hydrometric data, as well as lumped hydrological modelling with automatic calibration facilities. Here the emphasis is given on the statistical module of Hydrognomon, which provides tools for data exploration, fitting of distribution functions, statistical prediction, Monte-Carlo simulation, determination of confidence limits, analysis of extremes, and construction of ombrian (intensity-duration-frequency) curves. Hydrognomon is available for download from http://www.hydrognomon.org/.

Gene expression profiling plays an important role in a broad range of areas in biology. The raw gene expression data, may contain missing values. It is an important preprocessing step to accurately estimate missing values in microarray data, because complete datasets are required in numerous expression profile analysis. Numerous methods have been developed to deal with missing values. In this paper, a new and robust method based on fuzzy clustering and gene ontology is proposed to estimate missing values in microarray data. In the proposed method, missing values are imputed with values generated from cluster centers. To determine the similar genes in clustering process, we have utilized the biological knowledge obtained from gene ontology as well as gene expression values. We have applied the proposed method on yeast cell cycle data and yeast environmental stress data, with different percentage of missing entries. We compared the estimation accuracy of our method with some other methods. The experimental results indicate that the proposed method outperforms other methods in terms of accuracy.

The software package AMDIS performs gas chromatography-mass spectrometry (GC-MS) peak deconvolution but tends to produce false positives and leaves missing values where peaks are found in only a proportion of a set of chromatograms. We have developed a software complement to AMDIS that (i) allows rapid manual inspection of chromatographic peaks across all samples to confirm data quality and (ii) for a given sample set, integrates peak areas across all samples even where AMDIS deconvolution would leave missing values. The freely available package runs within the commercial Matlab environment and is useful where GC-MS is used to profile complex mixtures.

Several models for longitudinal data with nonrandom missingness are available. The selection model of Diggle and Kenward is one of these models. It has been mentioned by many authors that this model depends on untested modelling assumptions, such as the response distribution, from the observed data. So, a sensitivity analysis of the study's conclusions for such assumptions is needed. The stochastic EM algorithm is proposed and developed to handle continuous longitudinal data with nonrandom intermittent missing values when the responses have non-normal distribution. This is a step in investigating the sensitivity of the parameter estimates to the change of the response distribution. The proposed technique is applied to real data from the International Breast Cancer Study Group.

The use of Patient-reported Outcomes (PROs) as secondary endpoints in the development of new antidepressants has grown in recent years. The objective of this study was to assess the psychometric properties of the 9-item, patient-administered version of the Montgomery-Åsberg Depression Rating Scale (MADRS-S).

Objective: To develop and validate a clinically feasible measure of communication effectiveness for people with any type of communication problem following stroke. Design: Cross-sectional, interview-based, psychometric study, building on the development phase for construction of the Communication Outcome after Stroke (COAST) scale. Setting: A community sample from the northwest of England, UK. Subjects: One hundred and two people with communication problems (aphasia and/or dysarthria) following a stroke, within the previous 4-12 months. Interventions: Administration of the COAST scale, on two occasions, within a two-week period, and collection of demographic and other data relating to disability, degree of aphasia (where appropriate) and hospital diagnosis of aphasia/dysarthria. Main measures: Acceptability (missing values), reliability (internal consistency and test-retest reliability) and item analysis (item redundancy). Results: Ninety-seven (visit 1) and 98 (visit 2) respondents provided usable data for the psychometric analysis. The 29-item COAST scale showed good acceptability (few missing values, sample spread 28-100%), internal consistency and test-retest reliability for the scale (a ¼ 0.95; ICC ¼ 0.90) and its subscales (a ¼ 0.65-0.93; ICC ¼ 0.72-0.88), but possible item redundancy. A revised scale of 20 items was produced, demonstrating good internal consistency and test-retest reliability (a ¼ 0.83-92; ICC ¼ 0.72-0.88). Conclusions: The COAST is a patient-centred, practical and reliable measure that can be used to assess self-perceived communication effectiveness for people with aphasia and/or dysarthria. Further testing on construct validity and responsiveness to change is needed before the measure can be firmly recommended for use within clinical practice and research.

There were 19 submissions from 11 countries. Each paper has rigorously been reviewed by at least two international experts who were mostly members of the program committee. The reviewing process of each paper was coordinated by the co-chairs. As a result, 17 papers were accepted for presentation in this workshop. Unfortunately, two accepted papers were not included in the proceedings of DCAP02 because the authors cannot present this workshop.

Classification and regression trees are prediction models constructed by recursively partitioning a data set and fitting a simple model to each partition. Their name derives from the usual practice of describing the partitioning process by a decision tree. This article reviews some widely available algorithms and compares their capabilities, strengths and weaknesses in two examples.

This impressive book contains formulae for computing sample size in a wide range of settings. Onesample studies and two-sample comparisons for quantitative, binary and time-to-event outcomes are covered comprehensively, with separate sample size formulae for testing equality, non-inferiority and equivalence. Many less familiar topics are also covered, including sample size for comparing k samples, bioequivalence and dose-response studies, and (new in this second edition) microarray studies and Bayesian sample size determination. Generic modifications are given for group sequential studies, as well as for dropout, treatment switching and prognostic covariates. The authors give statistical background to the procedures, the derivation of many formulae and realistic examples.

Missing data are quite common in practical applications of statistical methods. Imputation is general statistical method for the analysis of incomplete data sets. The goal of the paper is to review selected imputation techniques. Special attention is paid to methods implemented in some packages working in the R environment. An example is presented to show how to handle missing values using a few procedures of single and multiple imputation implemented in R.

A web-based application has been designed from a genetic-epidemiology point of view to analyze association studies. Main capabilities include: descriptive analysis, test for Hardy-Weinberg equilibrium and linkage disequilibrium. Analysis of association is based on linear or logistic regression according to the response variable (quantitative or binary disease status respectively). Analysis of single SNPs: multiple inheritance models (co-dominant, dominant, recessive, additive and super-dominant), and analysis of interactions (gene-gene or gene-environment). Analysis of multiple SNPs: haplotype frequency estimation, analysis of association of haplotypes with the response, including analysis of interactions. Availability: Main page: http://bioinfo.iconcologia.net/SNPstats. Source code for local installation is available under GNU license. Contact: [email protected] Supplementary information: Figures with a sample run are available on Bioinformatics online. A detailed online tutorial is available within the application.

A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. As part of this framework, several algorithms are examined, each of which is applicable to fixed and random-valued impulse noise models. First, a simple two-state approach is described in which the algorithm switches between the output of an identity filter and a rank-ordered mean (ROM) filter. The technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter. For a small additional cost in memory, this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and ROM filter in which the weighting coefficients can be optimized using image training data. Extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40% impulse noise corruption. Moreover, the method can effectively restore images corrupted with Gaussian noise and mixed Gaussian and impulse noise. Finally, the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise

In real life situations, we often encounter data sets containing missing observations. Statistical methods that address missingness have been extensively studied in recent years. One of the more popular approaches involves imputation of the missing values prior to the analysis, thereby rendering the data complete. Imputation broadly encompasses an entire scope of techniques that have been developed to make inferences about incomplete data, ranging from very simple strategies (e.g., mean imputation) to more advanced approaches that require estimation, for instance, of posterior distributions using MCMC methods. Additional complexity arises when the number of missingness patterns increases and/or when both categorical and continuous random variables are involved. Implementation of routines, procedures, or packages capable of generating imputations for incomplete data are now widely available. We review some of these in the context of a motivating example, as well as in a simulation study, under two missingness mechanisms (missing at random; missing not at random). Thus far, evaluation of existing implementations have frequently centered on the resulting parameter estimates of the prescribed model of interest after imputing the missing data. In some situations, however, interest may very well be on the quality of the imputed values at the level of the individual -an issue that has received relatively little attention. In this paper, we focus on the latter to provide further insight about the performance of the different routines, procedures and packages in this respect.

The statistical analysis of compositional data based on logratios of parts is not suitable when zeros are present in a data set. Nevertheless, if there is interest in using this modeling approach, several strategies have been published in the specialized literature ...

We review second-and third-order multivariate calibration, based on the growing literature in this field, the variety of data being produced by modern instruments, and the proliferation of algorithms capable of dealing with higher-order data. We primarily emphasize the relevance of the subject to analytical chemistry. We intend, in the terminology section, to clarify some confusing features relating to the definition of sample constituents in second-order calibration. We then classify and compare instrumental data and available algorithms. We provide insight into the relative advantages and disadvantages of the existing algorithms (e.g., in terms of: achieving second-order advantage (the ability to cope with varying amounts of potential interferents in test samples), presence of linear dependency in the data, handling trilinear deviations, using incomplete calibration data, extension to higherorder information, handling missing values; and, providing physico-chemical information. Finally, we present a number of applications, selected from recent second-and third-order experimental works based on data obtained through excitationemission fluorescence spectroscopy, spectral-kinetic and spectral-pH measurements, and hyphenated techniques.

Incomplete data is a common drawback in many pattern classification applications. A classical way to deal with unknown values is missing data estimation. Most machine learning techniques work well with missing values, but they do not focus the missing data estimation to solve the classification task. This paper 1 presents effective neural network approaches based on Multi-Task Learning (MTL) for pattern classification with missing inputs. These MTL networks are compared with representative procedures used for handling incomplete data on two wellknown data sets. The experimental results show the superiority of our approaches with respect to alternative techniques.

The growing demand on geospatial services requires an intensified study of geoinformation from various sources covering the same geographic space. Data matching is one of the fundamental measures that help make different datasets interoperable. This paper reports a special case of data matching between the road layer from the digital landscape model ''Basis DLM'' maintained by German surveying and mapping agencies and the road database supplied by TeleAtlas Corp. The authors put forward a generic approach which is able to handle three unfavorable matching conditions: (1) missing values of essential road attributes, e.g. street names are only sporadically available in Basis DLM, (2) unsystematic geometric discrepancies between the corresponding road objects, and (3) unknown extent of geometric discrepancies between the two datasets. The proposed approach is implemented in Arc GIS 9.0 as a tool used to match street networks as well as transfer of information between the matched datasets. By means of an innovative matching algorithm termed as ''unsymmetrical buffer growing'', this matching approach has gained some self-learning abilities and yielded high matching performance indicated by an average matching rate of 96.1% on large data sets of road networks. Meanwhile, a measurement of matching certainty on the basis of geometrical and topological similarity is introduced, which supports the human operator to judge the quality of matching results and easily detect possible matching errors.

Homogeneity analysis combines the idea of maximizing the correlations between variables of a multivariate data set with that of optimal scaling. In this article we present methodological and practical issues of the R package homals which performs homogeneity analysis and various extensions. By setting rank constraints nonlinear principal component analysis can be performed. The variables can be partitioned into sets such that homogeneity analysis is extended to nonlinear canonical correlation analysis or to predictive models which emulate discriminant analysis and regression models. For each model the scale level of the variables can be taken into account by setting level constraints. All algorithms allow for missing values.

This paper tests the sensitivity of poverty indexes to the choice of adult equivalence scales, assumptions about the existence of economies of scale in consumption, methods for treating missing and zero incomes, and different adjustments to handle income misreporting. We also perform sensitivity analysis to the use of different poverty lines and poverty indexes, which are issues that have been much more explored in the literature. The sensitivity analysis is applied to household survey data from 17 Latin American countries, which include 92% of the population in the region. By varying these parameters within reasonable boundaries, we find that the proportion of poor could be said to be either 12.7 percent or 65.8 percent of the total population. Additionally, the ranking of countries with respect to poverty is also highly sensitive. This points to the need of justifying and being explicit about the underlying choices and definitions behind poverty statistics, and to the need of performing sensitivity analysis illustrating the menu of options that can answer the question of how much poverty there is.

An efficient methodology for dealing with missing values and outlying observations simultaneously in principal component analysis (PCA) is proposed. The concept described in the paper consists of using a robust technique to obtain robust principal components combined with the expectation maximization approach to process data with missing elements. It is shown that the proposed strategy works well for highly contaminated data containing different amounts of missing elements. The authors come to this conclusion on the basis of the results obtained from a simulation study and from analysis of a real environmental data set.

Environmental data contains lengthy records of sequential missing values. Practical problem arose in the analysis of adverse health effects of sulphur dioxide (SO 2 ) levels and asthma hospital admissions for Sydney, Nova Scotia, Canada. Reliable missing values imputation techniques are required to obtain valid estimates of the associations with sparse health outcomes such as asthma hospital admissions. In this paper, a new method that incorporates prediction errors to impute missing values is described using mean daily average sulphur dioxide levels following a stationary time series with a random error. Existing imputation methods failed to incorporate the prediction errors. An optimal method is developed by extending a between forecast method to include prediction errors. Validity and efficacy are demonstrated comparing the performances with the values that do not include prediction errors. The performances of the optimal method are demonstrated by increased validity and accuracy of the b coefficient of the Poisson regression model for the association with asthma hospital admissions. Visual inspection of the imputed values of sulphur dioxide levels with prediction errors demonstrated that the variation is better captured. The method is computationally simple and can be incorporated into the existing statistical software.