A benchmark of kriging-based infill criteria for noisy optimization

Responses of many real-world problems can only be evaluated perturbed by noise. In order to make an efficient optimization of these problems possible, intelligent optimization strategies successfully coping with noisy evaluations are required. In this article, a comprehensive review of existing kriging-based methods for the optimization of noisy functions is provided. In summary, ten methods for choosing the sequential samples are described using a unified formalism. They are compared on analytical benchmark problems, whereby the usual assumption of homoscedastic Gaussian noise made in the underlying models is meet. Different problem configurations (noise level, maximum number of observations, initial number of observations) and setups (covariance functions, budget, initial sample size) are considered. It is found that the choices of the initial sample size and the covariance function are not critical. The choice of the method, however, can result in significant differences in the performance. In particular, the three most intuitive criteria are found as poor alternatives. Although no criterion is found consistently more efficient than the others, two specialized methods appear more robust on average.

KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging

Several strategies relying on kriging have recently been proposed for adaptively estimating contour lines and excursion sets of functions under severely limited evaluation budget. The recently released R package KrigInv 3 is presented and offers a sound implementation of various sampling criteria for those kinds of inverse problems. KrigInv is based on the DiceKriging package, and thus benefits from a number of options concerning the underlying kriging models. Six implemented sampling criteria are detailed in a tutorial and illustrated with graphical examples. Different functionalities of KrigInv are gradually explained. Additionally, two recently proposed criteria for batch-sequential inversion are presented, enabling advanced users to distribute function evaluations in parallel on clusters or clouds of machines. Finally, auxiliary problems are discussed. These include the fine tuning of numerical integration and optimization procedures used within the computation and the optimization of the considered criteria.

Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package

Kriging-based optimization relying on noisy evaluations of complex systems has recently motivated contributions from various research communities. Five strategies have been implemented in the DiceOptim package. The corresponding functions constitute a user-friendly tool for solving expensive noisy optimization problems in a sequential framework, while offering some flexibility for advanced users. Besides, the implementation is done in a unified environment, making this package a useful device for studying the relative performances of existing approaches depending on the experimental setup. An overview of the package structure and interface is provided, as well as a description of the strategies and some insight about the implementation challenges and the proposed solutions. The strategies are compared to some existing optimization packages on analytical test functions and show promising performances.

Factorial designs: an overview with applications to orthodontic clinical trials.

Factorial designs for clinical trials are often encountered in medical, dental, and orthodontic research. Factorial designs assess two or more interventions simultaneously and the main advantage of this design is its efficiency in terms of sample size as more than one intervention may be assessed on the same participants. However, the factorial design is efficient only under the assumption of no interaction (no effect modification) between the treatments under investigation and, therefore, this should be considered at the design stage. Conversely, the factorial study design may also be used for the purpose of detecting an interaction between two interventions if the study is powered accordingly. However, a factorial design powered to detect an interaction has no advantage in terms of the required sample size compared to a multi-arm parallel trial for assessing more than one intervention. It is the purpose of this article to highlight the methodological issues that should be considered when planning, analysing, and reporting the simplest form of this design, which is the 2 × 2 factorial design. An example from the field of orthodontics using two parameters (bracket type and wire type) on maxillary incisor torque loss will be utilized in order to explain the design requirements, the advantages and disadvantages of this design, and its application in orthodontic research.

Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Using Factorial Surveys and Stated Choice Experiments to Investigate Discriminatory Attitudes and Preferences

Empirical research on discriminatory attitudes and behaviour grapples with the social undesirability of its object. In many studies using regular survey methods, estimates are biased, and the social context of discrimination is not taken into account. Several methods have been developed, especially to deal with the first problem. In this regard, the estimation of the ‘true value’ of discriminatory attitudes is at the centre of interest. However, methodological contributions focusing on the social context of attitude communication and discriminatory behaviour, as well as the correlation between both, are rare. We present two experimental methods which address those issues: factorial surveys and stated choice experiments. In a first study, the usefulness of factorial surveys is demonstrated with data on German anti-Semitism (N=279). We show that the rate of approval with anti-Semitic statements increases if (a) respondents are told that the majority of fellows agree with such statements, (b) the term “Jews” is replaced by the term “Israelis”, and (c) reference to the Holocaust is made. Apart from the main effects of these experimental factors, significant interaction effects regarding the political attitudes and social status of respondents are observed. In a second study, a stated choice experiment on the purchase of olive oil and tomatoes was conducted in Germany (N=440). We find that respondents prefer Italian and Dutch products (control treatment) compared to Israeli and Palestinian ones (discrimination treatments). There are no significant differences between preferences for a so called ‘Peace product’ (which is produced jointly by Israelis and Palestinians) and products from Italy as well as the Netherlands. Yet, taking discriminatory attitudes (anti-Semitic and anti-Arabic attitudes) into account, a strong correlation between those attitudes and stated behaviour (purchase of Israeli, Palestinian and jointly produced products) can be found. This adds support to the hypothesis that discriminatory attitudes hold behavioural consequences.

Predictors of healthcare professionals' attitudes towards family involvement in safety-relevant behaviours: a cross-sectional factorial survey study.

OBJECTIVES To investigate predictors of healthcare professionals' (HCPs) attitudes towards family involvement in safety-relevant behaviours. DESIGN A cross-sectional fractional factorial survey that assessed HCPs' attitudes towards family involvement in two error scenarios relating to hand hygiene and medication safety. Each survey comprised two randomised vignettes that described the potential error, how the family member communicated with the HCP about the error and how the HCP responded to the family member's question. SETTING 5 teaching hospitals in London, the Midlands and York. HCPs were approached on a range of medical and surgical wards. PARTICIPANTS 160 HCPs (73 doctors; 87 nurses) aged between 21 and 65 years (mean 37) 102 were female. OUTCOME MEASURES HCP approval of family member's behaviour; HCP reaction to the family member; anticipated effects on the family member-HCP relationship; HCP support for being questioned about hand hygiene/medication; affective rating responses. RESULTS HCPs supported family member's intervening (88%) but only 41% agreed this would have positive effects on the family member/HCP relationship. Across vignettes and error scenarios the strongest predictors of attitudes were how the HCP (in the scenario) responded to the family member and whether an error actually occurred. Doctors (vs nurses) provided systematically more positive affective ratings to the vignettes. CONCLUSIONS Important predictors of HCPs' attitudes towards family members' involvement in patient safety have been highlighted. In particular, a discouraging response from HCP's decreased support for family members being involved and had strong perceived negative effects on the family member/HCP relationship.

The impact of the position effect on the factorial structure of the Culture Fair Test (CFT)

The Culture Fair Test (CFT) is a psychometric test of fluid intelligence consisting of four subtests; Series, Classification, Matrices, and Topographies. The four subtests are only moderately intercorrelated, doubting the notion that they assess the same construct (i.e., fluid intelligence). As an explanation of these low correlations, we investigated the position effect. This effect is assumed to reflect implicit learning during testing. By applying fixed-links modeling to analyze the CFT data of 206 participants, we identified position effects as latent variables in the subtests; Classification, Matrices, and Topographies. These position effects were disentangled from a second set of latent variables representing fluid intelligence inherent in the four subtests. After this separation of position effect and basic fluid intelligence, the latent variables representing basic fluid intelligence in the subtests Series, Matrices, and Topographies could be combined to one common latent variable which was highly correlated with fluid intelligence derived from the subtest Classification (r=.72). Correlations between the three latent variables representing the position effects in the Classification, Matrices, and Topographies subtests ranged from r=.38 to r=.59. The results indicate that all four CFT subtests measure the same construct (i.e., fluid intelligence) but that the position effect confounds the factorial structure

The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Adolescent tobacco use: Studies of prevalence, factorial validity, and factorial invariance between African Americans and Whites

In the last thirty years, increasing efforts have been made to reduce the prevalence of adolescent tobacco use in the United States. Although the prevalence has declined dramatically over the past decade, there are still sharp differences in adolescent smoking-initiation rates across racial/ethnic groups. Large-scale surveys frequently assess smoking-related attitudes, self-efficacy, and intentions to explain the differences in smoking rates between African Americans and Whites. However, there is little agreement about which constructs are significant. Moreover, the psychometric properties of smoking-related attitude, self-efficacy, and intention constructs have not been fully examined. More studies are needed to understand existing patterns of tobacco use and to validate and fully exploit the constructs' relationship to adolescent smoking initiation across racial/ethnic groups. ^ This dissertation reports on a secondary analysis of data from a large multi-ethnic convenience sample of sixth- through eighth-grade students in 22 schools in East Texas and the city of Houston. The specific aims of this dissertation were to (1) describe smoking and alternate tobacco product use rates by race/ethnicity, gender, age, and grade level (Article 1); (2) test the factorial validity of smoking-related attitudes, self-efficacy, and intentions using confirmatory factor analysis techniques (Article 2); and (3) test the factorial invariance of smoking-related attitudes, self-efficacy, and intentions between African Americans and Whites (Article 3). ^ The prevalence findings confirm the disparities in tobacco use among African American, Hispanic, and White adolescents that other surveys have reported (Article 1). This study also demonstrates the usefulness of examining use patterns of not only cigarettes but also alternative tobacco products in younger multiethnic populations, as well as of providing epidemiological data estimates about different phases of smoking. The confirmatory factor analysis provides evidence of construct validity of attitude, self-efficacy, and intention scales for the multiethnic sample (Article 2). Finally, the factorial invariance analyses indicates that some measures representing smoking-related attitudes, self-efficacy, and intentions may not be appropriate for use among both African Americans and Whites (Article 3). Additional research is needed to further our understanding of the patterns and predictors of youth tobacco use initiation. ^

Comparing the factorial structure, invariance, and predictive validity of transtheoretical model constructs for alcohol use across restricted and unrestricted settings

With substance abuse treatment expanding in prisons and jails, understanding how behavior change interacts with a restricted setting becomes more essential. The Transtheoretical Model (TTM) has been used to understand intentional behavior change in unrestricted settings, however, evidence indicates restrictive settings can affect the measurement and structure of the TTM constructs. The present study examined data from problem drinkers at baseline and end-of-treatment from three studies: (1) Project CARE (n = 187) recruited inmates from a large county jail; (2) Project Check-In (n = 116) recruited inmates from a state prison; (3) Project MATCH, a large multi-site alcohol study had two recruitment arms, aftercare (n = 724 pre-treatment and 650 post-treatment) and outpatient (n = 912 pre-treatment and 844 post-treatment). The analyses were conducted using cross-sectional data to test for non-invariance of measures of the TTM constructs: readiness, confidence, temptation, and processes of change (Structural Equation Modeling, SEM) across restricted and unrestricted settings. Two restricted (jail and aftercare) and one unrestricted group (outpatient) entering treatment and one restricted (prison) and two unrestricted groups (aftercare and outpatient) at end-of-treatment were contrasted. In addition TTM end-of-treatment profiles were tested as predictors of 12 month drinking outcomes (Profile Analysis). Although SEM did not indicate structural differences in the overall TTM construct model across setting types, there were factor structure differences on the confidence and temptation constructs at pre-treatment and in the factor structure of the behavioral processes at the end-of-treatment. For pre-treatment temptation and confidence, differences were found in the social situations factor loadings and in the variance for the confidence and temptation latent factors. For the end-of-treatment behavioral processes, differences across the restricted and unrestricted settings were identified in the counter-conditioning and stimulus control factor loadings. The TTM end-of-treatment profiles were not predictive of drinking outcomes in the prison sample. Both pre and post-treatment differences in structure across setting types involved constructs operationalized with behaviors that are limited for those in restricted settings. These studies suggest the TTM is a viable model for explicating addictive behavior change in restricted settings but calls for modification of subscale items that refer to specific behaviors and caution in interpreting the mean differences across setting types for problem drinkers. ^

Caracterización de poblaciones nativas de maíz mediante Análisis de Procrustes Generalizado y Análisis Factorial Múltiple

El establecimiento de relaciones entre taxones es un paso esencial en el proceso de catalogación y evaluación del material conservado en un Banco de Germoplasma. Existen distintos métodos de evaluación en función del tipo de caracteres estudiados. Cuando el registro de caracteres se repite en el tiempo y en distintos ambientes, se debe separar la variabilidad intrínsecamente genética entre los taxones de aquella que se debe al ambiente, y más aún, de la posible variabilidad debida a la interacción genotipo*ambiente para el posterior establecimiento de relaciones puramente filogenéticas. En el presente trabajo se estudia comparativamente la factibilidad de aplicación de dos estrategias de análisis estadístico para dar solución a este problema. La primera corresponde al análisis tradicional donde se realiza un Análisis de Componentes Principales sobre los caracteres promedios a lo largo de los diferentes ambientes; y la segunda son métodos más complejos en los cuales cada dato es originado por tres modos: individuos, variables y condiciones ambientales, tales como el Análisis Factorial Múltiple y el Análisis de Procrustes Generalizado. Si bien las configuraciones resultantes fueron todas equivalentes, los métodos de tres vías permiten la interpretación de la interacción genotipo*ambiente.

Factorial structure and reliability of a perceived influence on selection of a specialized plan of studies, IPEP, in secondary school students of Chillan, Chile

To evaluate these factors, the scale of perceived influences on the election of a specialized plan of studies, IPEP, was built and in this study its factorial structure and reliability were evaluated. The instrument was applied to 115 students, chosen by quote sampling. They were students of a subsidized private secondary school from the city of Chillan, Chile. An exploratory factorial analysis identified eight factors in the scale IPEP: Academic projection, Personal development, Maintenance of the social environment, Academic requirements, Satisfaction of others' expectations, Vocational information, Image of the plan and Family pressure. The results present an initial factorial structure, that empirically and theoretically adequate, whose factors were reliable and conceptually useful. These factors distinguish psychogenic and sociogenic aspects of the vocational process, and allow to initiate diagnostic and investigative actions in relation to this early vocational election that is established in secondary schools of the Chilean educational system

Estructura factorial y confiabilidad de la escala de influencias percibidas en la elección de un plan diferenciado, IPEP, en estudiantes de enseñanza media de Chillán, Chile

Los procesos de elección vocacional son influidos por factores individuales y externos al sujeto, no obstante no existe evidencia de cuál es su influencia en la elección del plan diferenciado de estudios al que, en el sistema educacional chileno, se debe ingresar en tercero medio. Para evaluar estos factores, se construyó la escala de Influencias Percibidas en la Elección de un Plan Diferenciado, IPEP, y en esta investigación se evaluó su estructura factorial y confiabilidad. El instrumento fue aplicado a 115 alumnos, elegidos mediante muestreo por cuotas, que cursaban tercer año medio en un colegio particular subvencionado de la cuidad de Chillán, Chile. A partir de un análisis factorial exploratorio se identificó ocho factores en la escala IPEP: Proyección académica, Desarrollo personal, Mantención del entorno social, Exigencia académica, Satisfacción de expectativas de otros, Información vocacional, Imagen del plan y Presión Familiar. Los resultados presentan evidencia inicial de una estructura factorial empírica y teóricamente adecuada, cuyos factores son internamente consistentes y conceptualmente útiles, ya que distinguen aspectos psicogénicos y sociogénicos de la toma de decisiones vocacionales, permitiendo iniciar acciones diagnósticas e investigativas en torno a esta decisión vocacional que el sistema educativo establece en medio de la educación secundaria