More than,less than,or minimum,maximum: how upper and lower bounds determine subjective interval estimates

Uncertain quantities can be described by single‐point estimates of lower interval bounds (X₁), upper interval bounds (X₂), two‐bound estimates (separate estimates of X₁ and X₂), and by ranges (X₁?X₂). A price estimation task showed that single‐bound estimates phrased as “T costs more than X₁” and “T costs less than X₂,” yielded much larger intervals than “minimum X₁” and “maximum X₂.” This difference can be attributed to exclusive interpretations of X₁ and X₂ in the first case (X₁ and X₂ are unlikely values), and inclusive interpretations in the second (X₁ and X₂ are likely values). This pattern of results was replicated in other domains where participants estimated single targets. When they estimated a distribution of targets, the pattern was reversed. “Minimum” and “maximum” values of variable quantities (e.g., flight prices) were found to delimit larger intervals than “more than” and “less than” estimates. Copyright © 2006 John Wiley & Sons, Ltd.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

Type II twinning in devitrite,Na2Ca3Si6O16

Nanometre-scale twins found in the triclinic crystalline phase devitrite, Na₂Ca₃Si₆O₁₆, are shown to exhibit the relatively rare form of twinning, Type II twinning, in which the crystal structure of one of the parts is related to the crystal structure of the other by a rotation of 180° about η ₁?=?[1?0?0]. Although formally, the twin plane K ₁ is irrational, it is in essence (0?1?0).     

Reversible phase transition in vanadium oxide films sputtered on metal substrates

Vanadium oxide films, deposited on aluminium (Al), titanium (Ti) and tantalum (Ta) metal substrates by pulsed RF magnetron sputtering at a working pressure of 1.5 x10^?2 mbar at room temperature are found to display mixed crystalline vanadium oxide phases viz., VO₂, V₂O₃, V₂O₅. The films have been characterized by field-emission scanning electron microscopy, X-ray diffraction, differential scanning calorimetry (DSC) and X-ray photoelectron spectroscopy, and their thermo-optical and electrical properties have been investigated. Studies of the deposited films by DSC have revealed a reversible-phase transition found in the temperature range of 45–49 °C.     

Investigations of the optical and EPR spectra for VO2+ in NaHC2O4 · H2O single crystals

Theoretical calculations of the optical absorption and electron paramagnetic resonance (EPR) spectra of VO²⁺ in NaHC₂O₄?·?H₂O single crystals were performed using the complete diagonalization energy matrix method (CDM) and the perturbation theory method (PTM) for the 3d ¹ electronic configuration. The calculated results are in good agreement with experimental results. The negative signs of hyperfine structure constants A _∥ and A _⊥ for VO²⁺ in NaHC₂O₄·H₂O single crystals are suggested from the calculations. Comparison of the two calculation methods indicates that the PTM is a good approximation of CDM and that both theoretical methods are valid in interpretation of the optical and EPR spectra for VO²⁺ ions in NaHC₂O₄?·?H₂O crystals.     

Anisotropic BaTiO3 thin films grown on MgO-buffered R-plane sapphire

Epitaxial BaTiO₃ thin films grown on MgO-buffered R-plane-cut Al₂O₃ substrates show a non-uniform distribution of planar defects. Transmission electron microscopy allows the determination of the distributions of planar defects with respect to the Al₂O₃ substrate. The BaTiO₃ film, the MgO buffer and the Al₂O₃ substrate have an orientation relationship of [100]_BaTiO3//[100]_MgO//[1120]_Al2O3, (010)_BaTiO3//(010)_MgO//(1104)_Al2O3 and (001)_BaTiO3//(001)_MgO// ≈ (1102)_Al2O3 (about 5°; deviation). Under the above relationship, most of the {111} stacking faults occur on (111) and (111) planes, that is two of four sets of {111}_BaTiO3, whereas cracks in the BaTiO₃ film (and MgO buffer) are situated on the (100) planes. The anisotropic distribution of planar defects is regarded as a consequence of an anisotropic stress in the films generated during their fabrication.     

Growth of carbon nanotubes: effect of Fe diffusion and oxidation

The diffusion and surface oxidation rates of Fe deposited on Si and barrier layers of Al/SiO₂ and Al₂O₃/SiO₂ have been comparatively studied and correlated with the growth of carbon nanotubes (CNTs). Initially, Fe/Si, Fe/Al/SiO₂/Si and Fe/Al₂O₃/SiO₂/Si samples were subjected to thermal chemical vapour deposition (CVD) at ～650°C for ～30?min to grow the CNTs. Scanning electron microscopy analysis showed that the height of the CNTs on the Fe/Al₂O₃/SiO₂/Si samples was relatively high (～9.5–11?µm), as compared with the other samples. To investigate this, a few as-prepared samples were thermally annealed at ～650°C for ～30?min and characterized by dynamic secondary ion mass spectroscopy (D-SIMS) and X-ray photoelectron spectroscopy (XPS). The D-SIMS results showed that the diffusion depth, x _Fe, and magnitude of the diffusivity, D _Fe, of the Fe atoms are highest for the Fe/Si sample. This is attributed to vacancy-mediated migration, which leads to the formation of unstable, non-stoichiometric Fe–Si and Fe–O–Si phases. However, for the Fe/Al₂O₃/SiO₂/Si samples, the magnitudes of x _Fe and D _Fe are found to be the lowest, which indicates steric hindrance to Fe by the Al₂O₃ layers. The XPS analysis revealed that the surface metallic state, after annealing, is almost unaffected for the Fe/Al₂O₃/SiO₂/Si samples, whereas the majority of the Fe precipitate was observed to be oxidized in the case of the other samples.     

Crystal structure of 1–2–3 superconductor precursor material: Vacancy distribution and lattice relaxation

Abstract

The crystal structure of tetragonal YBa₂Cu₃O_7-δ, with δ close to the critical composition for the tetragonal–orthorhombic transition, has been refined. The oxygen deficiency δ = 0·65(10) is accommodated by both the O(1) and O(2) sites which coordinate the ‘square planar’ Cu(1) site. Structural relaxation around the vacancies is indicated by large anisotropic Debye-Waller ellipsoids in the structural layer formed by these atomic sites. The Y, Ba, Cu(2) and O(3) sites are not involved in the relaxation mechanism. On comparing this structure with the δ ≈ 0 and δ ≈ 1 end-members, we find that with decreasing oxygen content of the structure the Cu(2) valence type transforms from square-pyramidal character towards square-planar character. This effect gives the main contribution to the increase of the c ₀ lattice constant with decreasing oxygen content.     

COMPOSITION AS A SECONDARY QUALITY

Abstract: The ‘special composition question’ is this: given objects O₁, . . . , O_n, under what conditions is there an object O, such that O₁, . . . , O_n compose O? This paper explores a heterodox answer to this question, one that casts composition as a secondary quality. According to the approach I want to consider, there is an O that O₁, . . . , O_n compose (roughly) just in case a normal intuiter would, under normal conditions, intuit that there is.     

Examining interrelationships between the Cigarette Purchase Task and delay discounting among pregnant women

Two common behavioral economic simulation tasks used to study cigarette smoking are the Cigarette Purchase Task, a measure of cigarette demand, and delay discounting, a measure of the subjective value of rewards as a function of delays to delivery. Few studies have evaluated whether combining these tasks enhances understanding of smoking beyond either alone. The current study represents an initial evaluation of the intersection between cigarette demand indices and delay discounting among pregnant smokers by examining associations between these measures and whether a woman makes antepartum quit attempts before entering prenatal care (a reliable predictor of eventual quitting). Participants were 159 pregnant women enrolled in a smoking‐cessation trial. Low O _max and shallow discounting were each associated with antepartum quit attempts. Participants were next categorized into four subgroups (low O _max, shallow discounting; low O _max, steep discounting; high O _max, shallow discounting; high O _max, steep discounting) using median splits. Those with shallow discounting and low O _max were more likely to have made quit attempts than each of the other three subgroups. That is, steep discounting appears to undermine the association of low O _max and efforts to quit smoking during pregnancy while high O _max overshadows any protective influence associated with shallow discounting.     

Identifying the Source of Misfit in Item Response Theory Models

When an item response theory model fails to fit adequately, the items for which the model provides a good fit and those for which it does not must be determined. To this end, we compare the performance of several fit statistics for item pairs with known asymptotic distributions under maximum likelihood estimation of the item parameters: (a) a mean and variance adjustment to bivariate Pearson's X², (b) a bivariate subtable analog to Reiser's (1996) overall goodness-of-fit test, (c) a z statistic for the bivariate residual cross product, and (d) Maydeu-Olivares and Joe's (2006) M₂ statistic applied to bivariate subtables. The unadjusted Pearson's X² with heuristically determined degrees of freedom is also included in the comparison. For binary and ordinal data, our simulation results suggest that the z statistic has the best Type I error and power behavior among all the statistics under investigation when the observed information matrix is used in its computation. However, if one has to use the cross-product information, the mean and variance adjusted X² is recommended. We illustrate the use of pairwise fit statistics in 2 real-data examples and discuss possible extensions of the current research in various directions.     

Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

Negative Equivalence of Extensions of Minimal Logic

Two logics L₁ and L₂ are negatively equivalent if for any set of formulas X and any negated formula ¬, ¬ can be deduced from the set of hypotheses X in L₁ if and only if it can be done in L₂. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.The author acknowledges support by the Alexander von Humboldt-StiftungPresented by Jacek Malinowski     

A new secretary problem with rank-based selection and cardinal payoffs

We present an extension of the secretary problem in which the decision maker (DM) sequentially observes up to n applicants whose values are random variables X₁,X₂,…,X_n drawn i.i.d. from a uniform distribution on [0,1]. The DM must select exactly one applicant, cannot recall released applicants, and receives a payoff of x_t, the realization of X_t, for selecting the tth applicant. For each encountered applicant, the DM only learns whether the applicant is the best so far. We prove that the optimal policy dictates skipping the first sqrt(n)-1 applicants, and then selecting the next encountered applicant whose value is a maximum.     

On the scales of measurement

Let $\text{X}$ = 〈X, ≧, R₁, R₂…〉 be a relational structure, 〈$\text{X, ≧}$〉 be a Dedekind complete, totally ordered set, and n be a nonnegative integer. $\text{X}$ is said to satisfy n-point homogeneity if and only if for each x₁,…, x_n, y₁,…, y_n such that x₁ ? x₂ ? … ? x_n and y₁ ? y₂ … ? y_n, there exists an automorphism α of $\text{X}$ such that α(x₁) = y_i. $\text{X}$ is said to satisfy n-point uniqueness if and only if for all automorphisms β and γ of $\text{X}$, if β and γ agree at n distinct points of $\text{X}$, then β and γ are identical. It is shown that if $\text{X}$ satisfies n-point homogeneity and n-point uniqueness, then n ≦ 2, and for the case n = 1, $\text{X}$ is ratio scalable, and for the case n = 2, interval scalable. This result is very general and may in part provide an explanation of why so few scale types have arisen in science. The cases of 0-point homogeneity and infinite point homogeneity are also discussed.     

Variation with density of the transport properties of YBaCuO superconductors

Abstract

The dependence of the normal-state resistivity, resistive superconducting transition (T _c, ΔT _c), and of the upper critical-field slope (dH _c2/dT|T=T_c) on density has been investigated for several YBa₂Cu₃O_9-x(x?2.1) samples. The resistivity decreases rapidly with increasing density, whereas T _c and ΔT _c are rather insensitive to a change in density. dH _c2/dT|T_c depends sensitively on the preparation conditions. The implications of these results both for the evaluation of the parameters relevant to the understanding of the nature of superconductivity and for the technological applications of granular superconductors are briefly discussed.     

On the asymptotic distribution of Pearson’s X 2 in cross-validation samples

In categorical data analysis, two-sample cross-validation is used not only for model selection but also to obtain a realistic impression of the overall predictive effectiveness of the model. The latter is of particular importance in the case of highly parametrized models capable of capturing every idiosyncracy of the calibrating sample. We show that for maximum likelihood estimators or other asymptotically efficient estimators Pearson's X ² is not asymptotically chi-square in the two-sample cross-validation framework due to extra variability induced by using different samples for estimation and goodness-of-fit testing. We propose an alternative test statistic, X _xval ², obtained as a modification of X ² which is asymptotically chi-square with C−1 degrees of freedom in cross-validation samples. Stochastically, X _xval ² ≤ X ². Furthermore, the use of X ² instead of X _xval ² with a χ _C −1² reference distribution may provide an unduly poor impression of fit of the model in the cross-validation sample. This paper is dedicated to the memory of Michael V. Levine. Requests for reprints should be sent to Albert Maydeu-Olivares, Faculty of Psychology, University of Barcelona, P. Valle de Hebrón, 171, 0835 Barcelona, Spain.     

Using logistic regression to estimate delay-discounting functions

The monetary choice questionnaire (MCQ) and similar computer tasks ask preference questions in order to ascertain indifference, the perceived equivalence of immediate versus larger delayed rewards. Indifference data are then fitted with a hyperbolic function, summarizing the decline in perceived value with delay time. We present a fitting method that estimates the hyperbolic parameterk directly from survey responses. Binary preferences are modeled as a function of time (X₂) and a transformed reward ratio (X ₁), yielding logistic regression coefficients β₂ and β₁. The hyperbolic parameter emerges ask = β₂/β₁, where the logistic predictedp = .5 (the definition of indifference). The MCQ was administered to 1,073 adolescents and was scored using both standard and logistic methods. The means for ln(k) were similar (standard, −4.53; logistic, −4.51), and the results were highly correlated (ρ = .973). Simulated MCQ data showed thatk was unbiased, except where β₁ ≥ −1, indicating a vague survey response. Jackknife standard errors provided excellent coverage.     

Local measures of association: Estimating the derivative of the regression line

A local measure of association that allows both heteroscedasticity and a non‐linear association was developed during the 1990s. The basic goal is to measure the strength of the association between X and Y, given X, when Y=θ(X)+τ(X)ε for some unknown functions θ(X) and τ(X). Application of this method requires the estimation of the derivative of θ(X). The focus in this paper is on four alternatives to a very slight modification of the method used by Doksum et al. when estimating this derivative. The main result is that in simulations, a certain robust analogue of their method dominates in terms of mean squared error, even under normality. The bias of the method is found to be small but a little larger than the bias associated with the method used by Doksum et al. The method is based in part on bootstrap bagging followed by a lowess smooth.