Don't Tie Yourself to an Onion: Don’t Tie Yourself to Assumptions of Normality

A structural measurement model (Adams, Wilson, & Wu, 1997) consists of an item response theory model for responses conditional on ability and a structural model that describes the distribution of ability in the population. As a rule, ability is assumed to be normally distributed in the population. However, there are situations where there is reason to assume that the distribution of ability is nonnormal. In this paper, we show that nonnormal ability distributions are easily modeled in a Bayesian framewor

A limited dependent variable model for heritability estimation with non-random ascertained samples

In a questionnaire study, a random sample of Dutch families was asked whether they suffered from asthma and related symptoms. From these families, a selected sample was invited to come to the hospital for further phenotyping. Families were selected if at least one family member reported a history of asthma and the twins were 18 years of age or older. Not all families that were thus selected volunteered, leaving us with a fraction of the original sample. The aim of this paper is to describe a limited dependent variable model that can be used in such situations in order to obtain estimates that are representative of the population from which the sample was originally drawn. The model is a linear (DeFries-Fulker) regression model corrected for sample selection. This correction is possible when (some of) the characteristics that determine whether subjects volunteer (or not) are known for all subjects, including those that did not volunteer. The questionnaire study is of interest by itself but serves mainly to provide a concrete illustration of our method. The present model is used to analyze the data and the results are compared to those obtained with other methods: raw (or direct) likelihood estimation, multiple imputation, and sample weighting. Throughout, Rubin's general theory of inference with missing data serves as an integrating framework

Bayesian inference for low-rank Ising networks

Estimating the structure of Ising networks is a notoriously difficult problem. We demonstrate that using a latent variable representation of the Ising network, we can employ a full-data-information approach to uncover the network structure. Thereby, only ignoring information encoded in the prior distribution (of the latent variables). The full-data-information approach avoids having to compute the partition function and is thus computationally feasible, even for networks with many nodes. We illustrate the full-data-information approach with the estimation of dense network

Engineering disorder in three-dimensional photonic crystals

We demonstrate the effect of introducing controlled disorder in self-assembled three-dimensional photonic crystals. Disorders are induced through controlling the self-assembling process using an electrolyte of specific concentrations. Structural characterization reveals increase in disorder with increase in concentrations of the electrolyte. Reflectivity and transmittance spectra are measured to probe the photonic stop gap at different levels of disorder. With increase in disorder the stop gap is vanished and that results in a fully random photonic nanostructure where the diffuse scattered intensity reaches up to 100%. Our random photonic nanostructure is unique in which all scatters have the same size and shape. We also observe the resonant characteristics in the multiple scattering of light.Comment: 13 pages, 3 figure

Multipole interaction between atoms and their photonic environment

Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are determined and in particular the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielectric a dipole couples to a field that is neither the (transverse) electric nor the macroscopic displacement field. The dielectric function is different from the bulk dielectric function at the position of the dipole, so that local-field effects must be taken into account.Comment: 17 pages, to be published in Physical Review

Angular redistribution of near-infrared emission from quantum dots in 3D photonic crystals

We study the angle-resolved spontaneous emission of near-infrared light sources in 3D photonic crystals over a wavelength range from 1200 to 1550 nm. To this end PbSe quantum dots are used as light sources inside titania inverse opal photonic crystals. Strong deviations from the Lambertian emission profile are observed. An attenuation of 60 % is observed in the angle dependent radiant flux emitted from the samples due to photonic stop bands. At angles that correspond to the edges of the stop band the emitted flux is increased by up to 34 %. This increase is explained by the redistribution of Bragg-diffracted light over the available escape angles. The results are quantitatively explained by an expanded escape-function model. This model is based on diffusion theory and adapted to photonic crystals using band structure calculations. Our results are the first angular redistributions and escape functions measured at near-infrared, including telecom, wavelengths. In addition, this is the first time for this model to be applied to describe emission from samples that are optically thick for the excitation light and relatively thin for the photoluminesence light.Comment: 24 pages, 8 figures (current format = single column, double spaced

A Rasch model and rating system for continuous responses collected in large-scale learning systems

An extension to a rating system for tracking the evolution of parameters over time using continuous variables is introduced. The proposed rating system assumes a distribution for the continuous responses, which is agnostic to the origin of the continuous scores and thus can be used for applications as varied as continuous scores obtained from language testing to scores derived from accuracy and response time from elementary arithmetic learning systems. Large-scale, high-stakes, online, anywhere anytime learning and testing inherently comes with a number of unique problems that require new psychometric solutions. These include (1) the cold start problem, (2) problem of change, and (3) the problem of personalization and adaptation. We outline how our proposed method addresses each of these problems. Three simulations are carried out to demonstrate the utility of the proposed rating system

Differential Item Functioning in PISA Due to Mode Effects

One of the most important goals of the Programme for International Student Assessment (PISA) is assessing national changes in educational performance over time. These so-called trend results inform policy makers about the development of ability of 15-year-old students within a specific country. The validity of those trend results prescribes invariant test conditions. In the 2015 PISA survey, several alterations to the test administration were implemented, including a switch from paper-based assessments to computer-based assessments for most countries (OECD 2016a). This alteration of the assessment mode is examined by evaluating if the items used to assess trends are subject to differential item functioning across PISA surveys (2012 vs. 2015). Furthermore, the impact on the trend results due to the change in assessment mode of the Netherlands is assessed. The results show that the decrease reported for mathematics in the Netherlands is smaller when results are based upon a separate national calibration.</p