Multiple Imputation Using Gaussian Copulas

Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this paper, we present a simple-to-use method for generating multiple imputations using a Gaussian copula. The Gaussian copula for multiple imputation (Hoff, 2007) allows scholars to attain estimation results that have good coverage and small bias. The use of copulas to model the dependence among variables will enable researchers to construct valid joint distributions of the data, even without knowledge of the actual underlying marginal distributions. Multiple imputations are then generated by drawing observations from the resulting posterior joint distribution and replacing the missing values. Using simulated and observational data from published social science research, we compare imputation via Gaussian copulas with two other widely used imputation methods: MICE and Amelia II. Our results suggest that the Gaussian copula approach has a slightly smaller bias, higher coverage rates, and narrower confidence intervals compared to the other methods. This is especially true when the variables with missing data are not normally distributed. These results, combined with theoretical guarantees and ease-of-use suggest that the approach examined provides an attractive alternative for applied researchers undertaking multiple imputations

Construction of rugged, ultrastable optical assemblies with optical component alignment at the few microradian level

A method for constructing quasimonolithic, precision-aligned optical assemblies is presented. Hydroxide-catalysis bonding is used, adapted to allow optimization of component fine alignment prior to the bond setting. We demonstrate the technique by bonding a fused silica mirror substrate to a fused silica baseplate. In-plane component placement at the submicrometer level is achieved, resulting in angular control of a reflected laser beam at the sub-10-μrad level. Within the context of the LISA Pathfinder mission, the technique has been demonstrated as suitable for use in space-flight applications. It is expected that there will also be applications in a wide range of areas where accuracy, stability, and strength of optical assemblies are important

Location, Location, Location: An MCMC Approach to Modeling the Spatial Context of War and Peace

This article demonstrates how spatially dependent data with a categorical response variable can be addressed in a statistical model. We introduce the idea of an autologistic model where the response for one observation is dependent on the value of the response among adjacent observations. The autologistic model has likelihood function that is mathematically intractable, since the observations are conditionally dependent upon one another. We review alternative techniques for estimating this model, with special emphasis on recent advances using Markov chain Monte Carlo (MCMC) techniques. We evaluate a highly simplified autologistic model of conflict where the likelihood of war involvement for each nation is conditional on the war involvement of proximate states. We estimate this autologistic model for a single year (1988) via maximum pseudolikelihood and MCMC maximum likelihood methods. Our results indicate that the autologistic model fits the data much better than an unconditional model and that the MCMC estimates generally dominate the pseudolikelihood estimates. The autologistic model generates predicted probabilities greater than 0.5 and has relatively good predictive abilities in an out-of-sample forecast for the subsequent decade (1989 to 1998), correctly identifying not only ongoing conflicts, but also new ones.</jats:p

Bimetallic Pt(II)-bipyridyl-diacetylide/Ln(III) tris-diketonate adducts based on a combination of coordinate bonding and hydrogen bonding between the metal fragments: syntheses, structures and photophysical properties

The luminescent Pt(II) complex [Pt(4,4'-Bu-t(2)-bipy){CC-(5-pyrimidinyl)}(2)] (1) was prepared by coupling of [Pt(4,4'-Bu-t(2)-bipy)Cl-2] with 5-ethynyl-pyrimidine, and contains two pyrimidinyl units pendant from a Pt(H) bipyridyl diacetylide core; it shows luminescence at 520 nm which is typical of Pt(II) luminophores of this type. Reaction with [Ln(hfac)(3)(H2O)(2)] (hfac = anion of hexafluoroacetylacetone) affords as crystalline solids the compounds [1 center dot {Ln(hfac)(3)(H2O)}{Ln(hfac)(3)(H2O)(2)}] (Ln = Nd, Gd, Er, Yb), in which the {Ln(hfac)(3)(H2O)} unit is coordinated to one pyrimidine ring via an N atom, whereas the {Ln(hfac)(3)(H2O)(2)} unit is associated with two N atoms, one from each pyrimidine ring of 1, via N center dot center dot center dot HOH hydrogen-bonding interactions involving the coordinated water ligands on the lanthanide centre. Solution spectroscopic studies show that the luminescence of 1 is partly quenched on addition of [Ln(hfac)(3)(H2O)(2)] (Ln = Er, Nd) by formation of Pt(II)/Ln(III) adducts in which Pt(II)-> Ln(III) photoinduced energy-transfer occurs to the low-lying f-f levels of the Ln(Ill) centre. Significant quenching occurs with both Er(Ill) and Nd(III) because both have several f-f states which match well the (MLCT)-M-3 emission energy of 1. Time-resolved luminescence studies show that Pt(II)-Er(III) energy-transfer (7.0 x 10(7) M-1) is around three times faster than Pt(II)-> Nd(III) energy-transfer (approximate to 2 x 10(7) M-1) over the same distance because the luminescence spectrum of l overlaps better with the absorption spectrum of Er(111) than with Nd(III). In contrast Yb(111) causes no significant quenching of 1 because it has only a single f-f excited level which is a poor energy match for the Pt(II)-based excited state

Automated precision alignment of optical components for hydroxide catalysis bonding

We describe an interferometric system that can measure the alignment and separation of a polished face of a optical component and an adjacent polished surface. Accuracies achieved are ∼ 1μrad for the relative angles in two orthogonal directions and ∼ 30μm in separation. We describe the use of this readout system to automate the process of hydroxide catalysis bonding of a fused-silica component to a fused-silica baseplate. The complete alignment and bonding sequence was typically achieved in a timescale of a few minutes, followed by an initial cure of 10 minutes. A series of bonds were performed using two fluids - a simple sodium hydroxide solution and a sodium hydroxide solution with some sodium silicate solution added. In each case we achieved final bonded component angular alignment within 10 μrad and position in the critical direction within 4 μm of the planned targets. The small movements of the component during the initial bonding and curing phases were monitored. The bonds made using the sodium silicate mixture achieved their final bonded alignment over a period of ∼ 15 hours. Bonds using the simple sodium hydroxide solution achieved their final alignment in a much shorter time of a few minutes. The automated system promises to speed the manufacture of precision-aligned assemblies using hydroxide catalysis bonding by more than an order of magnitude over the more manual approach used to build the optical interferometer at the heart of the recent ESA LISA Pathfinder technology demonstrator mission. This novel approach will be key to the time-efficient and low-risk manufacture of the complex optical systems needed for the forthcoming ESA spaceborne gravitational waves observatory mission, provisionally named LISA