Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals

This research proposes a new statistic for testing latent variable distribution fit for unidimensional item response theory (IRT) models. If the typical assumption of normality is violated, then item parameter estimates will be biased, and dependent quantities such as IRT score estimates will be adversely affected. The proposed statistic compares the specified latent variable distribution to the sample average of latent variable posterior distributions commonly used in IRT scoring. Formally, the statistic is an instantiation of a generalized residual and is thus asymptotically distributed as standard normal. Also, the statistic naturally complements residual-based item-fit statistics, as both are conditional on the latent trait, and can be presented with graphical plots. In addition, a corresponding unconditional statistic, which controls for multiple comparisons, is proposed. The statistics are evaluated using a simulation study, and empirical analyses are provided.

Oceanic Surface Environmental Severity

More than 30 years of temperature and humidity data from bodies of water across the globe were compared to a standard benchmark environment of 85 °C and 85% Relative Humidity (RH). The Peck Temperature Humidity Model provided this linkage. Results were organized by global region and severity to create a severity distribution of the natural oceanic temperature and humidity environments applicable in product testing. The severity distribution was achieved through a four-subpopulation mixed-Weibull distribution fit to the data. The result is the Oceanic Severity Model. The Oceanic Severity Model was compared to prior research that used land-based environmental data to create a similar percent-severity approach. The ocean-based model was less severe at the extremes, but overall similar to the results found in the land-based assessment. Several military-standard-defined environments were compared to the Oceanic Severity Model. One of the military environments was found to be extremely severe when considered as representative of a 10-year natural environment, such that it is highly improbable that the environment would occur in nature.

The critical role of uncertainty in projections of hydrological extremes

This paper aims to quantify the uncertainty in projections of future hydrological extremes in the Biala Tarnowska River at Koszyce gauging station, south Poland. The approach followed is based on several climate projections obtained from the EURO-CORDEX initiative, raw and bias-corrected realizations of catchment precipitation, and flow simulations derived using multiple hydrological model parameter sets. The projections cover the 21st century. Three sources of uncertainty are considered: one related to climate projection ensemble spread, the second related to the uncertainty in hydrological model parameters and the third related to the error in fitting theoretical distribution models to annual extreme flow series. The uncertainty of projected extreme indices related to hydrological model parameters was conditioned on flow observations from the reference period using the generalized likelihood uncertainty estimation (GLUE) approach, with separate criteria for high- and low-flow extremes. Extreme (low and high) flow quantiles were estimated using the generalized extreme value (GEV) distribution at different return periods and were based on two different lengths of the flow time series. A sensitivity analysis based on the analysis of variance (ANOVA) shows that the uncertainty introduced by the hydrological model parameters can be larger than the climate model variability and the distribution fit uncertainty for the low-flow extremes whilst for the high-flow extremes higher uncertainty is observed from climate models than from hydrological parameter and distribution fit uncertainties. This implies that ignoring one of the three uncertainty sources may cause great risk to future hydrological extreme adaptations and water resource planning and management.

Summed Score Likelihood–Based Indices for Testing Latent Variable Distribution Fit in Item Response Theory

In standard item response theory (IRT) applications, the latent variable is typically assumed to be normally distributed. If the normality assumption is violated, the item parameter estimates can become biased. Summed score likelihood–based statistics may be useful for testing latent variable distribution fit. We develop Satorra–Bentler type moment adjustments to approximate the test statistics’ tail-area probability. A simulation study was conducted to examine the calibration and power of the unadjusted and adjusted statistics in various simulation conditions. Results show that the proposed indices have tail-area probabilities that can be closely approximated by central chi-squared random variables under the null hypothesis. Furthermore, the test statistics are focused. They are powerful for detecting latent variable distributional assumption violations, and not sensitive (correctly) to other forms of model misspecification such as multidimensionality. As a comparison, the goodness-of-fit statistic M2 has considerably lower power against latent variable nonnormality than the proposed indices. Empirical data from a patient-reported health outcomes study are used as illustration.

The critical role of uncertainty in projections of hydrological Extremes

This paper aims to quantify the uncertainty in the projections of future hydrological extremes in the BialaTarnowska River basin, south Poland. We follow a multi-model approach based on several climate projections obtained from the EUROCORDEX initiative, raw and downscaled realizations of catchment precipitation and temperature, and flow simulations derived using the hydrological HBV model. The projections cover the 21st century. Three sources of uncertainty were considered: one related to the hydrological model parameters uncertainty, the second related to climate projection ensemble spread and the third related to the distribution fit. The uncertainty of projected extreme indices related to hydrological model parameters was conditioned on flow observations from the reference period using the Generalised Likelihood Uncertainty Estimation approach, with separate weighting for high and low flow extremes. Flood quantiles were estimated using Generalize Extreme Value (GEV) distribution at different return periods and were based on two different lengths of the flow time series. The sensitivity analysis based on ANOVA shows that the uncertainty introduced by the HBV model parameters can be larger than the climate model variability and distribution fit uncertainty for the low-flow extremes whilst for the high-flow extremes higher uncertainty is observed from climate models than from hydrological parameter and distribution fit uncertainties. This implies that ignoring one of the three uncertainty sources may cause great risk to future hydrological extreme adaptations and water resource planning and management.

Can Tsallis Distribution Fit All the Particle Spectra Produced at RHIC and LHC?

The Tsallis distribution has been tested to fit all the particle spectra at mid-rapidity from central events produced in d + Au, Cu + Cu, and Au + Au collisions at RHIC and p + Pb, Pb + Pb collisions at LHC. Even though there are strong medium effects in Cu + Cu and Au + Au collisions, the results show that the Tsallis distribution can be used to fit most of particle spectra in the collisions studied except in Au + Au collisions where some deviations are seen for proton andΛat lowpT. In addition, as the Tsallis distribution can only fit part of the particle spectra produced in Pb + Pb collisions wherepTis up to 20 GeV/c, a new formula with one more fitting degree of freedom is proposed in order to reproduce the entirepTregion.