Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Effects of 830 and 670 nm Laser on Viability of Random Skin Flap in Rats

Objective: This study aimed to investigate the effect of 830 and 670 nm diode laser on the viability of random skin flaps in rats. Background data: Low-level laser therapy (LLLT) has been reported to be successful in stimulating the formation of new blood vessels and reducing the inflammatory process after injury. However, the efficiency of such treatment remains uncertain, and there is also some controversy regarding the efficacy of different wavelengths currently on the market. Materials and methods: Thirty Wistar rats were used and divided into three groups, with 10 rats in each. A random skin flap was raised on the dorsum of each animal. Group 1 was the control group, group 2 received 830 nm laser radiations, and group 3 was submitted to 670 nm laser radiation (power density = 0.5 mW/cm(2)). The animals underwent laser therapy with 36 J/cm(2) energy density (total energy = 2.52 J and 72 sec per session) immediately after surgery and on the 4 subsequent days. The application site of laser radiation was one point at 2.5 cm from the flap's cranial base. The percentage of skin flap necrosis area was calculated on the 7th postoperative day using the paper template method. A skin sample was collected immediately after to determine the vascular endothelial growth factor (VEGF) expression and the epidermal cell proliferation index (KiD67). Results: Statistically significant differences were found among the percentages of necrosis, with higher values observed in group 1 compared with groups 2 and 3. No statistically significant differences were found among these groups using the paper template method. Group 3 presented the highest mean number of blood vessels expressing VEGF and of cells in the proliferative phase when compared with groups 1 and 2. Conclusions: LLLT was effective in increasing random skin flap viability in rats. The 670 nm laser presented more satisfactory results than the 830 nm laser.

Mean-Field critical behavior and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction w of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that w = 1/2, corresponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase (w < 1/2) from a region with spin-glass, ferromagnetic, mixed and paramagnetic phases (w > 1/2).

Modeling random corrosion processes via polynomial chaos expansion

Polynomial Chaos Expansion (PCE) is widely recognized as a flexible tool to represent different types of random variables/processes. However, applications to real, experimental data are still limited. In this article, PCE is used to represent the random time-evolution of metal corrosion growth in marine environments. The PCE coefficients are determined in order to represent data of 45 corrosion coupons tested by Jeffrey and Melchers (2001) at Taylors Beach, Australia. Accuracy of the representation and possibilities for model extrapolation are considered in the study. Results show that reasonably accurate smooth representations of the corrosion process can be obtained. The representation is not better because a smooth model is used to represent non-smooth corrosion data. Random corrosion leads to time-variant reliability problems, due to resistance degradation over time. Time variant reliability problems are not trivial to solve, especially under random process loading. Two example problems are solved herein, showing how the developed PCE representations can be employed in reliability analysis of structures subject to marine corrosion. Monte Carlo Simulation is used to solve the resulting time-variant reliability problems. However, an accurate and more computationally efficient solution is also presented.

Model for the Dynamics of the Cytoskeleton.

Particle tracking of microbeads attached to the cytoskeleton (CSK) reveals an intermittent dynamic. The mean squared displacement (MSD) is subdiffusive for small Δt and superdiffusive for large Δt, which are associated with periods of traps and periods of jumps respectively. The analysis of the displacements has shown a non-Gaussian behavior, what is indicative of an active motion, classifying the cells as a far from equilibrium material. Using Langevin dynamics, we reconstruct the dynamic of the CSK. The model is based on the bundles of actin filaments that link themself with the bead RGD coating, trapping it in an harmonic potential. We consider a one- dimensional motion of a particle, neglecting inertial effects (over-damped Langevin dynamics). The resultant force is decomposed in friction force, elastic force and random force, which is used as white noise representing the effect due to molecular agitation. These description until now shows a static situation where the bead performed a random walk in an elastic potential. In order to modeling the active remodeling of the CSK, we vary the equilibrium position of the potential. Inserting a motion in the well center, we change the equilibrium position linearly with time with constant velocity. The result found exhibits a MSD versus time ’tau’ with three regimes. The first regime is when ‘tau’ < ‘tau IND 0’, where ‘tau IND 0’ is the relaxation time, representing the thermal motion. At this regime the particle can diffuse freely. The second regime is a plateau, ‘tau IND 0’ < ‘tau’ < ‘tau IND 1’, representing the particle caged in the potential. Here, ‘tau IND 1’ is a characteristic time that limit the confinement period. And the third regime, ‘tau’ > ‘tau IND 1’, is when the particles are in the superdiffusive behavior. This is where most of the experiments are performed, under 20 frames per second (FPS), thus there is no experimental evidence that support the first regime. We are currently performing experiments with high frequency, up to 100 FPS, attempting to visualize this diffusive behavior. Beside the first regime, our simple model can reproduce MSD curves similar to what has been found experimentally, which can be helpful to understanding CSK structure and properties.