Methodology for Creating of Objective and Balanced Linear Tests Based on the Item Response Theory

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Is the consumption-income ratio stationary? Evidence from linear and nonlinear panel unit root tests for OECD and non-OECD countries

This paper applies recently developed heterogeneous nonlinear and linear panel unit root tests that account for cross-sectional dependence to 24 OECD and 33 non-OECD countries’ consumption-income ratios over the period 1951–2003. We apply a recently developed methodology that facilitates the use of panel tests to identify which individual cross-sectional units are stationary and which are nonstationary. This extends evidence provided in the recent literature to consider both linear and nonlinear adjustment in panel unit root tests, to address the issue of cross-sectional dependence, and to substantially expand both time-series and cross sectional dimensions of the data analysed. We find that the majority (65%) of the series are nonstationary with slightly fewer OECD countries’ (61%) series exhibiting a unit root than non-OECD countries (68%).

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Exact tests for correlation and for the slope in simple linear regressions without making assumptions

We present an exact test for whether two random variables that have known bounds on their support are negatively correlated. The alternative hypothesis is that they are not negatively correlated. No assumptions are made on the underlying distributions. We show by example that the Spearman rank correlation test as the competing exact test of correlation in nonparametric settings rests on an additional assumption on the data generating process without which it is not valid as a test for correlation.We then show how to test for the significance of the slope in a linear regression analysis that invovles a single independent variable and where outcomes of the dependent variable belong to a known bounded set.

Simulation-Based Finite-Sample Normality Tests in Linear Regressions

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size normality tests for the disturbances of standard linear regression, which is based on using the technique of Monte Carlo tests.

Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

A comparison of tests of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We test whether there are nonlinearities in the response of short- and long-term interest rates to the spread in interest rates, and assess the out-of-sample predictability of interest rates using linear and nonlinear models. We find strong evidence of nonlinearities in the response of interest rates to the spread. Nonlinearities are shown to result in more accurate short-horizon forecasts, especially of the spread.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Tests of anomalous quartic couplings at the Next Linear Collider

We analyze the potential of the Next Linear e+e- Collider to study anomalous quartic vector-boson interactions through the processes e+e-→W+W-Z and ZZZ. In the framework of SU(2)L⊗U(1)Y chiral Lagrangians, we examine all effective operators of order p4 that lead to four-gauge-boson interactions but do not induce anomalous trilinear vertices. In our analysis, we take into account the decay of the vector bosons to fermions and evaluate the efficiency in their reconstruction. We obtain the bounds that can be placed on the anomalous quartic interactions and we study the strategies to distinguish the possible couplings.

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

Shaking table tests of structures with hysteretic dampers: experimental results vs. prediction using non-linear static methods

The use of seismic hysteretic dampers for passive control is increasing exponentially in recent years for both new and existing buildings. In order to utilize hysteretic dampers within a structural system, it is of paramount importance to have simplified design procedures based upon knowledge gained from theoretical studies and validated with experimental results. Non-linear Static Procedures (NSPs) are presented as an alternative to the force-based methods more common nowadays. The application of NSPs to conventional structures has been well established; yet there is a lack of experimental information on how NSPs apply to systems with hysteretic dampers. In this research, several shaking table tests were conducted on two single bay and single story 1:2 scale structures with and without hysteretic dampers. The maximum response of the structure with dampers in terms of lateral displacement and base shear obtained from the tests was compared with the prediction provided by three well-known NSPs: (1) the improved version of the Capacity Spectrum Method (CSM) from FEMA 440; (2) the improved version of the Displacement Coefficient Method (DCM) from FEMA 440; and (3) the N2 Method implemented in Eurocode 8. In general, the improved version of the DCM and N2 methods are found to provide acceptable accuracy in prediction, but the CSM tends to underestimate the response.

Assessment Of The Fixation Of Mandibular Symphysis Fractures Using Conical Cannulated Screws: Mechanical And Photoelastic Tests.

The aim of this study was to use mechanical and photoelastic tests to compare the performance of cannulated screws with other fixation methods in mandibular symphysis fractures. Ten polyurethane mandibles were allocated to each group and fixed as follows: group PRP, 2 perpendicular miniplates; group PLL, 1 miniplate and 1 plate, parallel; and group CS, 2 cannulated screws. Vertical linear loading tests were performed. The differences between mean values were analyzed with the Tukey test. The photoelastic test was carried out using a polariscope. The results revealed differences between the CS and PRP groups at 1, 3, 5, and 10 millimeters of displacement. The photoelastic test confirmed higher stress concentration in all groups close to the mandibular base, whereas the CS group showed it throughout the region assessed. Conical cannulated screws performed well in mechanical and photoelastic tests.