Statnote 12: the split-plot analysis of variance

In some experimental situations, the factors may not be equivalent to each other and replicates cannot be assigned at random to all treatment combinations. A common case, called a ‘split-plot design’, arises when one factor can be considered to be a major factor and the other a minor factor. Investigators need to be able to distinguish a split-plot design from a fully randomized design as it is a common mistake for researchers to analyse a split-plot design as if it were a fully randomised factorial experiment.

Low-temperature single-crystal Raman and neutron-diffraction study of the hydrogenous ammonium copper(II) tutton salt and the deuterated analogue in the metastable state

Low-temperature (15 K) single-crystal neutron-diffraction structures and Raman spectra of the salts (NX4)(2)[CU(OX2)(6)](SO4)(2), where X = H or D, are reported. This study is concerned with the origin of the structural phase change that is known to occur upon deuteration. Data for the deuterated salt were measured in the metastable state, achieved by application of 500 bar of hydrostatic pressure at similar to303 K followed by cooling to 281 K and the subsequent release of pressure. This allows for the direct comparison between the hydrogenous and deuterated salts, in the same modification, at ambient pressure and low temperature. The Raman spectra provide no intimation of any significant change in the intermolecular bonding. Furthermore, structural differences are few, the largest being for the long Cu-O bond, which is 2.2834(5) and 2.2802(4) Angstrom for the hydrogenous and the deuterated salts, respectively. Calorimetric data for the deuterated salt are also presented, providing an estimate of 0.17(2) kJ/mol for the enthalpy difference between the two structural forms at 295.8(5) K. The structural data suggest that substitution of hydrogen for deuterium gives rise to changes in the hydrogen-bonding interactions that result in a slightly reduced force field about the copper(II) center. The small structural differences suggest different relative stabilities for the hydrogenous and deuterated salts, which may be sufficient to stabilize the hydrogenous salt in the anomalous structural form.

Analysis of the electronic structure, hyperfine structure, and volume isotope shifts in the low lying states of BA I and BA II

Relativistic multi-configuration Dirac Fock (MCDF) wavefunctions coupled to good angular momentum J have been calculated for low lying states of Ba I and Ba II. These wavefunctions are compared with semiempirical ones derived from experimental atomic energy levels. It is found that significantly better agreement is obtained when close configurations are included in the MCDF wavefunctions. Calculations of the electronic part of the field isotope shift lead to very good agreement with electronic factors derived from experimental data. Furthermore, the slopes of the lines in a King plot analysis of many of the optical lines are predicted accurately by these calculations. However, the MCDF wavefunctions seem not to be of sufficient accuracy to give agreement with the experimental magnetic dipole and electric quadrupole hyperfine structure constants.

Fuzzy analysis: a vague way of dealing with uncertainty in real estate analysis?

Risk and uncertainty are, to say the least, poorly considered by most individuals involved in real estate analysis - in both development and investment appraisal. Surveyors continue to express 'uncertainty' about the value (risk) of using relatively objective methods of analysis to account for these factors. These methods attempt to identify the risk elements more explicitly. Conventionally this is done by deriving probability distributions for the uncontrolled variables in the system. A suggested 'new' way of "being able to express our uncertainty or slight vagueness about some of the qualitative judgements and not entirely certain data required in the course of the problem..." uses the application of fuzzy logic. This paper discusses and demonstrates the terminology and methodology of fuzzy analysis. In particular it attempts a comparison of the procedures with those used in 'conventional' risk analysis approaches and critically investigates whether a fuzzy approach offers an alternative to the use of probability based analysis for dealing with aspects of risk and uncertainty in real estate analysis

Bayesian analysis of skew-t multivariate null intercept measurement error model

The multivariate skew-t distribution (J Multivar Anal 79:93-113, 2001; J R Stat Soc, Ser B 65:367-389, 2003; Statistics 37:359-363, 2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew-normal ones as limiting cases. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763-771, 2003) where the random errors and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of dentistry.

Statistical analysis of proficiency testing results under elliptical distributions

The use of inter-laboratory test comparisons to determine the performance of individual laboratories for specific tests (or for calibration) [ISO/IEC Guide 43-1, 1997. Proficiency testing by interlaboratory comparisons - Part 1: Development and operation of proficiency testing schemes] is called Proficiency Testing (PT). In this paper we propose the use of the generalized likelihood ratio test to compare the performance of the group of laboratories for specific tests relative to the assigned value and illustrate the procedure considering an actual data from the PT program in the area of volume. The proposed test extends the test criteria in use allowing to test for the consistency of the group of laboratories. Moreover, the class of elliptical distributions are considered for the obtained measurements. (C) 2008 Elsevier B.V. All rights reserved.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Leverage analysis for linear mixed models

We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Regression analysis of mean quality-adjusted survival time based on pseudo-observations

Regression models for the mean quality-adjusted survival time are specified from hazard functions of transitions between two states and the mean quality-adjusted survival time may be a complex function of covariates. We discuss a regression model for the mean quality-adjusted survival (QAS) time based on pseudo-observations, which has the advantage of directly modeling the effect of covariates in the QAS time. Both Monte Carlo Simulations and a real data set are studied. Copyright (C) 2009 John Wiley & Sons, Ltd.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

Bayesian Analysis for Errors in Variables with Changepoint Models

Changepoint regression models have originally been developed in connection with applications in quality control, where a change from the in-control to the out-of-control state has to be detected based on the avaliable random observations. Up to now various changepoint models have been suggested for differents applications like reliability, econometrics or medicine. In many practical situations the covariate cannot be measured precisely and an alternative model are the errors in variable regression models. In this paper we study the regression model with errors in variables with changepoint from a Bayesian approach. From the simulation study we found that the proposed procedure produces estimates suitable for the changepoint and all other model parameters.

Full threshold vs. Swedish interactive threshold algorithm (SITA) em pacientes glaucomatosos submetidos à perimetria computadorizada pela primeira vez

PURPOSE: To compare the Full Threshold (FT) and SITA Standard (SS) strategies in glaucomatous patients undergoing automated perimetry for the first time. METHODS: Thirty-one glaucomatous patients who had never undergone perimetry underwent automated perimetry (Humphrey, program 30-2) with both FT and SS on the same day, with an interval of at least 15 minutes. The order of the examination was randomized, and only one eye per patient was analyzed. Three analyses were performed: a) all the examinations, regardless of the order of application; b) only the first examinations; c) only the second examinations. In order to calculate the sensitivity of both strategies, the following criteria were used to define abnormality: glaucoma hemifield test (GHT) outside normal limits, pattern standard deviation (PSD) <5%, or a cluster of 3 adjacent points with p<5% at the pattern deviation probability plot. RESULTS: When the results of all examinations were analyzed regardless of the order in which they were performed, the number of depressed points with p<0.5% in the pattern deviation probability map was significantly greater with SS (p=0.037), and the sensitivities were 87.1% for SS and 77.4% for FT (p=0.506). When only the first examinations were compared, there were no statistically significant differences regarding the number of depressed points, but the sensitivity of SS (100%) was significantly greater than that obtained with FT (70.6%) (p=0.048). When only the second examinations were compared, there were no statistically significant differences regarding the number of depressed points, and the sensitivities of SS (76.5%) and FT (85.7%) (p=0.664). CONCLUSION: SS may have a higher sensitivity than FT in glaucomatous patients undergoing automated perimetry for the first time. However, this difference tends to disappear in subsequent examinations.

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.