Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. 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) 2012 Elsevier B.V. All rights reserved.

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.

Six minute walk test Z score: Correlations with cystic fibrosis severity markers

Background: The six-minute-walk-test (6MWT) has been increasingly used in cystic fibrosis (CF) patients. However, few studies in children have correlated 6MWT with current parameters used to evaluate CF severity. Moreover, no study transformed the values of distance walked from meters into Z scores to avoid bias like age and gender, which are sources of 6MWT variability. Methods: A cross-sectional descriptive study was performed to analyze the correlations (Spearman) among forced expiratory volume in one second (FEV1), body mass index (BMI), chest radiography (CXR), chest tomography (CT), and 6MWT Z score (Z-6MWT). Clinically stable CF patients, aged 6-21 years, were included. Results: 34 patients, 14F/20M, mean age 12.1 +/- 4.0 years were studied. The mean Z-6MWT was -1.1 +/- 1.106. The following correlations versus Z-6MWT were found: FEV1 (r=0.59, r(2)=0.32, p=0.0002), BMI Z score (r=0.42, r(2)=0.17, p=0.013), CXR (r=0.34, r(2)=0.15, p=0.0472) and CT (r=-0.45, r(2)=0.23, p=0.0073). Conclusions: In conclusion there was a significant, but poor, correlation between the six minute walk test Z score and the cystic fibrosis severity markers currently in use. (C) 2011 European Cystic Fibrosis Society. Published by Elsevier B.V. All rights reserved.