Modeling covariance matrices via partial autocorrelations

AbstractWe study the role of partial autocorrelations in the reparameterization and parsimonious modeling of a covariance matrix. The work is motivated by and tries to mimic the phenomenal success of the partial autocorrelations function (PACF) in model formulation, removing the positive-definiteness constraint on the autocorrelation function of a stationary time series and in reparameterizing the stationarity-invertibility domain of ARMA models. It turns out that once an order is fixed among the variables of a general random vector, then the above properties continue to hold and follow from establishing a one-to-one correspondence between a correlation matrix and its associated matrix of partial autocorrelations. Connections between the latter and the parameters of the modified Cholesky decomposition of a covariance matrix are discussed. Graphical tools similar to partial correlograms for model formulation and various priors based on the partial autocorrelations are proposed. We develop frequentist/Bayesian procedures for modelling correlation matrices, illustrate them using a real dataset, and explore their properties via simulations

A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption on the PPZ. It can be easily adapted to many versions of EM.Comment: Accepted for publication in Statistics and Computin

Effectiveness of proprioceptive neuromuscular facilitation on pain intensity and functional disability in patients with low back pain: A systematic review and meta-analysis

Background: This systematic review aimed to investigate the effectiveness of proprioceptive neuromuscular facilitation (PNF) training on back pain intensity and functional disability in people with low back pain (LBP). Methods: Totally, five electronic databases, including PubMed/Medline (NLM), Scopus, Google Scholar, PEDro, and Cochrane Central Register of Controlled Clinical Trials were searched up to October 31, 2018. Clinical trials with a concurrent comparison group (s) that compared the effectiveness of PNF training with any other physical therapy intervention were selected. Publication language was restricted to English language articles. Methodologic quality was assessed using the PEDro scale. The measures of continuous variables were summarized as Hedges fs g. Results: In total, 20 eligible trials were identified with 965 LBP patients. A large effect size (standardized mean difference SMD=-2.14, 95% confidence interval CI=3.23 to -1.05) and significant effect were observed favoring the use of PNF training to alleviate back pain intensity in patients with LBP. Moreover, large effect size and the significant result were also determined for the effect of PNF training on functional disability improvement (SMD=-2.68, 95% CI=-3.36 to -2.00) in population with LBP. A qualitative synthesis of results indicated that PNF training can significantly improve sagittal spine ROM. Statistical heterogeneity analysis showed that there was considerable statistical heterogeneity among the selected trials for the primary outcomes (I2� 86.6%). Conclusion: There is a low quality of evidence and weak strength of recommendation that PNF training has positive effects on back pain and disability in LBP people. Further high-quality randomized clinical trials regarding long-term effects of PNF training versus validated control intervention in a clinical setting is recommendable. Level of evidence: I. © 2020 Mashhad University of Medical Sciences. All rights reserved

A fast Metropolis-Hastings method for generating random correlation matrices

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positive definite matrix and Markov chain Monte Carlo theory. We perform a detailed convergence analysis of the resulting Markov chain, and show how it benefits from fast convergence, both theoretically and empirically. Furthermore, in numerical experiments our algorithm is shown to be significantly faster than the current alternative approaches, thanks to its simple yet principled approach.Comment: 8 pages, 3 figures, 2018 conferenc

Bootstrap-assisted tests of symmetry for dependent data

The paper considers the problem of testing for symmetry (about an unknown centre) of the marginal distribution of a strictly stationary and weakly dependent stochastic process. The possibility of using the autoregressive sieve bootstrap and stationary bootstrap procedures to obtain critical values and P-values for symmetry tests is explored. Bootstrap-assisted tests for symmetry are straightforward to implement and require no prior estimation of asymptotic variances. The small-sample properties of a wide variety of tests are investigated using Monte Carlo experiments. A bootstrap-assisted version of the triples test is found to have the best overall performance

Reliability of real�time ultrasound imaging for the assessment of trunk stabilizer muscles: A systematic review of the literature

Rehabilitative ultrasound (US) imaging is one of the popular methods for investigating muscle morphologic characteristics and dimensions in recent years. The reliability of this method has been investigated in different studies. As studies have been performed with different designs and quality, reported values of rehabilitative US have a wide range. The objective of this study was to systematically review the literature conducted on the reliability of rehabilitative US imaging for the assessment of deep abdominal and lumbar trunk muscle dimensions. The PubMed/MEDLINE, Scopus, Google Scholar, Science Direct, Embase, Physiotherapy Evidence, Ovid, and CINAHL databases were searched to identify original research articles conducted on the reliability of rehabilitative US imaging published from June 2007 to August 2017. The articles were qualitatively assessed; reliability data were extracted; and the methodological quality was evaluated by 2 independent reviewers. Of the 26 included studies, 16 were considered of high methodological quality. Except for 2 studies, all high�quality studies reported intraclass correlation coefficients (ICCs) for intra�rater reliability of 0.70 or greater. Also, ICCs reported for inter�rater reliability in high�quality studies were generally greater than 0.70. Among low�quality studies, reported ICCs ranged from 0.26 to 0.99 and 0.68 to 0.97 for intra� and inter�rater reliability, respectively. Also, the reported standard error of measurement and minimal detectable change for rehabilitative US were generally in an acceptable range. Generally, the results of the reviewed studies indicate that rehabilitative US imaging has good levels of both inter� and intra�rater reliability. © 2018 by the American Institute of Ultrasound in Medicine

Effectiveness of slump stretching on low back pain: A systematic review and meta-analysis

Background. The slump test is a type of neurodynamic test that is believed to evaluate the mechanosensitivity of the neuromeningeal structures within the vertebral canal. The objective of this review was to investigate the effectiveness of slump stretching on back pain and disability in patients with low back pain (LBP). Methods. We searched eight electronic databases (PubMed/Medline, Scopus, Ovid, CINAHL, Embase, PEDro, Google Scholar, CENTRAL). The publication language was restricted to English, and we searched the full time period available for each database, up to October 2017. Our primary outcomes were pain and disability, and the secondary outcome was range of motion (ROM). Results. We identified 12 eligible studies with 515 LBP patients. All included studies reported short-term follow-up. A large effect size (standardized mean difference SMD ¼ �2.15, 95% confidence interval CI ¼ �3.35 to � 0.95) and significant effect were determined, favoring the use of slump stretching to decrease pain in patients with LBP. In addition, large effect sizes and significant results were also found for the effect of slump stretching on disability improvement (SMD ¼ �8.03, 95% CI ¼ �11.59 to �4.47) in the LBP population. A qualitative synthesis of results showed that slump stretching can significantly increase straight leg raise and active knee extension ROM. Conclusions. There is very low to moderate quality of evidence that slump stretching may have positive effects on pain in people with LBP. However, the quality of evidence for the benefits of slump stretching on disability was very low. Finally, it appears that patients with nonradicular LBP may benefit most from slump stretching compared with other types of LBP. © 2018 American Academy of Pain Medicine. All rights reserved

Gender-related differences in reliability of thorax, lumbar, and pelvis kinematics during gait in patients with non-specific chronic low back pain

Objective To evaluate test-retest reliability of trunk kinematics relative to the pelvis during gait in two groups (males and females) of patients with non-specific chronic low back pain (NCLBP) using three-dimensional motion capture system. Methods A convenience sample of 40 NCLBP participants (20 males and 20 females) was evaluated in two sessions. Participants were asked to walk with self-selected speed and kinematics of thorax and lumbar spine were captured using a 6-infrared-cameras motion-analyzer system. Peak amplitude of displacement and its measurement errors and minimal detectable change (MDC) were then calculated. Results Intraclass correlation coefficients (ICCs) were relatively constant but small for certain variables (lower lumbar peak flexion in female: inter-session ICC=0.51 and intra-session ICC=0.68; peak extension in male: inter-session ICC=0.67 and intra-session ICC=0.66). The measurement error remained constant and standard error of measurement (SEM) difference was large between males (generally �4.8°) and females (generally �5.3°). Standard deviation (SD) was higher in females. In most segments, females exhibited higher MDCs except for lower lumbar sagittal movements. Conclusion Although ICCs were sufficiently reliable and constant in both genders during gait, there was difference in SEM due to difference in SD between genders caused by different gait disturbance in chronic low back pain. Due to the increasing tendency of measurement error in other areas of men and women, attention is needed when measuring lumbar motion using the method described in this study. © 2018 by Korean Academy of Rehabilitation Medicine

Gender-related differences in reliability of thorax, lumbar, and pelvis kinematics during gait in patients with non-specific chronic low back pain

Objective To evaluate test-retest reliability of trunk kinematics relative to the pelvis during gait in two groups (males and females) of patients with non-specific chronic low back pain (NCLBP) using three-dimensional motion capture system. Methods A convenience sample of 40 NCLBP participants (20 males and 20 females) was evaluated in two sessions. Participants were asked to walk with self-selected speed and kinematics of thorax and lumbar spine were captured using a 6-infrared-cameras motion-analyzer system. Peak amplitude of displacement and its measurement errors and minimal detectable change (MDC) were then calculated. Results Intraclass correlation coefficients (ICCs) were relatively constant but small for certain variables (lower lumbar peak flexion in female: inter-session ICC=0.51 and intra-session ICC=0.68; peak extension in male: inter-session ICC=0.67 and intra-session ICC=0.66). The measurement error remained constant and standard error of measurement (SEM) difference was large between males (generally �4.8°) and females (generally �5.3°). Standard deviation (SD) was higher in females. In most segments, females exhibited higher MDCs except for lower lumbar sagittal movements. Conclusion Although ICCs were sufficiently reliable and constant in both genders during gait, there was difference in SEM due to difference in SD between genders caused by different gait disturbance in chronic low back pain. Due to the increasing tendency of measurement error in other areas of men and women, attention is needed when measuring lumbar motion using the method described in this study. © 2018 by Korean Academy of Rehabilitation Medicine