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

Neural Network Model of Estimation of Body Mass Index Based on Indirect Input Factors

A well-prepared One of the main concerns of people in developing and developed societies is increasing the Body Mass Index (BMI) level. BMI, in fact can be considered as an indicator of overall health condition. Genetic aspects aside, the BMI level is affected by different factors, such as socio-economic, environmental, and physical activity level. This study investigated the effect of different factors on the BMI level of a sample population of 470 adults of three residential neighborhoods in Shiraz, Iran. The Pearson correlation coefficient, independent sample T-test and One Way ANOVA were used to extract the variables which significantly influenced the BMI. The statistical analysis showed that despite the apparent association of BMI with physical activity level, it is influenced by several factors such as age, residence record, number of children, distance to bus or taxi stop, indoor or sport exercise. Then, an Artificial Neural Network (ANN) was applied to predict the level of personal BMI. Artificial Neural Network-based methodology results showed that the generalized estimating ANN model was satisfactory in estimating the BMI based on the introduced pattern

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

Reliability and validity of an iPhone® application for the measurement of lumbar spine flexion and extension range of motion

Background: Measurement of lumbar spine range of motion (ROM) is often considered to be an essential component of lumbar spine physiotherapy and orthopedic assessment. The measurement can be carried out through various instruments such as inclinometers, goniometers, and etc. Recent smartphones have been equipped with accelerometers and magnetometers, which, through specific software applications (apps) can be used for inclinometric functions. Purpose: The main purpose was to investigate the reliability and validity of an iPhone® app (TiltMeter© -advanced level and inclinometer) for measuring standing lumbar spine flexion-extension ROM in asymptomatic subjects. Design: A cross-sectional study was carried out. Setting: This study was conducted in a physiotherapy clinic located at School of Rehabilitation Sciences, Iran University of Medical Science and Health Services, Tehran, Iran. Subjects: A convenience sample of 30 asymptomatic adults (15 males; 15 females; age range = 18-55 years) was recruited between August 2015 and December 2015. Methods: Following a 2-minute warm-up, the subjects were asked to stand in a relaxed position and their skin was marked at the T12-L1 and S1-S2 spinal levels. From this position, they were asked to perform maximum lumbar flexion followed by maximum lumbar extension with their knees straight. Two blinded raters each used an inclinometer and the iPhone® app to measure lumbar spine flexion-extension ROM. A third rater read the measured angles. To calculate total lumbar spine flexion-extension ROM, the measurement from S1-S2 was subtracted from T12-L1. The second (2 hours later) and third (48 hours later) sessions were carried out in the same manner as the first session. All of the measurements were conducted 3 times and the mean value of 3 repetitions for each measurement was used for analysis. Intraclass correlation coefficient (ICC) models (3, k) and (2, k) were used to determine the intra-rater and inter-rater reliability, respectively. The Pearson correlation coefficients were used to establish concurrent validity of the iPhone® app. Furthermore, minimum detectable change at the 95 confidence level (MDC95) was computed as 1.96 � standard error of measurement � �2. Results: Good to excellent intra-rater and inter-rater reliability were demonstrated for both the gravity-based inclinometer with ICC values of �0.84 and �0.77 and the iPhone® app with ICC values of �0.85 and �0.85, respectively. The MDC95 ranged from 5.82°to 8.18°for the intra-rater analysis and from 7.38°to 8.66° for the inter-rater analysis. The concurrent validity for flexion and extension between the 2 instruments was 0.85 and 0.91, respectively. Conclusions: The iPhone®app possesses good to excellent intra-rater and inter-rater reliability and concurrent validity. It seems that the iPhone® app can be used for the measurement of lumbar spine flexion-extension ROM. © 2016 Pourahmadi et al

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

Learning a Factor Model via Regularized PCA

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those produced by pre-existing factor analysis approaches. We also establish theoretical results that explain how our algorithm corrects the biases induced by conventional approaches. An important feature of our algorithm is that its computational requirements are similar to those of PCA, which enjoys wide use in large part due to its efficiency

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