Residual Variance-covariance Matrix Research Articles

The Effectiveness of Music Interventions for Improving Anxiety Symptoms in Cancer Patients Undergoing Radiation Therapy.

Being alone in the treatment room during radiation therapy (RT) often causes anxiety which may lead to treatment failure. The benefit of music interventions in reducing anxiety among cancer patients during RT simulations is still controversial. The goal of this study is to evaluate the effect of music on anxiety symptoms among patients undergoing initial RT and a randomized trial was conducted. Patients who received RT for the first time were enrolled and were randomly allocated into groups of experiment and control. The questionnaire of mood thermometer (BSRS-5), distress thermometer (DT), and the Beck Anxiety Inventory (BAI-C) and were given before and after RT. We also measured the changes in physiological symptoms for ten consecutive days since the first day of RT. The experimental group was given music during RT, while the control group was not. The generalized linear mixed model was used to estimate the pre-post difference of music interventions on the BSRS-5, DT, and BAI-C compared with control group after considering the random intercept and the unstructured residual variance-covariance matrix. A total of 50 patients in the experimental group and 50 patients in the control group were enrolled in this study. The satisfaction degree of treatment in the experimental group was 100%, but it was 96% in control group (p = 0.0048). The pre-test BSRS-5 was 3.4±2.3 for the experimental group versus 2.6±2.3 for the control group (p = 0.0815), the post-test BSRS-5 score was significantly reduced in the experimental group (1.6±1.4 for experimental group versus 2.7±2.2 for the control group, p = 0.0057), the significant pre-post difference of BSRS-5 between group was found (p = 0.0024). When the experimental group withdrew from the music intervention, the BSRS-5 rebounded to 3.7±3.0. The pre-test DT was 4.3±1.5 and 3.4±1.7 in the experimental group and control group (p = 0.0051), and the post-test DT score was significantly reduced in the experimental group (2.7±1.2 for the experimental group and 3.5±1.3 for the control group, p = 0.0021), the significant pre-post difference of DT between group was found (p<.0001). When the experimental group withdrew from the music intervention, the DT rebounded to 3.7±1.4. The pre-test BAI-C was 6.7±11.7 and 7.8±8.5 in the experimental group and control group (p = 0.5878), and the post-test BAI-C score was significantly lower in the experimental group (1.7±3.7 for the experimental group and 7.4±8.0 for the control group, p<.0001), however, the pre-post difference of BAI-C between group was not significant (p = 0.0619). When the experimental group withdrew from the music intervention, the BAI-C rebounded to 6.5±8.7. There is a significantly increased systolic blood pressure in the control group compared with the patients had music intervention. This study's results provide evidence that playing music routinely (music intervention) during RT can be an excellent way to relieve patients' anxiety and improve their comfort.

A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form

This paper considers the characterization of the reduced-form solution of a large class of linear rational expectations models. I show that under certain conditions, if a solution exists and is unique, it can be cast in finite-order VAR form. I also investigate the conditions for the VAR form to be stationary with a well-defined residual variance-covariance matrix in equilibrium, for the shocks to be recoverable, and for local identification of the structural parameters for estimation from the sample likelihood. An application to the workhorse New Keynesian model with accompanying Matlab codes illustrates the practical use of the finite-order VAR representation. In particular, I argue that the identification of monetary policy shocks based on structural VARs can be more closely aligned with theory using the finite-order VAR form of the model solution characterized in this paper.

A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form

This paper considers the characterization of the reduced-form solution of a large class of linear rational expectations models. I show that under certain conditions, if a solution exists and is unique, it can be cast in finite-order VAR form. I also investigate the conditions for the VAR form to be stationary with a well-defined residual variance-covariance matrix in equilibrium, for the shocks to be recoverable, and for local identification of the structural parameters for estimation from the sample likelihood. An application to the workhorse New Keynesian model with accompanying Matlab codes illustrates the practical use of the finite-order VAR representation. In particular, I argue that the identification of monetary policy shocks based on structural VARs can be more closely aligned with theory using the finite-order VAR form of the model solution characterized in this paper.

Multivariate analytical figures of merit as a metric for evaluation of quantitative measurements using comprehensive two-dimensional gas chromatography–mass spectrometry

The present contribution is devoted to develop multivariate analytical figures of merit (AFOMs) as a new metric for evaluation of quantitative measurements using comprehensive two-dimensional gas chromatography–mass spectrometry (GC×GC–MS). In this regard, new definition of sensitivity (SEN) is extended to GC×GC–MS data and then, other multivariate AFOMs including analytical SEN (γ), selectivity (SEL) and limit of detection (LOD) are calculated. Also, two frequently used second- and third-order calibration algorithms of multivariate curve resolution-alternating least squares (MCR-ALS) as representative of multi-set methods and parallel factor analysis (PARAFAC) as representative of multi-way methods are discussed to exploit pure component profiles and to calculate multivariate AFOMs. Different GC×GC–MS data sets with different number of components along with various levels of artifacts are simulated and analyzed. Noise, elution time shifts in both chromatographic dimensions, peak overlap and interferences are considered as the main artifacts in this work. Additionally, a new strategy is developed to estimate the noise level using variance-covariance matrix of residuals which is very important to calculate multivariate AFOMs. Finally, determination of polycyclic aromatic hydrocarbons (PAHs) in aromatic fraction of heavy fuel oil (HFO) analyzed by GC×GC–MS is considered as real case to confirm applicability of the proposed metric in real samples. It should be pointed out that the proposed strategy in this work can be used for other types of comprehensive two-dimensional chromatographic (CTDC) techniques like comprehensive two dimensional liquid chromatography (LC×LC).

A stage‐wise approach for the analysis of multi‐environment trials

Plant breeders and variety testing agencies routinely test candidate genotypes (crop varieties, lines, test hybrids) in multiple environments. Such multi-environment trials can be efficiently analysed by mixed models. A single-stage analysis models the entire observed data at the level of individual plots. This kind of analysis is usually considered as the gold standard. In practice, however, it is more convenient to use a two-stage approach, in which experiments are first analysed per environment, yielding adjusted means per genotype, which are then summarised across environments in the second stage. Stage-wise approaches suggested so far are approximate in that they cannot fully reproduce a single-stage analysis, except in very simple cases, because the variance-covariance matrix of adjusted means from individual environments needs to be approximated by a diagonal matrix. This paper proposes a fully efficient stage-wise method, which carries forward the full variance-covariance matrix of adjusted means from the individual environments to the analysis across the series of trials. Provided the variance components are known, this method can fully reproduce the results of a single-stage analysis. Computations are made efficient by a diagonalisation of the residual variance-covariance matrix, which necessitates a corresponding linear transformation of both the first-stage estimates (e.g. adjusted means and regression slopes for plot covariates) and the corresponding design matrices for fixed and random effects. We also exemplify the extension of the general approach to a three-stage analysis. The method is illustrated using two datasets, one real and the other simulated. The proposed approach has close connections with meta-analysis, where environments correspond to centres and genotypes to medical treatments. We therefore compare our theoretical results with recently published results from a meta-analysis.

A Rapid Generalized Least Squares Model for a Genome-Wide Quantitative Trait Association Analysis in Families

Genome-wide association studies (GWAS) using family data involve association analyses between hundreds of thousands of markers and a trait for a large number of related individuals. The correlations among relatives bring statistical and computational challenges when performing these large-scale association analyses. Recently, several rapid methods accounting for both within- and between-family variation have been proposed. However, these techniques mostly model the phenotypic similarities in terms of genetic relatedness. The familial resemblances in many family-based studies such as twin studies are not only due to the genetic relatedness, but also derive from shared environmental effects and assortative mating. In this paper, we propose 2 generalized least squares (GLS) models for rapid association analysis of family-based GWAS, which accommodate both genetic and environmental contributions to familial resemblance. In our first model, we estimated the joint genetic and environmental variations. In our second model, we estimated the genetic and environmental components separately. Through simulation studies, we demonstrated that our proposed approaches are more powerful and computationally efficient than a number of existing methods are. We show that estimating the residual variance-covariance matrix in the GLS models without SNP effects does not lead to an appreciable bias in the p values as long as the SNP effect is small (i.e. accounting for no more than 1% of trait variance).

Spatial Autocorrelations and Urban Housing Market Segmentation

This paper seeks to let data define urban housing market segments, replacing the conventional administrative or any pre-defined boundaries used in the previous housing submarket literature. We model housing transaction data using a conventional hedonic function. The hedonic residuals are used to estimate an isotropic semi-variogram, from which residual variance–covariance matrix is constructed. The correlations between hedonic residuals are used as identifier to assign housing units into clusters. Standard submarket identification tests are applied to each cluster to examine the segmentation of housing market. The results are compared with the prevailing structure of market segments. Weighted mean square test shows that the defined submarket structure can improve the precision of price prediction by 17.5%. This paper is experimental in the sense that it represents one of the first attempts at investigating market segmentation through house price spatial autocorrelations.

A general framework for analyzing the genetic architecture of developmental characteristics.

The genetic architecture of growth traits plays a central role in shaping the growth, development, and evolution of organisms. While a limited number of models have been devised to estimate genetic effects on complex phenotypes, no model has been available to examine how gene actions and interactions alter the ontogenetic development of an organism and transform the altered ontogeny into descendants. In this article, we present a novel statistical model for mapping quantitative trait loci (QTL) determining the developmental process of complex traits. Our model is constructed within the traditional maximum-likelihood framework implemented with the EM algorithm. We employ biologically meaningful growth curve equations to model time-specific expected genetic values and the AR(1) model to structure the residual variance-covariance matrix among different time points. Because of a reduced number of parameters being estimated and the incorporation of biological principles, the new model displays increased statistical power to detect QTL exerting an effect on the shape of ontogenetic growth and development. The model allows for the tests of a number of biological hypotheses regarding the role of epistasis in determining biological growth, form, and shape and for the resolution of developmental problems at the interface with evolution. Using our newly developed model, we have successfully detected significant additive x additive epistatic effects on stem height growth trajectories in a forest tree.

Genetic and Phenotypic Parameters for Production and Days Open in the First Three Lactations of Swedish Dairy Cattle

Abstract The material consisted of completed 305-day records of daughters of Al bulls. The analyses were carried out for each of the two predominant breeds where one of the breeds was divided into two separate geographical areas. The material was further divided into five years of first calving (1977–81) giving a total of 15 data sets. The traits were 305-day lactation milk (M) or fat (F) yield and days open (DO) in the first three lactations (1, 2, 3). All traits were preadjusted for month and age of calving, production was also adjusted for days open. The multiple trait mixed model used had the same effects for all traits analyzed simultaneously. These were effects of herd (fixed), group (fixed) and sire within group. The latter was random if the sire was a young bull and fixed for old progeny-tested bulls. The fixed sires were not used for estimating variance components. A triangular transformation was applied which made the residual variance-covariance matrix an identity matrix. The EM-algorithm was used to get approximate REML estimates of the variance components. Forty rounds of iteration were carried out. Overall average h 2 for milk yield were 0.268, 0.246 and 0.248 for the first three lactations respectively. The genetic correlations between the lactations were high, 0.855, 0.836 and 0.966 for r g12, r g13 and r g23 respectively. Heritabilities for fat yield were somewhat lower: 0.250, 0.213 and 0.228 respectively. Genetic correlations were 0.920, 0.846 and 0.938 respectively. For days open low heritabilities were found: 0.040, 0.050 and 0.066 respectively. Fairly high genetic correlations were found between these traits, however: 0.582, 0.493 and 0.220. Genetic correlations between milk yield in first lactation (Ml) and days open in first and second lactations (DO1, DO2) were moderately high and unfavourable: 0.414 and 0.335 respectively. There were no systematic trends in the estimated parameters over the different production years. The unfavourable genetic correlations obtained in this study between milk production and days open was not reflected in the estimated genetic trends for days open in a previous study.

Growth and Feed Efficiency of Pureline and Crossline Dairy Heifers

Data on 3957 heifers from the Holstein H line, Ayrshire-based A line, and C line (crossbreds between H and A lines) were used. Growth, feed consumption, and feed efficiency from 26 to 34 wk were examined. The full model included the fixed effects of herd, year of birth, season of birth, and additive, maternal, and heterotic genetic effects with 26-wk weight as a covariate. Heterotic and maternal effects were not significant. Adjusted for the 26-wk weight covariate, H line heifers gained 3kg more than A line heifers with C line heifers intermediate. Adjusted for 26 and 34-wk weight covariates, H line heifers ate 2kg less TDN than A line heifers and, hence, were more efficient. Correlations among traits were estimated using the residual variance-covariance matrix from the full model. Body weight at 34 wk was correlated with 26-wk weight (r = .88) but essentially independent of rate of gain (r = .02). It was correlated with feed consumed (r = .51) and negatively associated with gain/feed consumed (r = −.25). Gain was correlated (r = .84) with gain/feed consumed but mildly so (r = .28) with feed consumed. Feed consumption was negatively correlated (r = −.25) with gain/feed consumed when the 26-wk weight covariate was included but became much larger (r = −.95) when both 26 and 34 wk weight covariates were included. Although genetic differences in feed consumption and feed efficiency of growing heifers exist, these are small and closely associated with weights and weight gains.

Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable

Abstract We consider a model in which one observes multiple indicators and multiple causes of a single latent variable. In terms of the multivariate regression of the indicators on the causes, the model implies restrictions of two types: (i) the regression coefficient matrix has rank one, (ii) the residual variance-covariance matrix satisfies a factor analysis model with one common factor. The first type of restriction is familiar to econometricians and the second to psychometricians. We derive the maximum-likelihood estimators and their asymptotic variance-covariance matrix. Two alternative “limited information” estimators are also considered and compared with the maximum-likelihood estimators in terms of efficiency.

A note on invariance in three-mode factor analysis.

Previous results of the application of Lawley's selection theorem to the common factor analysis model are extended to a revision of Tucker's three-mode principal components model. If the regression of the three-mode manifest variates on variates used to select subpopulations is both linear and homoscedastic, the two factor pattern matrices, the core matrix, and the residual variance-covariance matrix in the three-mode model can all be assumed to be invariant across subpopulations. The implication of this finding for simple structure is discussed.