Generalized Least-squares Approach Research Articles

Companys characteristics and corporate sustainability reporting practice of listed manufacturing companies in Nigeria

The research looks at how company variables, such as size, leverage, and profitability, affect sustainability reporting in Nigeria. The study used an ex-post design and the sample included 15 publicly traded manufacturing enterprises in Nigeria. These companies were chosen because they have the potential to be environmentally conscious. The study covers a period of five years, from 2016 to 2020. Thus, because econometric modelling of bounded dependent variables reveals the limitations of linear estimation, the researchers employed the generalized least-squares approach to estimate the panel data first, followed by fractional regression. To correct for potential non-uniform variation in the estimation, the white-adjusted standard error was utilized, resulting in an estimation result with no non-uniform variance. In terms of panel duration and cross-section, the estimations were found to be free of non-uniform variance. To confirm the probability of continuous error correlation, the research utilized the Peselan interdependence test. As shown in the results, the residuals are cross-section independent. According to the coefficient values, the only variable that has a positive and significant impact on sustainability reporting is firm size. The report advises relevant government agencies to introduce sustainability tax incentives as it may enhance sustainability reporting practices in the country.

A generalized least-squares approach regularized with graph embedding for dimensionality reduction

In current graph embedding methods, low dimensional projections are obtained by preserving either global geometrical structure of data or local geometrical structure of data. In this paper, the PCA (Principal Component Analysis) idea of minimizing least-squares reconstruction errors is regularized with graph embedding, to unify various local manifold embedding methods within a generalized framework to keep global and local low dimensional subspace. Different from the well-known PCA method, our proposed generalized least-squares approach considers data distributions together with an instance penalty in each data point. In this way, PCA is viewed as a special instance of our proposed generalized least squares framework for preserving global projections. Applying a regulation of graph embedding, we can obtain projection that preserves both intrinsic geometrical structure and global structure of data. From the experimental results on a variety of face and handwritten digit recognition, our proposed method has advantage of superior performances in keeping lower dimensional subspaces and higher classification results than state-of-the-art graph embedding methods.

Sperm size is negatively related to relative testis size in West African riverine cichlid fishes.

Fishes show a great diversity of mating systems and fertilization mechanisms. This diversity creates an enormous potential for sperm competition. Typically, monogamous species face a low risk of sperm competition and invest less into sperm, and thus show smaller relative testis mass compared to polygamous species with high sperm competition. In cichlids, sperm competition risk is very variable. In lacustrine East African cichlids, large sperm are interpreted as an adaptation to sperm competition, as in those species sperm length correlates with sperm swimming speed. The aim of the present study was to examine variation in sperm and testis traits of substrate breeding cichlids from West African river systems and its relationship to sperm competition. Therefore, sperm traits (total sperm size, flagellum-, midpiece-, and head size) and sperm number were related to the gonadosomatic index (GSI), an indicator of sperm competition, in eight species of two large informal tribes, the chromidotilapiines and the haplotilapiines. We found significant differences between species in all examined sperm traits, sperm number, and GSI with pronounced differences between chromidotilapiines and haplotilapiines. We used a generalized least-squares approach to control for non-independence of data. GSI was positively correlated with sperm number but negatively correlated with total sperm size (also negatively with the flagellum and head size but not significantly with midpiece size). Sperm number and sperm size were negatively correlated suggesting a trade-off between sperm size and quality. Our results suggest that large sperm can evolve in species with relatively low sperm expenditure and probably in absence of high sperm competition between males.

Socioeconomic analysis of domestic water end-use consumption in the Federal District, Brazil

This paper explores the relationship between domestic water consumption and dwelling typology, household income and number of occupants. It describes the data and methods used to estimate domestic water consumption and related end-uses for the different household income and residential building typologies of the Federal District, Brazil. To verify the consistency of estimated water end-use data acquired at a fixture-appliance level with metered consumption at the dwelling level, covariance error models were built. The error models were also used in the regularization of the regression of water consumption over socioeconomic variables, using a generalized least-squares approach. Based on linear regression using log-transformed data, this study validates and presents an indoor and outdoor domestic water consumption model. Findings suggest that dwelling characteristics, number of residents, and household income affect both indoor and outdoor water consumption patterns and, therefore, should be considered for adequate water demand predictions, rainwater harvesting, and water reuse system design dimensioning and quantifying potential water savings for different water conservation measures.

Elevated bilirubin levels and risk of developing chronic kidney disease: a dose–response meta-analysis and systematic review of cohort studies

Previous studies have indicated the link of bilirubin levels and risk of developing chronic kidney disease (CKD); however, the findings were inconsistent. We searched for cohort studies examining bilirubin as an exposure and CKD as an outcome in the Medline, EMBASE, and Web of Science databases from inception through November 31, 2016. A generalized least-squares approach was applied to assess the dose-response relationship between them by pooling rate ratios with 95% confidence intervals. Subgroup analyses, sensitivity analysis, meta-regression, and publication bias were also conducted. Seven cohort studies with 1316 cases and 21,076 participants were identified for inclusion in the meta-analysis. The combined RR for the highest versus lowest bilirubin level was 0.36 (95% CI 0.19-0.68; P heterogeneity=0.001; Power=0.72; n=6). In the linear dose-response analysis, each 1-μmol/L increase in bilirubin was associated with a 5% reduced risk of CKD (RR=0.95; 95% CI 0.92-0.97; P for trend test=0.113; P heterogeneity=0.001; Power=0.99; n=7). The subgroup analyses and sensitivity analyses showed consistent results, and publication bias may exist. This meta-analysis suggests that elevated bilirubin level may be associated with decreased risk of developing CKD.

Normal Theory GLS Estimator for Missing Data: An Application to Item-Level Missing Data and a Comparison to Two-Stage ML.

Structural equation models (SEMs) can be estimated using a variety of methods. For complete normally distributed data, two asymptotically efficient estimation methods exist: maximum likelihood (ML) and generalized least squares (GLS). With incomplete normally distributed data, an extension of ML called “full information” ML (FIML), is often the estimation method of choice. An extension of GLS to incomplete normally distributed data has never been developed or studied. In this article we define the “full information” GLS estimator for incomplete normally distributed data (FIGLS). We also identify and study an important application of the new GLS approach. In many modeling contexts, the variables in the SEM are linear composites (e.g., sums or averages) of the raw items. For instance, SEMs often use parcels (sums of raw items) as indicators of latent factors. If data are missing at the item level, but the model is at the composite level, FIML is not possible. In this situation, FIGLS may be the only asymptotically efficient estimator available. Results of a simulation study comparing the new FIGLS estimator to the best available analytic alternative, two-stage ML, with item-level missing data are presented.

How genome size variation is linked with evolution within Chenopodium sensu lato

The significance of the wide interspecific variation in nuclear genome size of angiosperms is still not fully understood. It has been repeatedly suggested, however, that genome size can impose phenotypic constraints on plant development, phenology and ecological performance. We analysed nuclear genome size variation in diploid and polyploid species of Chenopodium s. lat. within a phylogenetic framework using flow cytometry of 456 accessions from 175 populations of 49 species: 32 diploids, 12 tetraploids, 4 hexaploids, and one decaploid. To this end, we also determined chromosome numbers and did an ITS-based phylogenetic reconstruction to analyze genome size variation using the phylogenetic generalized least-squares approach (PGLS). Results of these experiments can be summarized as follows. (1) We report the first chromosome counts for five Chenopodium species. (2) Flow cytometry determined that 2C and 1Cx DNA values differed up to 7.83- and 3.60-fold, respectively, with the lowest 1Cx value for C. schraderianum (0.412pg) [excluding tetraploid (2n=4x=32)C. ambrosioides with x=8 and 1Cx DNA content 0.279pg] and the highest for C. californicum (1.484pg). (3) Our extended phylogeny confirms the existence of previously recognized basic evolutionary lineages while underscoring the need to further increase taxon sampling for a full understanding of relationships in Chenopodioideae. (4) Our analysis of genome size evolution estimated the ancestral genome size of Chenopodium s. lat. at 0.541pg/1Cx. In addition, the data revealed a correlation between 1Cx DNA content and ploidy level. Moreover, the PGLS approach indicated that the genome size variation (i) followed the random walk model, indicating no unambiguous trend towards genome size increase or decrease; (ii) was correlated with phylogeny (λ=0.987); (iii) evolved gradually (κ=2.256); and (vi) occurred rather late after speciation, which can be attributed to species-specific adaptation (δ=3.000). (5) There are indications that several ecological traits were significantly associated with 2C DNA content. While mean plant height, maximum plant height, fruit diameter and life form were positively correlated with genome size, the species’ continent of origin showed no correlation. In summary, the strong phylogenetic signal detected in genome size of Chenopodium indicates that its genome size variation is significantly associated with phylogenetic divergence. We herein suggest a pattern of species-specific adaptations in the evolution of Chenopodium genome size.

SEM modeling with singular moment matrices Part III: GLS estimation

We discuss generalized least squares (GLS) and maximum likelihood (ML) estimation for structural equations models (SEM), when the sample moment matrices are possibly singular. This occurs in several instances, for example, for panel data when there are more panel waves than independent replications or for time series data where the number of time points is large, but only one unit is observed. In previous articles, it was shown that ML estimation of the SEM is possible by using a correct Gaussian likelihood function. In this article, the usual GLS fit function is modified so that it is also defined for singular sample moment matrices S. In large samples, GLS and ML estimation perform similarly, and the modified GLS approach is a good alternative when S becomes nearly singular. Both GLS approaches do not work for N = 1, since here S = 0 and the modified GLS approach yields biased estimates. In conclusion, ML estimation (and pseudo ML under misspecification) is recommended for all sample sizes including N = 1.

Regionalisation of the parameters of the log-Pearson 3 distribution: a case study for New South Wales, Australia

The index flood method is widely used in regional flood frequency analysis (RFFA) but explicitly relies on the identification of ‘acceptable homogeneous regions’. This paper presents an alternative RFFA method, which is particularly useful when ‘acceptably homogeneous regions’ cannot be identified. The new RFFA method is based on the region of influence (ROI) approach where a ‘local region’ can be formed to estimate statistics at the site of interest. The new method is applied here to regionalize the parameters of the log-Pearson 3 (LP3) flood probability model using Bayesian generalized least squares (GLS) regression. The ROI approach is used to reduce model error arising from the heterogeneity unaccounted for by the predictor variables in the traditional fixed-region GLS analysis. A case study was undertaken for 55 catchments located in eastern New South Wales, Australia. The selection of predictor variables was guided by minimizing model error. Using an approach similar to stepwise regression, the best model for the LP3 mean was found to use catchment area and 50-year, 12-h rainfall intensity as explanatory variables, whereas the models for the LP3 standard deviation and skewness only had a constant term for the derived ROIs. Diagnostics based on leave-one-out cross validation show that the regression model assumptions were not inconsistent with the data and, importantly, no genuine outlier sites were identified. Significantly, the ROI GLS approach produced more accurate and consistent results than a fixed-region GLS model, highlighting the superior ability of the ROI approach to deal with heterogeneity. This method is particularly applicable to regions that show a high degree of regional heterogeneity. Copyright © 2014 John Wiley & Sons, Ltd.

New results exploiting correlation in wind noise to enhance detection of transient infrasound

A previous ASA presentation introduced a signal processing method for exploiting the correlation observed in pressure fluctuations measured by infrasound sensors on small spatial-temporal scales in order to achieve enhanced signal detection and estimation performance. An algorithm based on representing the pressure field with Fourier series and finite-element bases was presented and applied to time series data in the 0.1 to 1.0 Hz band with inter-sensor spacing of 1 m using small domes as wind screens. The coherence of the data was not inspiring, but the performance was consistent with this low coherence. In this presentation new data collected using flush-to-the-earth installed sensors spaced 1 and 0.5 m apart will be presented and analyzed. In addition, application of a generalized least-squares approach to estimating the infrasound signal will be examined and compared to the previous method. Results demonstrate significant improvements over previous results at frequencies below 1.0 Hz.

Corrected portmanteau tests for VAR models with time-varying variance

The problem of test of fit for Vector AutoRegressive (VAR) processes with unconditionally heteroscedastic errors is studied. This problem is motivated by numerous examples of series presenting such a pattern. Our analysis is based on the residual autocorrelations obtained from Ordinary Least Squares (OLS), Generalized Least Squares (GLS) and Adaptive Least Squares (ALS) estimation of the autoregressive parameters. The GLS approach requires the knowledge of the variance structure while the ALS method is adapted to the unknown time-varying unconditional covariance which is estimated by kernel smoothing. It is shown that the ALS and GLS residual autocorrelations are asymptotically equivalent. It is also found that the asymptotic distribution of the OLS residual autocorrelations can be quite different from the standard chi-square asymptotic distribution obtained in a correctly specified VAR model with i.i.d. innovations. As a consequence the standard portmanteau tests which are available in routinely used software are unreliable in our framework. Using our results modified portmanteau tests based on the OLS and ALS residual autocorrelations and which take into account time varying covariance are proposed. The finite sample properties of the goodness-of-fit tests we consider are investigated by Monte Carlo experiments. The theoretical results are also illustrated using a U.S. economic data set.

The Limit of Detection in Generalized Least-Squares Calibrations: An Example Using Alprazolam Liquid Chromatography-Tandem Mass Spectrometry Data

Limit of detection (LOD) values provide useful indicators for the suitability of an analytical method for samples with low analyte levels. An LOD value can also be used to estimate the false positive probability (p(x >or= LOD)) of a result for a sample with no analyte present, as well as the false negative probability (p(x <or= 0)) for a sample analyte level at the LOD. In straight line least-squares calibrations, the LOD of a calculated concentration (LOD(x)) results from uncertainties in low-level signal (y) measurements and in the calibration intercept (a(1)) and slope (a(2)) parameters. In generalized least-squares (GLS) calibrations, uncertainties in both the concentration (x(i)) and signal (y(i)) calibration data contribute to the fit parameter uncertainties. We define LOD(X) as 3 sigma(x = 0), where the calculated standard deviation, sigma(x = 0), includes all of these uncertainty contributions. Our GLS results can be understood in terms of small nonlinear distortions of the weighted ordinary least-squares (WOLS) problem. Because these distortions lead to skewed distributions of calculated x values, we also obtain exact GLS results for the asymmetric values. Differences between WOLS and GLS approaches are smallest when calibration uncertainties in x(i) are small, as in our alprazolam example. A second example, using synthetic data from earlier GLS work, shows greater differences between sigma(x = 0) and sigma(+/-)(x). Monte Carlo calculations for this example show that GLS-derived false positive and negative probabilities can differ by factors of two or more from normal distribution predictions, even when sigma(+)(x = 0) is used in place of sigma(x = 0) in the LOD definition. From a user standpoint, spreadsheet or other computational implementations of the GLS approach are as easy to use as those for a WOLS treatment, and GLS results will be the same as WOLS results when x uncertainties are ignored. Therefore, because GLS is a more complete and correct approach, it should be used as the standard method for weighted least-squares calibrations.

Socioecological correlates of facial mobility in nonhuman anthropoids

Facial mobility, or the variety of facial movements a species can produce, is likely influenced by selection for facial expression in diurnal anthropoids. The purpose of this study is to examine socioecological correlates of facial mobility independent of body size, focusing on social group size and arboreality as possible evolutionary agents. Group size was chosen because facial expressions are important for group cohesion, while arboreality may limit the utility of facial expressions. Data for 12 nonhuman anthropoid species were taken from previous studies and analyzed using a phylogenetic generalized least-squares approach. Regression results indicate that group size is a good predictor of facial mobility independent of body size. No statistical support was found for the hypothesis that arboreality constrains the evolution of facial mobility. The correlation between facial mobility and group size may be a consequence of selection for more effective facial expression to help manage conflicts and facilitate bonding in larger groups. These findings support the hypothesis that the ultimate function of facial expression is related to group cohesion.

Effects of genomic imprinting on quantitative traits

Standard Mendelian genetic processes incorporate several symmetries, one of which is that the level of expression of a gene inherited from an organism's mother is identical to the level should that gene have been inherited paternally. For a small number of loci in a variety of taxa, this symmetry does not hold; such genes are said to be "genomically imprinted" (or simply "imprinted"). The best known examples of imprinted loci come from mammals and angiosperms, although there are also cases from several insects and some data suggesting that imprinting exists in zebra fish. Imprinting means that reciprocal heterozygotes need not be, on average, phenotypically identical. When this difference is incorporated into the standard quantitative-genetic model for two alleles at a single locus, a number of standard expressions are altered in fundamental ways. Most importantly, in contrast to the case with euMendelian expression, the additive and dominance deviations are correlated. It would clearly be of interest to be able to separate imprinting effects from maternal genetic effects, but when the latter are added to the model, the well-known generalized least-squares approach to deriving breeding values cannot be applied. Distinguishing these two types of parent-of-origin effects is not a simple problem and requires further research.

Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes

A moving-horizon state estimation problem is addressed for a class of nonlinear discrete-time systems with bounded noises acting on the system and measurement equations. As the statistics of such disturbances and of the initial state are assumed to be unknown, we use a generalized least-squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding-window strategy. For the resulting estimator, the existence of bounding sequences on the estimation error is proved. In the absence of noises, exponential convergence to zero is obtained. Moreover, suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value. The approximate solution can be determined either on-line by directly minimizing the cost function or off-line by using a nonlinear parameterized function. Simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended Kalman filter.

Weight‐matrix structured regularization provides optimal generalized least‐squares estimate in diffuse optical tomography

Diffuse optical tomography (DOT) involves estimation of tissue optical properties using noninvasive boundary measurements. The image reconstruction procedure is a nonlinear, ill-posed, and ill-determined problem, so overcoming these difficulties requires regularization of the solution. While the methods developed for solving the DOT image reconstruction procedure have a long history, there is less direct evidence on the optimal regularization methods, or exploring a common theoretical framework for techniques which uses least-squares (LS) minimization. A generalized least-squares (GLS) method is discussed here, which takes into account the variances and covariances among the individual data points and optical properties in the image into a structured weight matrix. It is shown that most of the least-squares techniques applied in DOT can be considered as special cases of this more generalized LS approach. The performance of three minimization techniques using the same implementation scheme is compared using test problems with increasing noise level and increasing complexity within the imaging field. Techniques that use spatial-prior information as constraints can be also incorporated into the GLS formalism. It is also illustrated that inclusion of spatial priors reduces the image error by at least a factor of 2. The improvement of GLS minimization is even more apparent when the noise level in the data is high (as high as 10%), indicating that the benefits of this approach are important for reconstruction of data in a routine setting where the data variance can be known based upon the signal to noise properties of the instruments.

Characterizing Clutter in the Context of Detecting Weak Gaseous Plumes in Hyperspectral Imagery

Weak gaseous plume detection in hyperspectral imagery requires thatbackground clutter consisting of a mixture of components such as water, grass, and asphaltbe well characterized. The appropriate characterization depends on analysis goals.Although we almost never see clutter as a single-component multivariate Gaussian(SCMG), alternatives such as various mixture distributions that have been proposed mightnot be necessary for modeling clutter in the context of plume detection when the chemicaltargets that could be present are known at least approximately. Our goal is to show to whatextent the generalized least squares (GLS) approach applied to real data to look for evidenceof known chemical targets leads to chemical concentration estimates and to chemicalprobability estimates (arising from repeated application of the GLS approach) that aresimilar to corresponding estimates arising from simulated SCMG data. In some cases,approximations to decision thresholds or confidence estimates based on assuming the clutterhas a SCMG distribution will not be sufficiently accurate. Therefore, we also describe astrategy that uses a scene-specific reference distribution to estimate decision thresholds forplume detection and associated confidence measures.

Carrier phase component removal: a generalized least-squares approach: errata

Carrier phase component removal: a generalized least-squares approach: errata

Carrier phase component removal: a generalized least-squares approach

In fringe projection profilometry, an object shape is evaluated through phase distribution extracted from a projected fringe pattern. For parallel illumination geometry, the carrier phase component introduced by the fringes is spatially linear, whereas nonparallel illumination would lead to a nonlinear carrier. In this study, a general approach for the removal of a nonlinear-carrier phase component is proposed. A series expansion technique is used to approximate the carrier phase function, and a least-squares method is developed to estimate the unknown coefficients of the series. The theoretical analysis is given on the basis of a divergent illumination geometry with carrier fringes in the x direction. The method is also extended to include a curved surface-fitting approach, which is applicable to various measurement system geometries.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi‐analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at‐site estimator.