Variance-covariance Matrix Research Articles

Elevating performance in BDS-3 Precise Point Positioning Ambiguity Resolution through LEO augmented constellations

With the help of constellations combined BDS-3 (BeiDou Navigation Satellite System) and LEO (Low Earth Orbit), we aim to improve the performances of PPP (Precise Point Positioning) and PPP Ambiguity Resolution (PPP-AR). First, LEO constellations with 66, 96, 156, 192, 270, and 288 satellites are designed to establish six LEO augmented constellations. Based on four challenge scenarios, PPP of six LEO augmented constellations are performed. Even in the strip-shaped obstruction area losing more than 60% of observations, the positioning accuracies of static PPP are improved by (1.0%, 5.7%, 0.2%) for BDS+66LEO, and (14.9%, 33.7%, 7.5%) for BDS+288LEO in the east, north, and up components. The positioning accuracy and convergence time improve quickly as the number of LEO satellites increased from 66 to 156, and slowdown from 192 to 288. Two constellations, BDS+156LEO and BDS+192LEO, are considered to strike the balance of acceptable PPP performance and constellation load. Then, the performance of PPP-AR is realized with the estimated UPD (Uncalibrated Phase Delay). The correlations among geodetic parameters and ambiguities deriving from the post-fit variance–covariance matrix are analyzed to illustrate the enhancement of LEO augmented constellations. Under the condition of 20°elevation angle occlusion with azimuth ranging from 0 to 360°, BDS+156LEO can achieve an ambiguity fix rate of up to 98.37% with a faster mean TTFF (Time To First Fix) of 12.76 min, and the positioning accuracies in the east, north, and up components are improved by 28.2%, 21.4%, and 15.1% respectively, compared with BDS-3. BDS+192LEO realized an 98.42% ambiguity fixing rate, and improved BDS-3 by 31.4%, 26.7% and 11.5% with its TTFF been 12.25 min.

Entropy associated with conformational and solvent-density fluctuations in biomolecular solutions

Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned with the conformational fluctuation of a biomolecule, and the other with the density fluctuation of solvent around a solute. The formula derived for the entropy associated with the conformational fluctuation is Sconf=12kBlog2π3NA+3N2kBwhere N is the number of atoms in the solute, and A is the determinant of the inverse of the variance–covariance matrix of conformational fluctuation.The formula for the entropy of solvent at a pair of positions around a solute is also derived to be, ssolv(r,r′)=12kBlog2πnB+3n2kBwhere n is the number of atoms in a solvent molecule, and B is essentially the determinant of the matrix of the density-pair-correlation functions. The entropy at a local position r may be obtained by integrating the expression by r′ over the entire volume of the system.The feasibility of the calculation to find the entropies is discussed.

A structural after measurement approach to structural equation modeling.

In structural equation modeling (SEM), the measurement and structural parts of the model are usually estimated simultaneously. In this article, we revisit the long-standing idea that we should first estimate the measurement part, and then estimate the structural part. We call this the "structural-after-measurement" (SAM) approach to SEM. We describe a formal framework for the SAM approach under settings where the latent variables and their indicators are continuous. We review earlier SAM methods and establish how they are specific instances of the SAM framework. Decoupled estimation for the measurement and structural parts using SAM possesses three key advantages over simultaneous estimation in standard SEM. First, estimates are more robust against local model misspecifications. Second, estimation routines are less vulnerable to convergence issues in small samples. Third, estimates exhibit smaller finite sample biases under correctly specified models. We propose two variants of the SAM approach. "Local" SAM expresses the mean vector and variance-covariance matrix of the latent variables as a function of the observed summary statistics and the parameters of the measurement model. "Global" SAM holds the parameters of the measurement part fixed while estimating the parameters of the structural part. Our framework includes two-step corrected standard errors, and permits computing both local and global fit measures. Nonetheless, the SAM approach is an estimation strategy, and should not be regarded as a model-building tool. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A Nonlinear Quantile Regression for Accelerated Destructive Degradation Testing Data

Traditional regression approaches to accelerated destructive degradation test (ADDT) data have modeled the mean curve as representative. However, maximum likelihood estimates (MLEs) of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear quantile regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization (GEM) framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the τ th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

Negative variance components and intercept-slope correlations greater than one in magnitude: How do such "non-regular" random intercept and slope models arise, and what should be done when they do?

Statistical models with random intercepts and slopes (RIAS models) are commonly used to analyze longitudinal data. Fitting such models sometimes results in negative estimates of variance components or estimates on parameter space boundaries. This can be an unlucky chance occurrence, but can also occur because certain marginal distributions are mathematically identical to those from RIAS models with negative intercept and/or slope variance components and/or intercept-slope correlations greater than one in magnitude. We term such parameters "pseudo-variances" and "pseudo-correlations," and the models "non-regular." We use eigenvalue theory to explore how and when such non-regular RIAS models arise, showing: (i) A small number of measurements, short follow-up, and large residual variance increase the parameter space for which data (with a positive semidefinite marginal variance-covariance matrix) are compatible with non-regular RIAS models. (ii) Non-regular RIAS models can arise from model misspecification, when non-linearity in fixed effects is ignored or when random effects are omitted. (iii) A non-regular RIAS model can sometimes be interpreted as a regular linear mixed model with one or more additional random effects, which may not be identifiable from the data. (iv) Particular parameterizations of non-regular RIAS models have no generality for all possible numbers of measurements over time. Because of this lack of generality, we conclude that non-regular RIAS models can only be regarded as plausible data-generating mechanisms in some situations. Nevertheless, fitting a non-regular RIAS model can be acceptable, allowing unbiased inference on fixed effects where commonly recommended alternatives such as dropping the random slope result in bias.

A cautionary tale on the effects of different covariance structures in linear mixed effects modeling of fMRI data.

With the steadily increasing abundance of longitudinal neuroimaging studies with large sample sizes and multiple repeated measures, questions arise regarding the appropriate modeling of variance and covariance. The current study examined the influence of standard classes of variance-covariance structures in linear mixed effects (LME) modeling of fMRI data from patients with pediatric mild traumatic brain injury (pmTBI; N = 181) and healthy controls (N = 162). During two visits, participants performed a cognitive control fMRI paradigm that compared congruent and incongruent stimuli. The hemodynamic response function was parsed into peak and late peak phases. Data were analyzed with a 4-way (GROUP×VISIT×CONGRUENCY×PHASE) LME using AFNI's 3dLME and compound symmetry (CS), autoregressive process of order 1 (AR1), and unstructured (UN) variance-covariance matrices. Voxel-wise results dramatically varied both within the cognitive control network (UN>CS for CONGRUENCY effect) and broader brain regions (CS>UN for GROUP:VISIT) depending on the variance-covariance matrix that was selected. Additional testing indicated that both model fit and estimated standard error were superior for the UN matrix, likely as a result of the modeling of individual terms. In summary, current findings suggest that the interpretation of results from complex designs is highly dependent on the selection of the variance-covariance structure using LME modeling.

Life Function Analysis of a Two-Parameter Exponential Distribution Using Robust Rank Regression

In this research, a proposed method is presented to estimate the life function of the two-parameter exponential distribution by using the robust rank regression on the dependent variable, which depends on the robust variance-covariance matrix (the FMCD and OGK method) and the robust mean vector through which the rank regression coefficients are estimated using the method of ordinary least squares and employing it in estimating the scale and location parameters of the exponential distribution and thus analyzing the life function on its basis. A comparison was also made between the proposed method and the classical method of rank regression on the dependent variable of life data at different sample sizes (from 10 to 25) to show the efficiency of the proposed method based on the mean square error of the estimated parameters, through a program prepared by the researcher in MATLAB language dedicated to this purpose. The practical application results concluded that the proposed robust method of rank regression on the dependent variable in estimating the parameters of the exponential distribution was more efficient than the classical method. Paper type: Research paper.

Intrinsic Information-Theoretic Models.

With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions N (μ, σ0), as before, but with a constant σ0 not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution Nm(μ,Σ0) with a constant variance-covariance matrix Σ0 not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger's equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of σ0, altogether leading to the concept of "intrinsic". Similarly, as in our previous work with the estimator's variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the "intrinsic" Cramér-Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes' theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of "intrinsic" information-theoretic models, which are essential for developing physics.

Equity markets and ESG dynamics: Assessing spillovers and portfolio strategies through time-varying parameters

Motivated by the recent surge of socially responsible activism, we examine the return and volatility transmission between the global Environmental, Governance, and Social index and traditional equity markets of G7 countries. For this purpose, we employ the TVP-VAR model on the returns and volatilities from 04 April 2011 to 09 September 2023. The variance co-variance matrix of the TVP-VAR model is used for portfolio analysis. Our finding indicates a significant level of connectedness between green and traditional equity markets. Moreover, green equity functions as a transmitter of both return and volatility spillovers to the traditional equity markets. In addition, our analysis of dynamic connectedness reflects a spike in both total return and volatility spillover amid the COVID-19 period. This indicates that the relationship between green and traditional equity markets intensifies during times of market stress and uncertainty which further infer implications for portfolio diversification. Furthermore, we calculated optimal asset allocation within portfolios and identified effective hedging ratios for different ESG and G7 equity pairs. The implications of the study include informing portfolio diversification strategies, and guiding decision-making for policymakers, hedge fund managers, and portfolio professionals amidst market uncertainties, based on identified market dynamics and connectedness.

Estimating time-varying factors’ variance in the string-term structure model with stochastic volatility

This paper presents a novel term structure of interest rate (TSIR) model with stochastic volatility and jumps (SVJ) that combines the market framework proposed by Brace et al. (1997) with the string-shock framework of Santa-Clara and Sornette (2001). In this model, the factors’ variance is estimated through the eigendecomposition of a variance–covariance matrix obtained with a measure of market volatility derived from out-of-the-money option prices and historical correlations of interest rates traded in the futures market. The stochastic evolution of the factors’ variance is governed by the 4/2 model developed by Grasselli (2017), including jumps. A novel method is employed to estimate the parameters of the SVJ model that minimizes the distance between the sample moments and the moments of a gamma distribution. The empirical application of the model in the Brazilian derivatives market demonstrates its effectiveness in accurately capturing the volatility smile of interest rate options.

BLUP Estimation and Genotype Stability in Arachis hypogaea L. Variety Testing using Mixed Model Equations

Background: One of the major goals of plant breeding is the selection of high yielding superior cultivars having wide or specific adaptation. However, there is a fluctuation in the annual production due to the sensitive behaviour of the genotypes under different environmental conditions referred to as Genotype by Environment Interaction (GEI). The current study aimed to study the contribution of GEI for the adaptation of groundnut lines for spring and/or kharif season. Methods: To assess the contribution of GEI, Multi-Environment Trials (METs) were conducted for 40 confectionery purpose groundnut genotypes at F9 generation along with checks, across three locations for two seasons (spring and kharif). The contribution of environmental effects, genotypic values and genotype × environment interaction values were obtained from genotypic variance-covariance matrix Gi = Σg⨂A using mixed models (MM) in Best linear unbiased predictions (BLUPs).The pooled data was first partitioned into fixed effects of sites across the seasons and BLUP genotypic values (Ggge). The BLUP genotypic values are further partitioned into genetic value (Gg) and their interaction with the environment (Gge) for the adaptability of genotypes across seasons. Result: The results of MET revealed the presence of significant crossover interaction. The demarcation of advance breeding lines for adaptability across the environment as well as for season specific adaptation was done for variety testing. Genotypes having moderate to high Gge values along with high Gg values in spring than kharif, owing to their better performance during the spring season. CGL-11, CGL-23 and CGL-04 were the highest yielding genotypes, with quite high Gge values. This is due to the more favourable environmental conditions interacting positively with genotypes during the spring. Thus, the high Gg value(s) of genotype(s) alone is not a capable factor for commercialization as Gge value is the deciding factor for the adaptability for the targeted season.

Accounting for residual errors in atmosphere–ocean background models applied in satellite gravimetry

The Atmosphere and Ocean non-tidal De-aliasing Level-1B (AOD1B) product is widely used in precise orbit determination and satellite gravimetry to correct for transient effects of atmosphere–ocean mass variability that would otherwise alias into monthly mean global gravity fields. The most recent release is based on the global ERA5 reanalysis and ECMWF operational data together with simulations from the general ocean circulation model MPIOM consistently forced with fields from the corresponding atmospheric dataset. As background models are inevitably imperfect, residual errors will consequently propagate into the resulting geodetic products. Accounting for uncertainties of the background model data in a statistical sense, however, has been shown before to be a useful approach to mitigate the impact of residual errors leading to temporal aliasing artefacts. In light of the changes made in the new release RL07 of AOD1B, previous uncertainty assessments are deemed too pessimistic and thus need to be revisited. We here present an analysis of the residual errors in AOD1B RL07 based on ensemble statistics derived from different atmospheric reanalyses, including ERA5, MERRA2 and JRA55. For the oceans, we investigate the impact of both the forced and intrinsic variability through differences in MPIOM simulation experiments. The atmospheric and oceanic information is then combined to produce a new time-series of true errors, called AOe07, which is applicable in combination with AOD1B RL07. AOe07 is further complemented by a new spatial error variance–covariance matrix. Results from gravity field recovery simulation experiments for the planned Mass-Change and Geosciences International Constellation (MAGIC) based on GFZ’s EPOS software demonstrate improvements that can be expected from rigorously implementing the newly available stochastic information from AOD1B RL07 into the gravity field estimation process.

The Vuong-Lo-Mendell-Rubin test for latent class and latent profile analysis: A note on the different implementations in Mplus and LatentGOLD

Mplus and LatentGOLD implement the Vuong-Lo-Mendell-Rubin test (comparing models with K and K + 1 latent classes) in slightly differ manners. While LatentGOLD uses the formulae from Vuong (1989; https://doi.org/10.2307/1912557), Mplus replaces the standard parameter variance-covariance matrix by its robust version. Our small simulation study showed why such a seemingly small difference may sometimes yield rather different results. The main finding is that the Mplus approximation of the distribution of the likelihood-ratio statistic is much more data dependent than the LatentGOLD one. This data dependency is stronger when the true model serves as the null hypothesis (H0) with K classes than when it serves as the alternative hypothesis (H1) with K + 1 classes, and it is also stronger for low class separation than for high class separation. Another important finding is that neither of the two implementations yield uniformly distributed p-values under the correct null hypothesis, indicating this test is not the best model selection tool in mixture modeling.

Approximated Uncertainty Propagation of Correlated Independent Variables Using the Ordinary Least Squares Estimator.

For chemical measurements, calibration is typically conducted by regression analysis. In many cases, generalized approaches are required to account for a complex-structured variance-covariance matrix of (in)dependent variables. However, in the particular case of highly correlated independent variables, the ordinary least squares (OLS) method can play a rational role with an approximated propagation of uncertainties of the correlated independent variables into that of a calibrated value for a particular case in which standard deviation of fit residuals are close to the uncertainties along the ordinate of calibration data. This proposed method aids in bypassing an iterative solver for the minimization of the implicit form of the squared residuals. This further allows us to derive the explicit expression of budgeted uncertainties corresponding to a regression uncertainty, the measurement uncertainty of the calibration target, and correlated independent variables. Explicit analytical expressions for the calibrated value and associated uncertainties are given for straight-line and second-order polynomial fit models for the highly correlated independent variables.

Forward starting options pricing under a regime-switching jump-diffusion model with Wishart stochastic volatility and stochastic interest rate

Vanilla options become effective immediately after they are entered, while some exotic options will only come to effective some time after they are bought or sold. Forward starting options are one kind of such exotic options started actually at some pre-specified future date. This paper presents an extension of regime-switching jump diffusion model, in which the parameters are driven by a continuous time and stationary Markov chain on a finite state space, by introducing the Wishart process into the instantaneous variance-covariance matrix of the risky asset price and stochastic interest rate. We derive the discounted conditional joint characteristic function and the forward characteristic function of the log-asset price and its the instantaneous variance-covariance process, and thereby the price of forward starting options are well evaluated by the probabilistic approach combined with the Fourier-cosine (COS) method. We also provide efficient Monte Carlo simulation of this proposed model, and simulated solutions to forward starting options pricing within a two-state regime switching framework. Numerical results show that the COS method is accurate and efficient for pricing forward starting options. Finally, we analyse impacts of some main parameters (especially, parameters in the Wishart stochastic volatility) in this proposed model on option prices and Δ values. Also, we consider the forward implied volatility. Furthermore, the forward starting options under the regime-switching jump diffusion model with Wishart stochastic volatility and stochastic interest rate which we derived are more generalized than those recently appeared in the derivatives pricing literature, and thus have wider application.

Pairwise fitting of piecewise mixed models for the joint modeling of multivariate longitudinal outcomes, in a randomized crossover trial.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi etal. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modelingframework.

An alternative multivariate exponential power distribution

In the existing multivariate Exponential Power Distribution (EPD), the shape parameter has the tendency to affect the variability in the data leading to distorted features of the distribution. This study resolves this problem by obtaining a generalized expression in place of the constant coefficient (0.5) of the quadratic form of the multivariate EPD as a function of the shape parameter, such that the variance-covariance matrix of the data is exactly equal to the scale parameter. The density function thus obtained is a more generalized multivariate EPD that provides flexibility in depicting the true underlying characteristics of the distribution for all sample sizes.

Анализ свойств региональных геодезических ГНСС-сетей, построенных относительным методом. Общий случай

In this paper, we continue to study the geodetic stations adjusted coordinates’ statistical properties in permanently operated networks. Analytical reconstructing the variance-covariance matrix of a real vector solution obtained from processing a redundant set of the same GNSS observation session’s measured vectors is performed. The mentioned matrix is compared with the same one, of the vector solution, resulted on the measured lines’ total set basis. Common properties of both arrays are revealed, as well as discrepancies in features for different types of solutions. As a suitable tool for studying the latter, the corresponding absolute way is offered

Scalable phylogenetic Gaussian process models improve the detectability of environmental signals on local extinctions for many Red List species

Abstract Conservation biologists have a daunting task of understanding the causes of species decline associated with anthropogenic factors and predicting the extinction risk of a growing number of endangered species. By reducing variances of estimates with information on closely related species, phylogenetic information among species can bridge gaps in information on species with small range sizes when modelling large numbers of endangered species. However, modelling many species with the Gaussian process (GP), which underlies the evolutionary process of phylogenetic random effects, remains a challenge owing to the computational burden in estimating the large variance–covariance matrix. Here, we applied a phylogenetic generalised mixed model with random slopes and random intercepts to 1010 endangered vascular plant taxa in Japan following phylogenetic GPs implemented by nearest neighbour GP (NNGP) approximation. NNGP enables flexibility in changing the proximity on the phylogenetic tree of species from which information is borrowed to reduce the variances of estimates with a realistic computational burden. We evaluated the effectiveness of phylogenetic models by comparing the predictive performance and descriptive power of phylogenetic and non‐phylogenetic models and identified the anthropogenic factors contributing to the decline of each of the studied endangered species. We found that the model with phylogenetic information had better prediction performance than the model without phylogenetic information. The results showed that across all explanatory variables, the phylogenetic model could detect interspecific differences in response to environmental factors in a number of species more clearly. Combined with the phylogenetic signal results, we could also detect a phylogenetic bias in the species that could benefit from the positive effects of protected areas but reduce the local extinctions of 95% of all studied taxa. In conclusion, our model, considering phylogenetic information with NNGP, allows the elucidation of factors causing the decline of many endangered species. In future analyses, the estimation of extinction probability linked to environmental change might be applied to future climate–land use scenarios, advancing the comprehensive assessment of biodiversity degradation and threats to species at multiple scales.

Interval State Estimation of Electricity-Gas Systems Considering Measurement Correlations

The popularization of electricity-gas systems leads to increasing demand for state management of systems. However, the existence of neglected measurement correlations brings uncertainties to the electricity-gas systems state estimation. In this paper, an interval state estimation method that considers measurement correlations existing in the electricity-gas systems is presented. We derive the linear measurement model for the electricity-gas systems through Taylor series expansion and estimate the measurement variance-covariance matrix with measurement correlations. The system parameter matrix and the measurement variance-covariance matrix containing measurement correlations are combined into an interval, and the interval state matrix considering measurement correlations is constructed. Then, the linear equations for the state estimation interval considering measurement correlations are established based on the measurement containing correlations and interval state matrix; as a result, the electricity-gas system state estimation model containing measurement correlations is established. In addition, a method for determining the range of state estimation intervals is proposed. Numerical tests on an integrated electricity-gas system comprising a 10-node natural gas network and IEEE 30-bus system indicate that the proposed approach has more advantages over the UT+KO approach in computation accuracy and computation efficiency.