Model Error Variance Research Articles

Note on the radical inflation in the estimates of error variance in measurement models

This note discusses the radical technical inflation in error variance and the related standard error of test scores from both conceptual and empirical viewpoints. This technical inflation arises as a direct consequence of the technical underestimation of item-score correlation by the product–moment coefficient of correlation (PMC), which is embedded in the traditional estimators of reliability such as coefficients alpha, theta, omega, or rho (maximal reliability). Specifically, in educational settings where compilations usually include both easy and difficult items, the estimate by PMC may substantially deviate from the true association between an item and the score. Consequently, the use of traditional estimators of reliability leads to technically inflated estimates of standard errors, as the error variance related to these traditional measurement models is significantly inflated, resulting in deflated reliability estimates. In educational testing, employing deflation-corrected standard errors, calculated using deflation-corrected reliability estimators, would provide a more accurate measure of the test score’s true precision.

How Important are Commodity Terms of Trade Shocks in Explaining Government Tax Revenue Fluctuations? Evidence from Ethiopia

Using a new database of commodity terms of trade and identifying country-specific commodity export and import price shocks separately, this article mainly aims to examine the importance of commodity export and import price shocks in explaining government tax revenue fluctuations using Ethiopia as an example over the sample period 1980–2019. This article employs a structural vector autoregressive model and forecast error variance decomposition analysis to address this objective. The results show that commodity export and import price shocks account for around 48% of government tax revenue fluctuations. While commodity export price shocks contribute to around 37% of fluctuations in government tax revenue, commodity import price shocks account for only 11% of government tax revenue fluctuations. These findings are discussed in terms of their policy implications. JEL Classification C32, F41, F44

Stage IV breast, colorectal, and lung cancer at diagnosis in adults living with intellectual or developmental disabilities: Apopulation-based cross-sectional study.

Cancer is a leading cause of death among people living with intellectual or developmental disabilities (IDD). Although studies have documented lower cancer screening rates, there is limited epidemiological evidence quantifying potential diagnostic delays. This study explores the risk of metastatic cancer stage for people with IDD compared to those without IDD among breast (female), colorectal, and lung cancer patients in Canada. Separate population-based cross-sectional studies were conducted in Ontario and Manitoba by linking routinely collected data. Breast (female), colorectal, and lung cancer patients were included (Manitoba: 2004-2017; Ontario: 2007-2019). IDD status was identified using established administrative algorithms. Modified Poisson regression with robust error variance models estimated associations between IDD status and the likelihood of being diagnosed with metastatic cancer. Adjusted relative risks were pooled between provinces using random-effects meta-analyses. Potential effect modification was considered. The final cohorts included 115,456, 89,815, and 101,811 breast (female), colorectal, and lung cancer patients, respectively. Breast (female) and colorectal cancer patients with IDD were 1.60 and 1.44 times more likely to have metastatic cancer (stage IV) at diagnosis compared to those without IDD (relative risk [RR], 1.60; 95% confidence interval [CI], 1.16-2.20; RR, 1.44; 95% CI, 1.24-1.67). This increased risk was not observed in lung cancer. Significant effect modification was not observed. People with IDD were more likely to have stage IV breast and colorectal cancer identified at diagnosis compared to those without IDD. Identifying factors and processes contributing to stage disparities such as lower screening rates and developing strategies to address diagnostic delays is critical.

Scale‐Dependent Ocean Vertical Correlations in the California Current System

AbstractWe present observation and model estimates of temperature and salinity depth‐depth cross‐correlations in two different horizontal scale regimes. Glider data from the 2021 S‐MODE pilot campaign were assimilated into an ocean simulation using a three dimensional variational algorithm. We map the glider time series into distance allowing a Fourier analysis of model errors in wavenumber space. Power spectra indicate model error variance is less than the observed variance at scales larger than approximately 250 km. Based on this result, a Gaussian filter partitions the glider and model data into larger and smaller scale series at each depth. The larger and smaller scale temperature and salinity cross‐correlations between depths are compared and contrasted. Glider and model cross‐correlations are found to be similar, implying that the model physics at scales not constrained by the observations are similar to the true world.

State of Charge Estimation of Lithium-Ion Battery Using Robust Kernel Fuzzy Model and Multi-Innovation UKF Algorithm Under Noise

Accurate and robust state of charge (SOC) estimation of lithium-ion batteries is very important to prolong battery life and prevent catastrophic failures. However, the accuracy of SOC estimation is seriously affected by unknown noise, uncertain interference and temperature. In this article, a novel model fusion method is presented to achieve precise SOC estimation in the case of non-Gaussian noise and outliers. A state-space model of battery system is first developed to conduct SOC estimate. Then, a novel robust kernel Takagi–Sugeno fuzzy method to minimize the mean and variance of model error is developed to characterize the electrical performance of battery. This modeling strategy uses local nonlinear modeling mechanism, which the nonlinear relationship between data can be well represented, thus it can obtain a superior modeling performance. Finally, a multi-innovation unscented Kalman filter (UKF) algorithm considering the historical state information is designed to incorporate with the robust fuzzy model to filter out the noise in the observation and update the SOC estimation. Additional stability analysis shows the convergence of the proposed multi-innovation UKF algorithm. Experiments and verifications show that the presented estimation architecture is effective and has better modeling ability compared with several common methods.

Equal Precision Measurement Structural Models

Error variance in structural models is often specified as a conditional variance associated with a manifest variable or as a regression path from a standardized error variance. This paper describes scenarios in which specification of both terms is useful: (1) Corrections for attenuation in single indicator factor models; (2) Tests of the equality in the proportion of explained variance across multiple dependent variables in regression models; (3) Factor models with two indicators; and (4) Tests of invariance in the proportion of measurement error variance across occasions in growth curve models. Examples of such models using both simulated and real-world data are presented.

Estimation of Cs-137 emissions during wildfires and dust storm in Chernobyl Exclusion Zone in April 2020 using ensemble iterative source inversion method

The emission inventories of cesium-137 resulting from the wildfires in the Chernobyl Exclusion Zone (3–24 April 2020) and from the dust storm (16–17 April 2020), which resuspended contaminated ash, were estimated using inverse modeling. The goal of this work was to take into account uncertainties of inexactly known source term and meteorological input data for evaluation of emission inventories and their confidence limits, by developing Ensemble Iterative Source Inversion Method (EISIM). A set of source receptor matrices (SRMs) was calculated using FLEXPART atmospheric transport code with varying source term parameters (size distribution of emitted particles, height distribution of emissions) and meteorological input data. The covariance matrix of model errors was estimated by ensemble averaging of model results obtained after multiplication of the pre-calculated SRMs by the estimated emission inventories at the current iteration step. The emission inventories at each iteration step were evaluated for each of the ensemble members by solving the conventional variational source inversion problem. With iterations, the variance of model error was reduced by an order of magnitude. The estimated total emission of 137Cs from wildfires was 448 GBq, close to the first guess estimation. By using emission inventories within the obtained confidence limits (from 39 to 1530 GBq), different combinations of source term parameters and input meteorological data, FLEXPART could fit observations with a correlation coefficient of more than 0.6 and a normalized mean squared error of less than 10. The obtained estimate of the total emission resulting from the wind resuspension during the dust storm was 27 GBq. The respective estimated confidence interval was from 3 to 93 GBq. By analyzing model error statistics, some of the source term parameters could be reliably evaluated. The fraction of the fine particles (0.25 μm) in total emissions Wsf(0.25)≈0.1 and the fraction of emission below a bottom height of convective plume Wh(1)≈0.5.

An Empirical Analysis of the Relationship Between Capital, Market Risks, and Liquidity Shocks in the Banking Industry

Abstract This study explores the relation between capital, market risks and banks’ liquidity conditions. In estimating the SVAR regression model, Granger causality, impulse-response functions and forecast error variance decomposition were employed and used for estimation of the results. The data sample comprised of commercial banks over the 2009 to 2018 period. The empirical results showed that liquidity shocks are caused by a combination of structural shocks. The Granger causality, impulse-response functions and forecast error variance decomposition documented that sensitivity to market risk is the key factor affecting liquidity conditions in the banking sector in the long run. In addition, the empirical results showed that capital adequacy has minimal impact on liquidity conditions in the short run. The reforming rate to sensitivity to market risk policies, capital adequacy policies and liquidity policy measures can be valuable policy tools to minimize liquidity shortages and avoid insolvent banks.

Racial variations of adverse perinatal outcomes: A population-based retrospective cohort study in Ontario, Canada.

IntroductionRacial differences in adverse maternal and birth outcomes have been studied in other countries, however, there are few studies specific to the Canadian population. In this study, we sought to examine the inequities in adverse perinatal outcomes between Black and White pregnant people in Ontario, Canada.MethodsWe conducted a population-based retrospective cohort study that included all Black and White pregnant people who attended prenatal screening and had a singleton birth in any Ontario hospital (April 1st, 2012-March 31st, 2019). Poisson regression with robust error variance models were used to estimate the adjusted relative risks of adverse perinatal outcomes for Black people compared with White people while adjusting for covariates.ResultsAmong 412,120 eligible pregnant people, 10.1% were Black people and 89.9% were White people. Black people were at an increased risk of gestational diabetes mellitus, preeclampsia, placental abruption, preterm birth (<37, <34, <32 weeks), spontaneous preterm birth, all caesarean sections, emergency caesarean section, low birth weight (<2500g, <1500g), small-for-gestational-age (<10th percentile, <3rd percentile) neonates, 5-minute Apgar score <4 and <7, neonatal intensive care unit admission, and hyperbilirubinemia requiring treatment but had lower risks of elective caesarean section, assisted vaginal delivery, episiotomy, 3rd and 4th degree perineal tears, macrosomia, large-for-gestational-age neonates, and arterial cord pH≤7.1, as compared with White people. No difference in risks of gestational hypertension and placenta previa were observed between Black and White people.ConclusionThere are differences in several adverse perinatal outcomes between Black and White people within the Ontario health care system. Findings might have potential clinical and health policy implications, although more studies are needed to further understand the mechanisms.

Bayesian jackknife empirical likelihood for the error variance in linear regression models

Variance estimation is fundamental in the statistical inference. Due to the nonlinearity of the variance estimator, Lin et al. [Jackknife empirical likelihood for the error variance in linear models. J Nonparametr Stat. 2017;29:151–166.] proposed the jackknife empirical likelihood method for the error variance in a linear regression model. However, people may have some prior information about the error variance. In this article, we propose the Bayesian jackknife empirical likelihood (BJEL) for the error variance in a linear regression model. The validity of the proposed method is verified, and the asymptotic normal properties for the BJEL are also established. A simulation study shows that the new approach for the small sample performs better than its frequentist counterpart. Two real data sets are also used to illustrate the proposed methods.

Nonlinear model updating through a hierarchical Bayesian modeling framework

A new time-domain probabilistic technique based on hierarchical Bayesian modeling (HBM) framework is proposed for calibration and uncertainty quantification of hysteretic type nonlinearities of dynamical systems. Specifically, probabilistic hyper models are introduced respectively for material hysteretic model parameters as well as prediction error variance parameters, aiming to consider both the uncertainty of the model parameters as well as the prediction error uncertainty due to unmodeled dynamics. A new asymptotic approximation is developed to simplify the process of nonlinear model updating and substantially reduce the computational burden of the HBM framework. This asymptotic approximation is further employed to provide insightful expressions on the hyper parameters for both the model and prediction error variance parameters. Given a large number of data points within a dataset, the hyper model parameters are formulated to be independent of the hyper parameters for prediction error variance parameter. Two numerical examples are conducted to verify the accuracy and performance of the proposed method considering Bouc–Wen (BW) hysteretic type nonlinearities. Model error is manifested as uncertainty due to variability in the measured data from multiple datasets. Results from a five-story numerical structure indicate that the model error is the main source of error that can affect the uncertainty in the model parameters due to the variability in the experimental data. It is also demonstrated that the parameter uncertainty due to the variability arising from model error depends on the sensor locations. It is shown that the proposed approach is robust for not only quantifying uncertainties of structural parameters and prediction error parameters, but also predicting the system quantities of interests (QoI) with reasonable accuracy and providing reliable uncertainty bounds, as opposed to the conventional Bayesian approach which often severely underestimates the uncertainty bounds.

Using rheological monitoring to determine the gelation kinetics of chitosan-based systems.

The modeling of polymeric reactions is a topic of large interest. The gelation reactions that may result from self-crosslinking or hybrid (agent based-) crosslinking are examples with interest specially in biomaterials applications. The composition of polymer entities during the reaction is hard to follow, and their concentration is not a good measure of the system dynamics. One alternative is monitoring the rheological behavior of the reacting mass, and relate the elastic modulus of the mixture with the rheological degree of conversion. In this paper we use rheological data to fit Malkin and Kulichikin (1996) [1] based models to describe the crosslinking of chitosan. First, the self-crosslinking of chitosan is considered. Then, the agent-based crosslinking reaction promoted by genipin is addressed. We use dynamical rheological data to fit the reaction models. The model fitting problem generated using Maximum Likelihood principle with heteroscedastic prediction error variance is formulated as a Dynamic Optimization problem and subsequently solved with a sequential approach. Parametric confidence regions are computed using the linear approximation of the covariance matrix at the optimum. Further, the parameters correlation matrix is also determined and used to qualitatively infer about the practical identifiability. The reaction order obtained for self-crosslinking kinetics is 1.3375 ± (0.0151) - approximately of first order -, and is 2.2402 ± (0.0373) for hybrid crosslinking (approximately of second order). In both cases we prove the error variance model is heteroskedastic and the model is identifiable. The approach proposed herein can be extended to other polymer systems.

What should the optimal financial structure of FDI inflows to Poland be for stimulating growth processes?

The article aims to answer a question what should the optimal financial structure of FDI inflows to Poland be for stimulating growth processes. The study on the dependence between financial components of FDI inflows and GDP for Poland covers the period 2004: Q1–2019: Q4. Results of the VAR/VECM model and forecast error variance decomposition indicated that in the optimal (growth-enhancing) structure of FDI inflows the share of equities and the reinvestment of earnings should be maximised.

Impact of credit risk and profitability on liquidity shocks of Namibian banks: an application of the structural VAR model

The main purpose of this paper was to investigate the relationship between banks’ credit risk and profitability and liquidity shocks in Namibia for the period 2009 to 2018 using the SVAR model. In estimating the SVAR regression model, granger causality, impulse-response functions and forecast error variance decomposition were employed and evaluated. The sample consisted of Namibian commercial banks. By auditing liquidity data between 2009 and 2018, empirical results showed that liquidity risk is caused by a combination of structural shocks. The granger causality, impulse-response functions and forecast error variance decomposition documented that credit risk (non-performing loans) is key factor affecting liquidity conditions in Namibia in the medium to long run. In addition, the empirical results showed that quality earnings (ROA) have minimal impact on liquidity conditions in the short run. Reforming assets quality policies and earnings quality policies can be valuable policy tools to minimize liquidity shortages and avoid insolvent banks in Namibia.

Export Behavior Analysis of Air Cargo Using Error-Correction Model, Rolling Regression and Variance Decomposition

Purpose - We analyze the long-run and short-run relationship between air cargo export and its determinants, foreign industrial production and nominal effective exchange rate and clarify the export behavior of air cargo. Design/Methodology/Approach - This paper employs cointegration techniue, error correction model, rolling regression and forecast error variance decomposition. The analysis is based on monthly data for the nominal effective exchange rates, sectoral export values and foreign industrial production over the period from January 2000 to October 2020. Sectoral trade statistics used in this paper are taken from the Korea International Trade Association database for 4 three digit Ministry of Trade and Investment items. Findings - We show that all the variables are non-stationary at levels but become stationary after first differencing, so it is needed to find whether the variables are cointegrated. The cointegration test ensures the presence of a long-run relationship between the variables. The error correction terms for MTI8311, MTI8138, MTI8361 and MTI8128, which are 0.055, 0.198, 0.114 and 0.107, respectively, are negative and significant. The rolling regression indicates that the influence of exchange rate and foreign income on the four air cargo export products dwindles very quickly and the variance decomposition confirms that exports are very exogenous to exchange rate and foreign income Research Implications - The finding that the export growth adjusts toward its long-run about 20% and 6% of this adjustment indicates that if the export is exposed to a shock, it will converge or diverge to long-run equilibrium at a tolerable pace. The empirical results of the variance decomposition suggests that economic variables such as exchange rate and foreign income do not exert any strong influence on air transport export.

Data Assimilation of Satellite-Based Soil Moisture into a Distributed Hydrological Model for Streamflow Predictions

The authors examine the impact of assimilating satellite-based soil moisture estimates on real-time streamflow predictions made by the distributed hydrologic model HLM. They use SMAP (Soil Moisture Active Passive) and SMOS (Soil Moisture Ocean Salinity) data in an agricultural region of the state of Iowa in the central U.S. They explore three different strategies for updating model soil moisture states using satellite-based soil moisture observations. The first is a “hard update” method equivalent to replacing the model soil moisture with satellite observed soil moisture. The second is Ensemble Kalman Filter (EnKF) to update the model soil moisture, accounting for modeling and observational errors. The third strategy introduces a time-dependent error variance model of satellite-based soil moisture observations for perturbation of EnKF. The study compares streamflow predictions with 131 USGS gauge observations for four years (2015–2018). The results indicate that assimilating satellite-based soil moisture using EnKF reduces predicted peak error compared to that from the open-loop and hard update data assimilation. Furthermore, the inclusion of the time-dependent error variance model in EnKF improves overall streamflow prediction performance. Implications of the study are useful for the application of satellite soil moisture for operational real-time streamflow forecasting.

Model averaging prediction for nonparametric varying-coefficient models with B-spline smoothing

Model averaging has been demonstrated as a powerful tool in statistical prediction over the past decade. However, a majority of related works focus on the parametric model averaging. In this paper, we propose a model averaging estimation under nonparametric varying-coefficient models. Differing from existing works, our proposal concentrates on the development of the B-spline approximation to nonparametric varying coefficient functions for model average estimator, rendering the computational burden more cheaply than the kernel smoothing based estimator. Furthermore, our procedure is asymptotically optimal under mild conditions. The asymptotic optimality established in current paper is in terms of conditional quadratic loss function when the variance of model error is known or unknown, respectively. Three different cases of candidate models are considered. Extensive simulations are carried out to evaluate the finite-sample performance of our estimator. A real data is analyzed for illustration as well.

Using Bayes weights to remedy the heterogeneity problem of random error variance in linear models

In this research, it was suggested to use the InformativeBayes method in calculating the Bayes weights and use them to treat the of heterogeneity problem when estimating the linear regression model parameters using the weighted least squares method (BWLS). And compare it with the classical method through an experimental side to simulate the generated data from a normal distribution and for several different cases as well as an applied side of real data. The results of the research provided the preference of the proposed method on the classical method by relying on some statistical criteria through a program designed for this purpose in the language of MATLAB.

Using Bayes weights to remedy the heterogeneity problem of random error variance in linear models.

Using Bayes weights to remedy the heterogeneity problem of random error variance in linear models.

COV-OBS.x2: 180 years of geomagnetic field evolution from ground-based and satellite observations

We present the geomagnetic field model COV-OBS.x2 that covers the period 1840–2020. It is primarily constrained by observatory series, satellite data, plus older surveys. Over the past two decades, we consider annual differences of 4-monthly means at ground-based stations (since 1996), and virtual observatory series derived from magnetic data of the satellite missions CHAMP (over 2001–2010) and Swarm (since 2013). A priori information is needed to complement the constraints carried by geomagnetic records and solve the ill-posed geomagnetic inverse problem. We use for this purpose temporal cross-covariances associated with auto-regressive stochastic processes of order 2, whose parameters are chosen so as to mimic the temporal power spectral density observed in paleomagnetic and observatory series. We aim this way to obtain as far as possible realistic posterior model uncertainties. These can be used to infer for instance the core dynamics through data assimilation algorithms, or an envelope for short-term magnetic field forecasts. We show that because of the projection onto splines, one needs to inflate the formal model error variances at the most recent epochs, in order to account for unmodeled high frequency core field changes. As a by-product of the core field model, we co-estimate the external magnetospheric dipole evolution on periods longer than 2 years. It is efficiently summarized as the sum of a damped oscillator (of period 10.5 years and decay rate 55 years), plus a short-memory (6 years) damped random walk.