Efficient Identification of Multiple Parameter Errors in Power Grids by Mixed-Effects Models and Generalized Least Squares

Linear mixed effects (LME) models are important statistical tools for analysis of clustered and correlated data. High breakdown estimators are currently the robust methods of choice for multivariate linear regression, but extensions of such estimators have been developed only for completely balanced LME models. In this work, we propose a generalized S-estimator for a general unbalanced LME model. Our GS-estimator reduces to the classic high breakdown S-estimator when the LME model reduces to a multivariate normal location and scale model or mul- tivariate regression model. The asymptotic properties are established, and we show that the estimator may be viewed as a redescending M-estimator. A small simu- lation study is conducted to compare performance of the GS-estimates, monotone M-estimates, and restricted maximum likelihood (REML) estimates under various contamination patterns. The proposed estimator is used for analysis of age-related changes in hemoglobin levels of sickle cell disease patients.

Prediction of the herd somatic cell count of the following month using a linear mixed effect model

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Degradation in drylands is a critically important global issue that threatens ecosystem and environmental in many ways. Researchers have tried to use remote sensing data and meteorological data to perform residual trend analysis and identify human-induced vegetation changes. However, complex interactions between vegetation and climate, soil units and topography have not yet been considered. Data used in the study included annual accumulated Moderate Resolution Imaging Spectroradiometer (MODIS) 250 m normalized difference vegetation index (NDVI) from 2002 to 2013, accumulated rainfall from September to August, digital elevation model (DEM) and soil units. This paper presents linear mixed-effect (LME) modeling methods for the NDVI-rainfall relationship. We developed linear mixed-effects models that considered the random effects of sample points nested in soil units for nested two-level modeling and single-level modeling of soil units and sample points, respectively. Additionally, three functions, including the exponential function (exp), the power function (power), and the constant plus power function (CPP), were tested to remove heterogeneity, and an additional three correlation structures, including the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)] and the compound symmetry structure (CS), were used to address the spatiotemporal correlations. It was concluded that the nested two-level model considering both heteroscedasticity with (CPP) and spatiotemporal correlation with [ARMA(1,1)] showed the best performance (AMR = 0.1881, RMSE = 0.2576, adj-R 2 = 0.9593). Variations between soil units and sample points that may have an effect on the NDVI-rainfall relationship should be included in model structures, and linear mixed-effects modeling achieves this in an effective and accurate way.

This paper investigates identification of parameter and measurement errors in the power network model. A mixed integer quadratic programming (MIQP) model is proposed in this paper to precisely identify multiple parameter and measurement errors. In the proposed MIQP model, erroneous parameters and measurements are involved with penalty factor in the aim of minimizing weighted least-squares (WLS) objective function. The proposed method has the desired property of accurate identification with avoiding over identification in the meantime. Parameter and measurement errors can also be distinguished simultaneously in MIQP model. All these features are verified via simulations that are carried out on IEEE 14-bus system.

Recently a practical and efficient off-line approach for network branch parameter (series and shunt admittances) errors detection, identification and correction was developed. In comparison with other methodologies already proposed for branch parameters validation, the novel features of this off-line approach are the identification procedure of suspicious branches and the way the augmented state-parameter estimation problem is solved. Several simulation results (with IEEE bus systems) have demonstrated the high correctness and reliability of that off-line approach to deal with single and multiple parameter errors in adjacent (those having a terminal bus in common) and non-adjacent branches. Moreover the approach was also demonstrated on tests performed on the Hydro-Québec Trans-Énergie networks. One of these tests shows that approach enables the validation of series and shunt admittances of parallel transmission lines with series compensation. However, that offline approach does not have the desired property of distinguishing between bad data (bad analog measurements) and branch parameter errors. This paper presents a simple yet effective improvement by creating new indexes that enable the distinction between bad data and branch parameter errors, even when both appear simultaneously. Simulation results have sown the effectiveness of including the new indexes in that off-line approach.

BackgroundSince 2020, information regarding COVID-19 has been a constant presence in the news, in our conversations and thoughts. Continuous exposure to this type of stimuli could have an impact on cognitive processes essential for our everyday activities, such as prospective memory (PM). PM is the ability to remember to perform an intention at a specific point in the future, like remembering to take prescribed medicines at a specific time or to turn off the stove after cooking. Do COVID-related stimuli affect our ability to perform a PM task?MethodsTo answer this question, we proposed a novel version of the classical paradigm used to investigate PM. Namely, this paradigm includes a baseline condition, in which an ongoing task is presented alone, and a PM condition in which the same task is proposed again together with a second (prospective) task. In this study, a short video clip was presented between the baseline and the PM condition. The video clip displayed either neutral, negative, or COVID-related content. Additionally, participants were asked to respond to two questionnaires and a series of questions regarding their well-being and experience with the pandemic. Namely, the DASS-21 scale (evaluating depression, anxiety, and stress), and the COVID-19-PTSD questionnaire (a questionnaire evaluating post-traumatic stress disorder symptoms related to the pandemic experience) were administered. Participants’ performance and responses were analyzed using a linear mixed effect (LME) model approach, and correlation analyses were run to highlight possible correlations between participants’ scores in the DASS-21, the COVID-19-PTSD, and the additional questions on their personal experience with the pandemic.ResultsThe LME models revealed significant effects of the displayed video on performance: in line with previous studies, the clip displaying standard negative contents led to impaired accuracy in the ongoing task in the PM condition, compared to the Baseline. In contrast, participants who saw the COVID-related clip showed improved accuracy in the ongoing task compared to the other participants, selectively in the block performed after the video clip was displayed (PM condition). Furthermore, the explanatory power of the LME model calculated on accuracy to the ongoing trials was enhanced by the inclusion of the scores in the anxiety subscale of the DASS-21, suggesting a detrimental role of anxiety. Altogether, these results indicate a different effect of the exposure to classical negative contents (associated with a cost in terms of accuracy in the ongoing task between the baseline and the PM condition) and the pandemic-related one, which was instead characterized by a higher accuracy to ongoing trials compared to the other video clips. This counterintuitive finding seems to suggest that COVID-related stimuli are processed as “acute stressors” rather than negative stimuli, thus inducing a state of increased alertness and responsivity.

The United Kingdom's climate and topography enable multiple different calving patterns to operate within the same market, facilitated by industry infrastructure that allows for a variety of milk purchasing arrangements. All-year-round (AYR) calving is most common, and with current labor challenges, spring block (SB), autumn block (AB), and twin block (TB) calving systems could potentially become more popular, but research comparing the efficiency of AYR and block-calving systems operating within the same market conditions is limited. This study compared the costs of production of AYR against 3 block-calving systems on a pence per liter (PPL) of ECM basis (1 pence = ₤0.01, US$1 = £1.28 at the time of the study), to assist benchmarking activities, costs, and management decisions. Farm accounts data (from 2017 to 2020), from 604 farms broadly representing the national split of calving patterns in the United Kingdom were included in a linear mixed effects (LME) model used for inference with maximum likelihood estimation. Random effects included year and farm, with fixed effects including herd size (cows), farm size (hectares), and average annual milk yield per cow, which were each standardized to enable all calving patterns to be compared at the same scale (i.e., same herd size, farm size, and milk yield). Calving pattern was self-determined by the farmer under guidance from a trained data collector. Cost of production variables investigated included milk price, stock sales (calves, cull cows, breeding animals), total income (all dairy farm revenues), total purchased feed, purchased forage, variable costs, gross margin, labor and overhead costs, and net profit. The AB herds had lower total income, lower forage purchases, higher labor costs and lower net profit compared with AYR. The SB herds had higher total income, higher forage purchases, and lower labor and overhead costs compared with AYR. No differences were found between TB and AYR herds. Using the LME model, we estimated the impact of changing the fixed effects on costs of production based on a 1-SD change. Increasing herd size (1 SD, 345 cows) was associated with a reduction in net profit of AB herds by 3.34 PPL but an increase in net profit for SB herds by 5.57 PPL compared with AYR. For increasing farm size (1 SD, 164 ha), all 3 block-calving herds had different associations compared with AYR; net profits would be increased for AB and TB herds (by 1.33 and 2.12 PPL, respectively), whereas SB herds would have reduced net profit by 4.26 PPL. Increasing energy corrected milk yield (1 SD, 4,038 L) would only benefit the net profit of SB herds over AYR by 6.04 PPL, as SB herds had the lowest milk yield per cow. The results demonstrated that increasing land, cows, or milk yield per cow was associated with different responses in cost of production depending on calving pattern. Findings from this study could be used by extension services, farm advisors, and farmers for benchmarking purposes and when considering farm-scale decisions or switching from an AYR to a block-calving pattern.

OBJECTIVE—A recent meta-analysis demonstrated a nominal association of the ectonucleotide pyrophosphatase phosphodiesterase 1 (ENPP1) K→Q missense single nucleotide polymorphism (SNP) at position 121 with type 2 diabetes. We set out to confirm the association of ENPP1 K121Q with hyperglycemia, expand this association to insulin resistance traits, and determine whether the association stems from K121Q or another variant in linkage disequilibrium with it.RESEARCH DESIGN AND METHODS—We characterized the haplotype structure of ENPP1 and selected 39 tag SNPs that captured 96% of common variation in the region (minor allele frequency ≥5%) with an r2 value ≥0.80. We genotyped the SNPs in 2,511 Framingham Heart Study participants and used age- and sex-adjusted linear mixed effects (LME) models to test for association with quantitative metabolic traits. We also examined whether interaction between K121Q and BMI affected glycemic trait levels.RESULTS—The Q allele of K121Q (rs1044498) was associated with increased fasting plasma glucose (FPG), A1C, fasting insulin, and insulin resistance by homeostasis model assessment (HOMA-IR; all P = 0.01–0.006). Two noncoding SNPs (rs7775386 and rs7773477) demonstrated similar associations, but LME models indicated that their effects were not independent from K121Q. We found no association of K121Q with obesity, but interaction models suggested that the effect of the Q allele on FPG and HOMA-IR was stronger in those with a higher BMI (P = 0.008 and 0.01 for interaction, respectively).CONCLUSIONS—The Q allele of ENPP1 K121Q is associated with hyperglycemia and insulin resistance in whites. We found an adiposity-SNP interaction, with a stronger association of K121Q with diabetes-related quantitative traits in people with a higher BMI.

In this software review, we provide a brief overview of four R functions to estimate nonlinear mixed-effects programs: nlme (linear and nonlinear mixed-effects model), nlmer (from the lme4 package, linear mixed-effects models using Eigen and S4), saemix (stochastic approximation expectation maximization), and brms (Bayesian regression models using Stan). We briefly describe the approaches used, provide a sample code, and highlight strengths and weaknesses of each.

Tic-related impairment drives treatment decisions for Tourette syndrome and related tic disorders. The clinical features most strongly associated with impairment remain unclear. The aim of this analysis is to identify clinical predictors of tic-related impairment in children and adults with tic disorders in a prospective longitudinal study. Participants were drawn from the Calgary Tic Registries, undergoing prospective structured assessments. Baseline demographic and psychiatric data, psychotropic medication use, Yale Global Tic Severity Scale (YGTSS) dimension scores, and the number of different tics (NDT) were analyzed. Predictors of impairment were examined using Spearman's correlations, univariate associate screening with false discovery rate correction, least absolute shrinkage and selection operator (LASSO) regression with ordinary least squares refitting, and linear mixed-effects (LME) models to evaluate within-person changes over time. The sample included 496 participants (848 total assessments). Motor tic interference showed the strongest correlation with impairment (ρ = 0.50), followed by motor tic intensity and frequency. The NDTs correlated with impairment more strongly than most individual YGTSS dimensions. In LASSO regression, seven predictors remained significant: motor tic interference, frequency and complexity, phonic tic interference, older age, female sex, and absence of autism. The LME models analyzed data from all participants with at least one follow-up visit. LME models showed that increases in total tic score predicted higher impairment and that impairment decreased modestly over time. Motor tic interference is the most robust predictor of tic-related impairment. Older age and female sex further contribute to functional burden. © 2026 The Author(s). Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

Linear mixed‐effects (LME) models have become a popular tool for analyzing longitudinal data that arise in areas as diverse as clinical trials, epidemiology, agriculture, economics, and geophysics. The increasing popularity of these models is explained by the flexibility they offer in modeling the within‐subject correlation often present in longitudinal data, by the handling of both balanced and unbalanced data, and by the availability of reliable and efficient software for fitting them. This paper describes a general LME model for longitudinal Gaussian data, presenting the model definition and its underlying assumptions. Maximum likelihood and restricted maximum likelihood estimation methods are discussed, as well as asymptotic inference methods. Available software for fitting and analyzing LME models are briefly reviewed. The model and methods are illustrated through an example from a longitudinal growth study.

BackgroundAmong persons living with HIV (PLWH) with type 2 diabetes mellitus (DM) there is limited research on the effect of DM control on CD4 count. Current guidelines recommend that PLWH with DM maintain a hemoglobin A1c (HbA1c) <7%. This analysis examined the impact of HbA1c on trends in CD4 count among PLWH receiving care in Washington, DC.MethodsWe used data from the DC Cohort, a longitudinal observational cohort of patients receiving HIV care at 14 clinics between 2011–2018. Participants with DM on an ongoing antiretroviral regimen with ≥1 year of follow-up, ≥2 HbA1c results, and ≥2 CD4 count results were included. Participants were compared based on the most recent HbA1c result categorized into one of three control levels control: strict, HbA1c < 7.5%; moderate, HbA1c between 7.5–9.0%; and uncontrolled, HbA1c >9.0%. All statistical tests were performed within the framework of the linear mixed-effects (LME) model. The rates of increase in CD4 count by DM control were compared using an LME model with random slopes and random intercepts, adjusted for sex, BMI, nadir CD4, a history of AIDS, or cancer diagnosis.ResultsAmong 554 participants (median age 53.5; 70.8% male; 82.7% Black), there were 5,138 total CD4 count measurements. In unadjusted analysis, participants with moderate or uncontrolled HbA1c had higher mean CD4 counts over the follow-up period than those with strict HbA1c control (strict: 690 cells/μL, moderate: 712 cells/μL uncontrolled: 711 cells/μL; P = 0.0156 strict vs. moderate, 0.049 strict vs. uncontrolled). All DM control groups had a similar temporal increase over time in CD4 count (P = 0.46). In multivariate analysis, only moderate vs. strict control showed a significant difference in CD4 count (mean difference=18.1; P = 0.02). Results showed CD4 count change was not affected by the duration of HIV diagnosis or diabetes diagnosis. See Table 1 for additional results.ConclusionPLWH and DM with moderate HbA1c control had higher CD4 counts than those with strict HbA1c control and similar CD4 counts compared with those with uncontrolled HbA1c levels, while the rate of increase in CD4 count was similar in the three groups. These results show that moderate DM control may benefit CD4 count, which should be considered when revising DM control guidelines for PLWH.DisclosuresAll authors: No reported disclosures.

An interesting recent development in emotion research and clinical psychology is the discovery that affective states can be modeled as a network of temporally interacting moods or emotions. Additionally, external factors like stressors or treatments can influence the mood network by amplifying or dampening the activation of specific moods. Researchers have turned to multilevel autoregressive models to fit these affective networks using intensive longitudinal data gathered through ecological momentary assessment. Nonetheless, a more comprehensive examination of the performance of such models is warranted. In our study, we focus on simple directed intraindividual networks consisting of two interconnected mood nodes that mutually enhance or dampen each other. We also introduce a node representing external factors that affect both mood nodes unidirectionally. Importantly, we disregard the potential effects of a current mood/emotion on the perception of external factors. We then formalize the mathematical representation of such networks by exogenous linear autoregressive mixed-effects models. In this representation, the autoregressive coefficients signify the interactions between moods, while external factors are incorporated as exogenous covariates. We let the autoregressive and exogenous coefficients in the model have fixed and random components. Depending on the analysis, this leads to networks with variable structures over reasonable time units, such as days or weeks, which are captured by the variability of random effects. Furthermore, the fixed-effects parameters encapsulate a subject-specific network structure. Leveraging the well-established theoretical and computational foundation of linear mixed-effects models, we transform the autoregressive formulation to a classical one and utilize the existing methods and tools. To validate our approach, we perform simulations assuming our model as the true data-generating process. By manipulating a predefined set of parameters, we investigate the reliability and feasibility of our approach across varying numbers of observations, levels of noise intensity, compliance rates, and scalability to higher dimensions. Our findings underscore the challenges associated with estimating individualized parameters in the context of common longitudinal designs, where the required number of observations may often be unattainable. Moreover, our study highlights the sensitivity of autoregressive mixed-effect models to noise levels and the difficulty of scaling due to the substantial number of parameters.

Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if assuming Normal distributions on the random effects. However, in many applications of economy, business and medicine, it is often essential to impose constraints on the regression parameters after taking their real-world interpretations into account. Therefore, in this paper we extend the classical (unconstrained) LME models to allow for sign constraints on its overall coefficients. We propose to assume a symmetric doubly truncated Normal (SDTN) distribution on the random effects instead of the unconstrained Normal distribution which is often found in classical literature. With the aforementioned change, difficulty has dramatically increased as the exact distribution of the dependent variable becomes analytically intractable. We then develop likelihood-based approaches to estimate the unknown model parameters utilizing the approximation of its exact distribution. Simulation studies have shown that the proposed constrained model not only improves real-world interpretations of results, but also achieves satisfactory performance on model fits as compared to the existing model.