Biased Parameter Estimates Research Articles

Unobserved heterogeneity and temporal instability in an analysis of household water consumption under block rate pricing

Abstract There is a lack of studies investigating household water consumption while considering the possible heterogeneity in the observed data and its temporal instability, often resulting in inconsistent and biased parameter estimations and, as a result, inaccurate forecasting of household water consumption. To address these constraints, the current study investigates temporal shifts in the household water consumption pattern and the effects of different socioeconomic factors on forecasting household water consumption. Using the results of a household survey performed seasonally in three major cities in Northern Jordan over a 4-year period, separate seasonal models of water consumption are estimated using three alternate modeling approaches to account for possible unobserved heterogeneity. Likelihood ratio tests were performed to investigate the temporal stability of the models' estimations over different seasons across the 4-year period. The findings of these tests indicated that the data are temporally stable over two datasets (the summer and winter seasons). Also, the findings revealed that household water consumption is influenced by a variety of factors, with the impact of many of these factors varying across observations. Finally, the findings highlight the need for additional research into how unobserved heterogeneity can be best modeled in temporal contexts for accurate water consumption forecasting.

Inference for covariate-adjusted time-dependent prognosticaccuracy measures.

Evaluating the prognostic performance of candidate markers for future disease onset or progression is one of the major goals in medical research. A marker's prognostic performance refers to how well it separates patients at the high or low risk of a future disease state. Often the discriminative performance of a marker is affected by the patient characteristics (covariates). Time-dependent receiver operating characteristic (ROC) curves that ignore the informativeness of the covariates will lead to biased estimates of the accuracy parameters. We propose a time-dependent ROC curve that accounts for the informativeness of the covariates in the case of censored data. We propose inverse probability weighted (IPW) estimators for estimating the proposed accuracy parameters. We investigate the performance of the IPW estimators through simulation studies and real-life data analysis.

Numerical evaluation of photosensitive tracers as a strategy for separating surface and subsurface transient storage in streams

We numerically evaluated photosensitive tracers as a potential strategy for separating the effects of surface and hyporheic storage zones (SSZs and HSZs, respectively) on stream corridor transport. Correctly separating HSZ and SSZ effects is critical to estimating the hydro-biogeochemical function of a stream because HSZs and SSZs expose solutes to significantly different biogeochemical conditions, like sunlight exposure, microbial processes, and oxygen availability. Our numerical experiments used a multiscale river-corridor transport model implemented in the ATS code, which accommodates multiple storage zones with distinct travel time distributions and biogeochemical reactions. For parameter inferences, we used Bayesian inverse modeling. We found that breakthrough curves for photo-decaying tracers from day and night injection can delineate surface and hyporheic transient storage contributions, but only when interpreted jointly through a two-storage zone model. Numerical experiments that used only daytime injection or interpreted breakthrough curves with a single storage zone model yielded good fit to breakthrough curves, but parameter estimates were biased and controlling processes misattributed, examples of good model fits for the wrong reasons. Using those biased parameter estimates in reactive transport simulations resulted in significantly different projections of denitrification, which underscores the potential for stream function to be mischaracterized if tracer tests are interpreted through an inappropriately simplified model for transient storage. More generally, this study highlights the role of modeling in evaluating the experimental design and identifying the potential of system mischaracterization and its implications.

Improving the utility of weather radar for the spatial frequency analysis of extreme precipitation

Spatially seamless quantitative precipitation estimates (QPEs) from weather radars have the potential to address key limitations of intensity–duration–frequency (IDF) relations derived from sparse rain gage measurements. However, this potential has not been yet fully explored. Here, a methodological framework is designed for the spatial frequency analysis of extreme precipitation (P) with radar QPEs that leads to realistic quantile patterns while reducing the sampling uncertainty. The framework was applied with 19 years of QPEs from 1-h, 4-km Stage IV reanalysis from the Next Generation Weather Radar (NEXRAD) network and robustly tested against (1) a network of 204 high-resolution rain gages in central Arizona with one of the largest densities and spatial coverages in the world, and (2) extreme P quantiles from NOAA Atlas 14. It was first showed that (1) the generalized extreme value (GEV) is a suitable distribution to model the series of annual P maxima of gage records and radar QPEs across multiple durations from 1 h to 24 h, and (2) correcting the bias of the GEV shape parameter estimates due to the short sample size is a critical step. Spatial estimates of extreme P quantiles were then obtained through a hierarchical approach based on the index-flood method and the spatial smoothening (interpolation) of the GEV parameters estimated from radar QPEs (gage records). For each parameter, the most effective interpolation method was identified that limits the uncertainty caused by the short sample size and captures the local variability of extreme P. The extreme P quantiles generated from radar QPEs exhibited similar or, in some cases, higher accuracy than those generated by interpolating sparse gage information and exhibit more realistic patterns. While derived in central Arizona, the insights of this work are useful to incorporate radar QPEs into operational IDF curves in any region of the world monitored by weather radars.

Effects of misrepresentative length samples on individual growth and stock condition estimates

Despite its importance in fisheries studies, there is insufficient understanding on the effect of sampling error or bias on individual growth and other stock indicators. We show the influence of sample length distributions on parameter estimates, illustrating with an example. For the brown swimming crab, we simulated length samples in five configurations and estimated parameters of von Bertalanffy (k, L∞L∞ , t0), asymptotic weight ( W∞W∞ ), weight-length relationship (a, b), growth performance (ϕ’) and condition factor (Kn). Parameter estimates were compared with baseline values using relative bias, standard error and root mean square error. The results show that the accuracy and bias of parameter estimates depend on the lengths sampled. For example, the bias and accuracy of L∞L∞ and W∞W∞ vary inversely with sampled length, whereas combining length segments yields smaller biases of k and t0 than those of L∞L∞ and W∞W∞ . In general, the accuracy of parameter estimates does not always depend on sampling the entire length range, and errors are not the same for all parameters. These results are useful to guide sampling when resources are scarce. We discuss potential reasons for incomplete length sample structure and offer recommendations to obtain best estimates for parameters of interest.

Assessing the impact of recombination on the estimation of isolation-with-migration models using genomic data: a simulation study.

Recombination events complicate the evolutionary history of populations and species and have a significant impact on the inference of isolation-with-migration (IM) models. However, several existing methods have been developed, assuming no recombination within a locus and free recombination between loci. In this study, we investigated the effect of recombination on the estimation of IM models using genomic data. We conducted a simulation study to evaluate the consistency of the parameter estimators with up to 1,000 loci and analyze true gene trees to examine the sources of errors in estimating the IM model parameters. The results showed that the presence of recombination led to biased estimates of the IM model parameters, with population sizes being more overestimated and migration rates being more underestimated as the number of loci increased. The magnitude of the biases tended to increase with the recombination rates when using 100 or more loci. On the other hand, the estimation of splitting times remained consistent as the number of loci increased. In the absence of recombination, the estimators of the IM model parameters remained consistent.

Multi-step estimators and shrinkage effect in time series models

Many modern statistical models are used for both insight and prediction when applied to data. When models are used for prediction one should optimise parameters through a prediction error loss function. Estimation methods based on multiple steps ahead forecast errors have been shown to lead to more robust and less biased estimates of parameters. However, a plausible explanation of why this is the case is lacking. In this paper, we provide this explanation, showing that the main benefit of these estimators is in a shrinkage effect, happening in univariate models naturally. However, this can introduce a series of limitations, due to overly aggressive shrinkage. We discuss the predictive likelihoods related to the multistep estimators and demonstrate what their usage implies to time series models. To overcome the limitations of the existing multiple steps estimators, we propose the Geometric Trace Mean Squared Error, demonstrating its advantages. We conduct a simulation experiment showing how the estimators behave with different sample sizes and forecast horizons. Finally, we carry out an empirical evaluation on real data, demonstrating the performance and advantages of the estimators. Given that the underlying process to be modelled is often unknown, we conclude that the shrinkage achieved by the GTMSE is a competitive alternative to conventional ones.

Robust Bayesian Estimation of EEG-Based Brain Causality Networks.

The multivariate autoregression (MVAR) model is an effective model to construct brain causality networks. However, the accuracy of MVAR parameter estimation is considerably affected by outliers such as head movements and eye blinks contained in EEG signals, especially in short time windows. We proposed a robust MVAR parameter estimation method based on a Bayesian probabilistic framework and Laplace fitting error known as Lap-SBL. With the Bayesian inference framework, we can accurately estimate the MVAR parameters under short time windows. Additionally, to alleviate the influence of outliers, we model the fitting error using the Laplace distribution instead of the typical Gaussian distribution. We employ convex analysis to model the inference task by approximating the Laplace noise prior with a maximum over Gaussian functions with varying scales. The variational inference approach was used to efficiently estimate the MVAR parameters. The numerical results suggest that the proposed method obtains less parameter estimation bias and more consistent linkages than existing benchmark methods, i.e., LS, LASSO, LAPPS and SBL. The motor imagery experimental data analysis shows that Lap-SBL can better describe the lateralization characteristics of brain network. This lateralization is less apparent in a subject with poor MI classification accuracy. Lap-SBL effectively suppresses the influence of outliers and recovers reliable networks in the presence of outliers and short time windows.

Comparing Several Missing Data Estimation Methods in Linear Regression;Real Data Example and A Simulation Study

Analysis on incomplete could lead to biased estimation when using standard statistical procedure since it ignores the missing observations. The disadvantage of ignoring missing data is that the researcher might not have enough data to conduct an analysis. The main objective of the study is to compare the performance between listwise deletion (LD), mean substitution (MS) and multiple imputation (MI) method in estimating parameters. The performance will be measured through bias, standard error and 95% confidence interval of interested estimates for handling missing data with 10% missing observations. A complete empirical data set was used and assumed as population data. Ten percent of total observations in the population ere set as missing arbitrarily by generating random numbers from a uniform distribution, . Then, bias of parameter estimates and confidence interval of parameter estimates are calculated to compare the three methods. A Monte Carlo simulation was carried out to know the properties of missing data and investigated using simulated random numbers. Simulation of 1000 sampled data with 20, 50, and 100 observations and each sample is set to have 10% missing observations. Standard statistical analyses are run for each missing data and get the average of parameter estimates to calculate the bias and standard error of parameter estimates for every missing data method. The analysis was conducted by using SAS version 9.2. It was found that the MI method provided the smallest bias and standard error of parameter estimates and a narrower confidence interval compared to the LD and MS methods Meanwhile, the LD method gives a smaller bias of parameter estimates and standard error for small sample size of missing data. And, MS method is strongly recommended not to use for handling missing data because it will result in large bias and standard error of parameter estimates.

Modeling Rating Order Effects Under Item Response Theory Models for Rater-Mediated Assessments.

Rater effects are commonly observed in rater-mediated assessments. By using item response theory (IRT) modeling, raters can be treated as independent factors that function as instruments for measuring ratees. Most rater effects are static and can be addressed appropriately within an IRT framework, and a few models have been developed for dynamic rater effects. Operational rating projects often require human raters to continuously and repeatedly score ratees over a certain period, imposing a burden on the cognitive processing abilities and attention spans of raters that stems from judgment fatigue and thus affects the rating quality observed during the rating period. As a result, ratees' scores may be influenced by the order in which they are graded by raters in a rating sequence, and the rating order effect should be considered in new IRT models. In this study, two types of many-faceted (MF)-IRT models are developed to account for such dynamic rater effects, which assume that rater severity can drift systematically or stochastically. The results obtained from two simulation studies indicate that the parameters of the newly developed models can be estimated satisfactorily using Bayesian estimation and that disregarding the rating order effect produces biased model structure and ratee proficiency parameter estimations. A creativity assessment is outlined to demonstrate the application of the new models and to investigate the consequences of failing to detect the possible rating order effect in a real rater-mediated evaluation.

Inclusion Bayes factors for mixed hierarchical diffusion decision models.

Cognitive models provide a substantively meaningful quantitative description of latent cognitive processes. The quantitative formulation of these models supports cumulative theory building and enables strong empirical tests. However, the nonlinearity of these models and pervasive correlations among model parameters pose special challenges when applying cognitive models to data. Firstly, estimating cognitive models typically requires large hierarchical data sets that need to be accommodated by an appropriate statistical structure within the model. Secondly, statistical inference needs to appropriately account for model uncertainty to avoid overconfidence and biased parameter estimates. In the present work, we show how these challenges can be addressed through a combination of Bayesian hierarchical modeling and Bayesian model averaging. To illustrate these techniques, we apply the popular diffusion decision model to data from a collaborative selective influence study. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Understanding the characteristics of car-sharing users and what influences their usage frequency

Throughout the global market, the car-sharing industry continues to confront multiple headwinds. In China, the problem of the generally low frequency of car-sharing use by users (FCU) is a major constraint to its growth. In this study, we quantify the characteristics of car-sharing users and the main factors influencing the FCU based on the car-sharing order data and GPS trajectory data of users in Beijing, China. Considering that sample selection bias with car-sharing users can lead to biased and inconsistent parameter estimation, this paper constructs a multi-factor influence model of FCU based on the Heckman two-stage model. Particularly, whether users enter the market through coupons (IF-Coupons) is selected as the instrumental variable of the model. The results reveal that current car-sharing users are mainly young people aged 25–39 and predominantly men. Travelers tend to travel on weekdays, and those making short trips, and those who enter the car-sharing market using coupons are more likely to become car-sharing users. Based on the results for the FCU, the market potential of female car-sharing users is larger. Besides, the indicators of travel distance and duration, the tendency to use on weekdays, and station location can significantly influence the FCU. Our research contributes to provide scientific theoretical support for promoting the coordinated and sustainable development of the car-sharing market.

A Note on Latent Traits Estimates under IRT Models with Missingness

AbstractMissingness due to not‐reached items and omitted items has received much attention in the recent psychometric literature. Such missingness, if not handled properly, would lead to biased parameter estimation, as well as inaccurate inference of examinees, and further erode the validity of the test. This paper reviews some commonly used IRT based models allowing missingness, followed by three popular examinee scoring methods, including maximum likelihood estimation, maximum a posteriori, and expected a posteriori. Simulation studies were conducted to compare these examinee scoring methods across these commonly used models in the presence of missingness. Results showed that all the methods could infer examinees' ability accurately when the missingness is ignorable. If the missingness is nonignorable, incorporating those missing responses would improve the precision in estimating abilities for examinees with missingness, especially when the test length is short. In terms of examinee scoring methods, expected a posteriori method performed better for evaluating latent traits under models allowing missingness. An empirical study based on the PISA 2015 Science Test was further performed.

SIMULATION OF THE SARIMA MODEL WITH THREE-WAY ANOVA AND ITS APPLICATION IN FORECASTING LARGE CHILLIES PRICES IN FIVE PROVINCES ON JAVA ISLAND

Commodities that become potential in the Horticulture Sub-sector are large chilies, so supply and prices must be controlled. One of the efforts that can be made is to predict the price of large chili in the future. However, forecasting is sometimes constrained by several things, such as small sample sizes and outliers. The effect of several factors on the parameter estimation bias can be determined by experimental design by simulating the data obtained from the generation results with several scenarios. The results of the analysis show that all factors have a significant effect on the magnitude of the parameter bias, so that all factors can affect forecasting results. When applying forecasting methods to actual data, paying attention to these three factors is necessary. The application of actual data using the SARIMA method gives good results. It can be seen from the RMSE and MAPE values ​​, which tend to be small. Based on the forecast results for the following 12 periods, it is estimated that the price of big chili in 2022 in five provinces will still fluctuate. The high price of chili in five provinces is predicted to reach its highest in the first three months of 2022. The highest price is predicted to occur in DIY Province in February, which is Rp. 74.230.00/kg. However, from the middle to the end of the year, prices will tend to fall and stabilize. The price will be the lowest in Middle Java Province in December, which is Rp. 20,689.00/Kg.

Modeling and maximum likelihood based inference ofinterval-censored data with unknown upper limits andtime-dependent covariates.

Due to the nature of study design or other reasons, the upper limits of the interval-censored data with multiple visits are unknown. A naïve approach is to treat the last observed time as the exact event time, which may induce biased estimators of the model parameters. In this paper, we first develop a Cox model with time-dependent covariates for the event time and a proportional hazards model with frailty for the gap time. We then construct the upper limits using the latent gap times to resolve the issue of interval-censored event time data with unknown upper limits. A data-augmentation technique and a Monte Carlo EM (MCEM) algorithm are developed to facilitate computation. Theoretical properties of the computational algorithm are also investigated. Additionally, new model comparison criteria are developed to assess the fit of the gap time data as well as the fit of the event time data conditional on the gap time data. Our proposed method compares favorably with competing methods in both simulation study and real data analysis.

Consistent Subspace Identification of Errors-in-Variables Hammerstein Systems

In this article, a consistent subspace identification method (SIM) is proposed for block-oriented errors-in-variables Hammerstein systems. Due to that the existing SIMs using parity subspace based on noisy measurements may result in biased parameter estimates, we propose a scheme for the consistent system parameter estimation, which estimates the noise-free Hankel matrix using available noisy measurements and noise variances. A 2-D search method is proposed to estimate the unknown noise variances from available noisy measurements. After that consistent estimations of the Hammerstein system parameters can be then retrieved from the estimated noise-free Hankel matrix following the same algorithm framework of the existing SIMs using parity subspace. Two simulation examples are included to support the effectiveness and merits of the proposed method.

Federated Imitation Learning for UAV Swarm Coordination in Urban Traffic Monitoring

The popularization of unmanned aerial vehicles (UAVs) has boosted various civil applications such as traffic monitoring, in which the effective coordination of the UAV swarm plays a significant role in expanding the monitoring range and enhancing the execution efficiency. However, due to the isolated local environments as well as the heterogeneous execution capabilities, it is challenging to achieve highly consistent actions. In this article, we incorporate the federated learning framework with the imitation learning technique to coordinate the UAVs' maneuvers by interactively imitating the leader UAV's operations. During the interagent global model download phase, we utilize the generative adversarial imitation learning (GAIL) model to accurately follow the leader UAV's operations by removing the biased estimates of imitation parameters. While in the intraagent local model training phase, we utilize the self-imitation learning (SIL) model to correct delicate imitation errors by virtue of the follower UAVs' own historical valuable experiences. In order to achieve more efficient distributed parameter interactions, we regularize the federated gradient updates and eventually yield coordinated swarm policies. We evaluate the proposed algorithm in the UAV-based traffic monitoring scenario. Evaluation results demonstrate the superiorities on training and execution efficiencies.

A spatial econometric analysis of the environment Kuznets curve and pollution haven hypothesis in Sub-Saharan Africa

The aim of this study is to test the environment Kuznets curve (EKC) and pollution haven (PH) hypotheses in Sub-Saharan Africa (SSA). An important methodological point that has been over-looked by many studies is that environmental quality is not only correlated in time but also in space. For this purpose, the study applies spatial panel econometric analysis using a balanced panel of 35 SSA nations from 2002 to 2015 to examine the EKC and PH hypotheses. Both spatial interdependence and individual heterogeneity are accounted for through the application of the spatial Durbin model (SDM) so as to avoid potential bias and inefficiencies in parameter estimates. As proxies for environmental quality, panel data aggregates on carbon dioxide (CO2) emissions and the depletion of natural resources are utilised. The findings offer proof for the EKC theory about the depletion of natural resources in SSA. The EKC theory, however, does not apply to CO2 emissions. Moreover, the study finds that the positive scale effect of trade outweighs the negative technique effect of trade, which indicates that trade liberalisation has a negative effect on both environmental quality indices. This discovery supports the PH theory. The study also demonstrates positive spatial spill-over for natural resource depletion between neighbouring countries and negative spatial spill-over for carbon dioxide emission between close countries.

Comparison of Two Approaches to Detecting Switched Class Labels in LCA Simulations: Class Assignment vs. Class Similarity

The detection of switched class labels is required in latent class analysis (LCA) simulations involving parameter estimation. The present study proposed a class similarity (CS) algorithm to detect switched class labels based on the similarity of conditional probabilities between true and estimated classes, in contrast to Tueller et al.’s class assignment (CA) algorithm considering the number of participants in each true class assigned to every estimated class. The performances of CS and CA were compared by examining the average class assignment accuracy and the bias of parameter estimates in a numerical experiment. CS and CA were shown to perform similarly that either method can be used to detect switched class labels in future LCA simulations. The performance of the two algorithms warrants further investigation under a wider simulation condition.

Two Sample Approaches to Regression Calibration for Measurement Error Correction

The goal of this work is to create methods for enhancing measurement error using regression calibration as a strategy by combining two samples, thereby increasing the relative efficiency of linear regression models. Because two or more samples are more likely to provide an accurate representation of the population than a single sample under inquiry, utilizing two samples in regression calibration is likely to produce a realistic depiction of what the actual population is when error-free. This study has generated independent estimates from two samples and combined them with weights equal to the inverse of their estimated probabilities of sample inclusion. It has also integrated two data sets into a single data set and suitably adjusted the weights on each sampled unit. The regression calibration method is most commonly used to correct predictor-response bias caused by variable measurement imperfections. Because of its simplicity, this method is often used. The fundamental principle behind regression calibration is to estimate the conditional expectation of a genuine response, given predictors measured with error and other covariates supposed to be measured without error. The predicted values are then estimated and used to assess the relationship between the response and an outcome in place of the unknown genuine response. Further information on the unobservable true predictors is required by the regression calibration program. This data is frequently obtained from a validation study that employs unbiased measurements for genuine predictors. This study has employed and compared the results obtained from the two sample approaches. Measuring errors can be produced by a variety of sources, including instrument error, laboratory error, human error, problems in documenting or executing measurements, self-reporting errors, and natural oscillations in the underlying amount. Covariate measurement error has three effects: In addition to hiding the properties of the data, which makes graphical model analysis difficult, it produces bias in parameter estimates for statistical models, resulting in a sometimes significant loss of power for detecting fascinating correlations between variables. The two sample approaches employed by the study have yielded acceptable results.