Random Error Term Research Articles

A novel choice model combining utility maximization and the disjunctive decision rules, application to two case studies

Most choice models, e.g. Multinomial Logit (MNL), rely on random utility theory, which assumes that a compensatory utility maximization decision rule explains an individual’s choice behaviour. Research has shown, however, that behaviour is sometimes better explained by non-compensatory decision rules. While some research has used Latent Class Choice Models (LCCMs) to account for multiple decision rules, many of them – such as the disjunctive rule – have yet to be explored. This paper formulates, estimates, and evaluates a LCCM that combines the MNL with a Generalised Random Disjunctive Model (GRDM), a new choice model we develop. Addressing deficiencies of existing disjunctive choice models, the GRDM allows for relative importance between attributes and is insensitive to irrelevant attributes. Unlike most non-compensatory models, it is tractable and incorporates random error terms for capturing unobserved heterogeneity across choice situations. The GRDM can be expressed as a Universal Logit (UL) model, which helps derive welfare metrics such as Marginal Rates of Substitution and elasticities and makes it possible to estimate the model with traditional software packages. The LCCM combining the GRDM and the MNL is estimated in two large-scale case studies: cyclists’ route choice and public transport route choice. Results are compared with other relevant LCCM specifications and the individual choice models, where it is found that the MNL + GRDM LCCM provides the best fit to the data. We also interpret the fitted parameters and calculate the Marginal Rates of Substitution, which align with behavioural expectations.

Analytical Explanations of the Concept of the Fixed Term and the Random Error Term in Econometric Models

The error term or disturbance term plays an important role in the econometric model, and there are several reasons for including it in the econometric model, including issues related to measurement problems, the omission of variables from the econometric model, or for contingency reasons or related to abnormal human behavior from the general rule, or for inaccurate description of the models or inaccurate preparation of the data. The fixed term or intercept also has different meanings in the econometric model, such as the mathematical meaning, the econometric meaning, the fixed term without meaning, or the fixed term with a negative sign, and others.

Evaluating a 14-week neck strengthening protocol for neuromuscular indicators associated with head and neck trauma

Increased neck strength has been linked to a potential decrease in traumatic brain injuries (TBI). The purpose was to determine the efficacy of a neck-strengthening protocol using a novel neck-strengthening device to increase isometric neck strength and rate of force development (RFD). Utilizing self-generated centripetal force, participants trained for 14 weeks. A linear mixed model was used to analyze the relationship between post-assessment measurements and pre-assessments measurements, while accounting for repeated measure random effect at the individual level, and a regular random error term. RFD values were 4.344 times higher in the clockwise direction and 5.978 times higher in the counterclockwise direction when comparing pre and post assessment measurements. Isometric neck strength increased significantly (p ​< ​0.05) in the cervical extension (p ​= ​0.010) and left lateral flexion (p ​= ​0.009) directions. The results can be used in strength training and clinical settings to potentially reduce the incidence of TBI.

Bias correction based on AR model in spurious regression

&lt;abstract&gt;&lt;p&gt;The regression of mutually independent time series, whether stationary or non-stationary, will result in autocorrelation in the random error term. This leads to the over-rejection of the null hypothesis in the conventional t-test, causing spurious regression. We propose a new method to reduce spurious regression by applying the Cochrane-Orutt feasible generalized least squares method based on a bias-corrected method for a first-order autoregressive model in finite samples. This method eliminates the requirements for a kernel function and bandwidth selection, making it simpler to implement than the traditional heteroskedasticity and autocorrelation consistent method. A series of Monte Carlo simulations indicate that our method can decrease the probability of spurious regression among stationary, non-stationary, or trend-stationary series within a sample size of 10–50. We applied this proposed method to the actual data studied by Yule in 1926, and found that it can significantly minimize spurious regression. Thus, we deduce that there is no significant regressive relationship between the proportion of marriages in the Church of England and the mortality rate in England and Wales.&lt;/p&gt;&lt;/abstract&gt;

Tunable SRS-Aware Robust Coordinated Beamforming Design With Channel Aging

Coordinated beamforming holds tremendous potential to maximize network capacity, whose effect largely depends on the period sounding reference signal (SRS)-based channel sounding. However, the huge discrepancy between the sounding channel and the real-time channel is inevitable and nonnegligible with channel aging, which results in severe degradation of coordinated beamforming gain. In this paper, the discrepancy is modeled as a random error term with the effect of channel aging included, and a robust coordinated beamforming design with channel aging is further proposed, exploiting the potential capacity gain through the channel statistical information, which provides the potential for tuning the SRS period. Specifically, the joint correlation properties of channels are modeled in the random error matrix with the static statistical information collected from practical channel samples. To cope with multiple random terms, the deterministic equivalent method is adopted to obtain the approximate closed-form expression of the ergodic capacity, aiming at deriving a robust beamformer that can achieve a stationary point of the expected weighted sum-rate maximization problem. In addition, by adopting the proposed beamforming design, the tuning guidance for the SRS period is provided for practical networks satisfying different capacity requirements and mobile scenarios. Simulation results show that the proposed design can extend the SRS period more than 1× at 10% capacity loss when user speed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$v=30\rm {km/h}$</tex-math></inline-formula> , compared with the traditional beamforming design.

On variance estimation of target population created by inverse probability weighting

ABSTRACT Inverse probability weighting (IPW) is frequently used to reduce or minimize the observed confounding in observational studies. IPW creates a pseudo-sample by weighting each individual by the inverse of the conditional probability of receiving the treatment level that he/she has actually received. In the pseudo-sample there is no variation among the multiple individuals generated by weighting the same individual in the original sample. This would reduce the variability of the data and therefore bias the variance estimate in the target population. Conventional variance estimation methods for IPW estimators generally ignore this underestimation and tend to produce biased estimates of variance. We here propose a more reasonable method that incorporates this source of variability by using parametric bootstrapping based on intra-stratum variability estimates. This approach firstly uses propensity score stratification and intra-stratum standard deviation to approximate the variability among multiple individuals generated based on a single individual whose propensity score falls within the corresponding stratum. The parametric bootstrapping is then used to incorporate the target variability by re-generating outcomes after adding a random error term to the original data. The performance of the proposed method is compared with three existing methods including the naïve model-based variance estimator, the nonparametric bootstrap variance estimator, and the robust variance estimator in the simulation section. An example of patients with sarcopenia is used to illustrate the implementation of the proposed approach. According to the results, the proposed approach has desirable statistical properties and can be easily implemented using the provided R code.

The Effects of Urban Sprawl on Electricity Consumption: Empirical Evidence from 283 Prefecture-Level Cities in China

Under the urban development trend of sprawl, improving energy use efficiency is a proper way to promote green and low-carbon construction in cities. This paper uses panel data from 283 prefecture-level and above cities in China from 2008 to 2019 to measure the urban sprawl index, and analyze the spatial-temporal evolution law of urban sprawl and electricity consumption. The relationship between urban sprawl and electricity consumption is empirically examined, and the differential effect of urban sprawl on electricity consumption is analyzed. Finally, the impact of urban sprawl on electricity consumption based on a spatial perspective is explored in depth by establishing a spatial error model. We found the following: (1) The levels of urban sprawl and urban electricity consumption are on the rise. The spatial distribution of urban sprawl is more dispersed, and cities with high electricity consumption levels are mostly concentrated in the eastern coastal areas. (2) Urban sprawl exacerbates electricity consumption, and this conclusion is still robust after a series of robustness tests were conducted and endogeneity issues were taken into account. In terms of the influence mechanism, urban sprawl mainly affects electricity consumption by changing the allocation of land resources, increasing the dependence on private transportation, and inhibiting green technology innovation. (3) The incremental effect of urban sprawl on electricity consumption is more pronounced in cities with high sprawl levels, weak environmental regulations, and low green innovation levels, as well as in west cities. (4) Urban sprawl and electricity consumption both have a significant positive spatial correlation. Electricity consumption of cities is not only related to their own regions but also influenced by the adjacent regions, and the spatial correlation is mainly reflected in the random error term. This paper deepens the understanding of the basic laws of urban sprawl affecting urban low-carbon development, which also has implications for new urbanization strategies and green development.

Nonparametric spatial autoregressive model using deep neural networks

With the rapid development of social networks, spatial autoregressive models with covariates are increasingly used in practice. We introduce spatial effects into the artificial neural network model and propose a new method for spatial data prediction. Our method is based on artificial neural network, combined with the idea of nonparametric spatial autoregressive model. The spatial lag term is a input of the network, considering the spatial effect of variables. The feature of strong generalization ability of the artificial neural network model is given full play. The simulation results point out that the proposed method has better prediction accuracy than the maximum likelihood method, naive least squares method and B-spline method when the random error term obey non-normal distribution; in the case of spatial effects of the data, the proposed model has significantly improved the prediction effect compared with the common artificial neural network.

PRODUCTION FUNCTION FOR MEASURING RETURNS TO SCALE IN THE GARMENT SECTOR: A CASE STUDY OF BANGLADESH

This paper empirically examines whether the production function of the garment sector of Bangladesh is operating under increasing returns to scale. The Cobb-Douglas production function is estimated using the advanced level of econometric techniques based on primary data. GLS estimates indicate that the productivity of labor force is 22.17% and the productivity of capital investment is 61.02%, statistically significant at any significance level. Thus, the production function of the garment sector of Bangladesh is operating under decreasing return to scale. From the GLS estimate of R2 , it is clear that about 99.97% of the total variation of the dependent variable output is explained by the fitted regression equation. Thus, the model fits the data very well. The diagnostic test results show that there are no problems of autocorrelation, heteroscedasticity, autoregressive conditional heteroscedasticity and normality of the random error terms. The test results also confirm that the model is correctly specified. It is also found that the average marginal productivity of labor force is 0.0236 and the average marginal productivity of capital investment is 0.5222 in the garment sector of Bangladesh. Since the marginal productivity of labor force is smaller than the capital investment, it can be said that these factories cannot reduce production costs by shifting resources from capital intensive techniques to labor intensive techniques. As a result, this sector cannot generate additional employment opportunities, which is not a good sign. The CUSUM and CUSUMSQ tests results confirm that the preferred production function of the garment sector of Bangladesh can be used for policy decision-making purposes.

Statistical learning algorithms for dendritic neuron model artificial neural network based on sine cosine algorithm

Training of dendritic neuron model artificial neural networks is generally achieved by using nonlinear least square methods. The distribution of random error terms is ignored in training algorithms although error terms are random variables. Maximum likelihood estimators can be obtained for dendritic neuron model artificial neural networks by using some indefinite symmetric probability distributions. In this study, statistical learning algorithms are proposed for dendritic neuron model artificial neural networks. Maximum likelihood estimators for dendritic neuron model artificial neural networks are obtained by using Normal, Cauchy, Logistic, Gumbel and Laplace distributions. The Sine cosine algorithm is used for maximization of the likelihood function under error terms that have Normal, Cauchy, Logistic, Gumbel and Laplace distributions. The proposed learning algorithms are applied to Istanbul Stock Exchange time series data sets. At the end of the analysis of application results, the performance of the proposed method is statistically better than well-known deep and shallow artificial neural networks.

Efficiency Decomposition Analysis of the Marine Ship Industry Chain Based on Three-Stage Super-Efficiency SBM Model—Evidence from Chinese A-Share-Listed Companies

Based on the micro-data of 79 listed companies in the Chinese marine ship industry chain from 2015 to 2019, this paper calculates the comprehensive technical efficiency (TE), pure technical efficiency (PTE), and scale efficiency (SE) of the upstream, midstream, and downstream of China’s marine ship industry chain by using a three-stage super-efficiency slacks-based model (SBM), and further analyzes the weak links in industrial chain efficiency and their influencing factors. It is shown that (i) the TE and PTE of the upstream, midstream, and downstream of China’s marine ship industry chain are in a “V”-shaped distribution, high at both ends and low in the middle, but that the SE is ranked as follows: upstream &gt; midstream &gt; downstream. In addition, the PTE is the main factor which hinders the improvement of TE in the industrial chain. (ii) The environmental variables have significant impacts on industrial chain efficiency. When the influences of environmental variables and random error terms are excluded, the industrial chain efficiency changes significantly. The values of SE and TE decrease significantly, and the distribution characteristic of TE changes. However, the PTE is still in a “V”-shaped distribution and appears to be the main driving force for the progress of TE. (iii) China’s marine ship industry chain has obvious weak links in terms of efficiency, and the midstream and downstream areas need to focus on development. Each link of the industry chain has high coupling and low coordination, and they are all closely related to each other, but the coordination ability is insufficient. The industrial chain in terms of efficiency and coordinated development can still be improved.

Analysis of Perception Variance in Regret Choice Modeling Based on GPS Data Considering Building Environment Effects

The purpose of this paper is to deal with the perception variance problem in regret model by scaling perception variance and relaxing the distribution assumption of the random error term, which are corresponding to the attribute and alternative differences, respectively. Specifically, the power coefficient in regret function can capture individual perception variance of specific attributes and latent class structure is used to analyze individual heterogeneity of alternative differences by defining weight function. Accordingly, perceiving behaviors of individuals are analyzed in depth and generating absolute and relative behavior interpretation and asymmetric property. The proposed models are estimated and analyzed using GPS data of taxis in Guangzhou, and bicycle household surveys are collected in Tel Aviv metropolitan area. The results show both significant effects of attributes on drivers’ and cyclists’ route choice behavior and identification of different types (absolute or relative) of perceiving attribute and alternative regret differences of the two travelers by incorporating the ratio of length between chosen route and the shortest route.

Capturing and utilizing the random feature in Monte Carlo fission source distributions

The Monte Carlo algorithm commonly adopts the power iteration (PI) process in criticality calculations. Previous studies have shown that random error term in the PI process significantly influences the source convergence diagnosis and variance underestimation phenomenon. This paper uses the Sliced Wasserstein (SW) distance of the fission source distributions (FSDs) to estimate the error terms in the PI process. Three mesh-free SW-based methods are proposed to capture the random error term's 1m feature for the OECD source convergence fissile slab model, sphere array model, and the BEAVRS model. Then, a mesh-free source convergence auto-diagnosis algorithm is introduced based on the methods. The algorithm sets the batch size at five stages. The 1m feature of the random error term is utilized to achieve auto-diagnosis at the target batch size. Numerical calculation results show that the auto-diagnosis algorithm is practical and efficient for source convergence diagnosis and acceleration, which can automatically save 58 % to 81 % of the computational time to reach a converged fission source in models with the dominance ratio of around 0.99.

Sparsity enforced time–frequency decomposition in the Bayesian framework for bearing fault feature extraction under time-varying conditions

Fault characteristic extraction of rolling bearings is essential for fault diagnosis. Rolling bearings are usually operated at changing speeds, and the nonstationary signals of the bearings are covered by the heavy background noise, making the extraction task of fault features very difficult. To address this issue, a robust fault characteristic extraction approach based on the time–frequency analysis under variable speed conditions is proposed in this paper. Firstly, the sparse property of the time-variant fault characteristics and low-rankness of background noise are explored and utilized in the time–frequency representation (TFR). Then, the sparse and the low-rank components are integrated into a hierarchical Bayesian model, and a random error term is considered to make the Bayesian model more robust. The Gibbs sampler is applied to extract the desired sparsity-enhanced component of the TFR in the Bayesian framework. Eventually, the time–frequency reassignment technique is adopted further to optimize the time–frequency resolution of the sparse component. Two simulated scenarios and a real-data experiment are used to evaluate the suggested approach’s performance. It turns out that the proposed approach is robust to noise and can extract the bearing time-varying fault features effectively.

Z-score regression model for coronary artery diameter in healthy Chinese Han children.

Coronary artery distension and aneurysm are complications of Kawasaki disease in children. To develop a Z-score regression model for coronary artery diameter in children that could be used as reference. This retrospective analysis included children with normal heart structure between March 2013 and April 2017. Body surface area (BSA) was calculated. The diameters of the right coronary, left main coronary, left anterior descending, and circumflex arteries were measured by echocardiography. Pearson correlation analysis was used to establish linear, exponential, logarithmic, power, and square root regression models. The analysis included 509 children (280 boys) aged 1 day to 15.2 years. Coronary artery diameters were significantly correlated with age, height, body mass, BSA, and (r = 0.663-0.826; P < 0.05), with a stronger correlation for than BSA (P < 0.05). The adjusted determination coefficients () were higher for the exponential and square root models than for the other models (P < 0.05). The random error term variance was constant for the exponential model (P > 0.05), and processing with the weighted least-square methods eliminated heteroscedasticity in the other models. The Z-scores were normally distributed for the exponential and square root models (P > 0.05). Overall, the square root model was the optimal equation for the calculation of coronary artery Z-score in Chinese Han children. This model could be used to facilitate the diagnosis of coronary artery distension in children with suspected Kawasaki disease.

NONPARAMETRIC REGRESSION WITH ERROR-IN-VARIABLES MODEL BASED ON DIFFERENT KERNEL FUNCTIONS

Estimation of error-invariable models is a specific problem in different fields such as medicine, economics, industry, and biostatistics. The main different between classical regression and error-in-variable models is that explanatory variables involve random error terms. Therefore, classical estimation methods that do not include the necessary adjustments for the contaminated explanatory variables give biased results. Regarding the error-in variables, there are important studied in the literature such as [1], [2], [3], [4], [5] and [6]. In this paper, nonparametric regression with measurement error is considered and estimated by kernel smoothing estimator which is studied detailed by [6]. This paper differs from their study with the idea of using two different kernel functions to compared them on quality of estimations. These functions are suitable for different error behaviors (see [7]). The goal of the paper is encouraged by a Monte Carlo simulation study and results are presented.

The method of MEMS gyroscope random error compensation based on ARMA

In order to suppress the random error of micro electro-mechanical system (MEMS) gyroscope, the method based on optimized auto regressive moving average (ARMA) model is proposed to solve problems such as poor extraction of trend items during signal preprocessing and strong subjectivity in ARMA ordering. Firstly, the trend item of MEMS gyroscope data is extracted by empirical mode decomposition (EMD) to obtain a stable and zero-mean time series. In order to reduce the subjective influence of the traditional ARMA ordering method, genetic algorithm theory is used to optimize the ordering process. Choose the order corresponding to the highest fitness function as the modeling order and use the recursive augmented least squares method to estimate the model parameters. So far, a complete mathematical model can be established. Finally, adaptive Kalman filter (AKF) is used to compensate the random error of the MEMS gyroscope. Compensate the same MEMS gyroscope signal before and after optimization. Experiments show that the accuracy of EMD de-trending and optimized ARMA is better than the traditional method. After AKF compensation, under the premise that the mean does not change, the standard deviation is reduced by 27% in this paper. The coefficients of the main random error terms are significantly reduced, which further improves the accuracy of the MEMS gyroscope.

Fitting the Search Space of Weight-sharing NAS with Graph Convolutional Networks

Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from which exponentially many sub-networks can be sampled and efficiently evaluated. These methods enjoy great advantages in terms of computational costs, but the sampled sub-networks are not guaranteed to be estimated precisely unless an individual training process is taken. This paper owes such inaccuracy to the inevitable mismatch between assembled network layers, so that there is a random error term added to each estimation. We alleviate this issue by training a graph convolutional network to fit the performance of sampled sub-networks so that the impact of random errors becomes minimal. With this strategy, we achieve a higher rank correlation coefficient in the selected set of candidates, which consequently leads to better performance of the final architecture. In addition, our approach also enjoys the flexibility of being used under different hardware constraints, since the graph convolutional network has provided an efficient lookup table of the performance of architectures in the entire search space.

Dynamic prediction based on variability of a longitudinal biomarker

BackgroundTacrolimus is given post-kidney transplant to suppress the immune system, and the amount of drug in the body is measured frequently. Higher variability over time may be indicative of poor drug adherence, leading to more adverse events. It is important to account for the variation in Tacrolimus, not just the average change over time.MethodsUsing data from the University of Colorado, we compare methods of assessing how the variability in Tacrolimus influences the hazard of de novo Donor Specific Antibodies (dnDSA), an early warning sign of graft failure. We compare multiple joint models in terms of fit and predictive ability. We explain that the models that account for the individual-specific variability over time have the best predictive performance. These models allowed each patient to have an individual-specific random error term in the longitudinal Tacrolimus model, and linked this to the hazard of dnDSA model.ResultsThe hazard for the variance and coefficient of variation (CV) loading parameter were greater than 1, indicating that higher variability of Tacrolimus had a higher hazard of dnDSA. Introducing the individual-specific variability improved the fit, leading to more accurate predictions about the individual-specific time-to-dnDSA.ConclusionsWe showed that the individual’s variability in Tacrolimus is an important metric in predicting long-term adverse events in kidney transplantation. This is an important step in personalizing the dosage of TAC post-transplant to improve outcomes post-transplant.

Using The Fully Modified M Method In Estimating The Effect Of Cultivated Area On Barley Production In Iraq For The Period 1970-2018

The research is concerned with estimating the effect of the cultivated area of barley crop on the production of that crop by estimating the regression model representing the relationship of these two variables. The results of the tests indicated that the time series of the response variable values is stationary and the series of values of the explanatory variable were nonstationary and that they were integrated of order one ( I(1) ), these tests also indicate that the random error terms are auto correlated and can be modeled according to the mixed autoregressive-moving average models ARMA(p,q), for these results we cannot use the classical estimation method to estimate our regression model, therefore, a fully modified M method was adopted, which is a robust estimation methods, The estimated results indicate a positive significant relation between the production of barley crop and cultivated area.