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This chapter draws from an understanding of measurement error to address practical issues that arise in measurement and research design in the day-to-day conduct of research. The topics include constructs and measurement error, the measure development process, and the indicators of measurement error. The discussion covers types of measurement error, types of measures, and common scenarios in conducting research, linking measurement to research design.

Researchers in economics and other disciplines are often interested in the causal effect of a binary treatment on outcomes. Econometric methods used to estimate such effects are divided into one of two strands depending on whether they require unconfoundedness (i.e., independence of potential outcomes and treatment assignment conditional on a set of observable covariates). When this assumption holds, researchers now have a wide array of estimation techniques from which to choose. However, very little is known about their performance – both in absolute and relative terms – when measurement error is present. In this study, the performance of several estimators that require unconfoundedness, as well as some that do not, are evaluated in a Monte Carlo study. In all cases, the data-generating process is such that unconfoundedness holds with the ‘real’ data. However, measurement error is then introduced. Specifically, three types of measurement error are considered: (i) errors in treatment assignment, (ii) errors in the outcome, and (iii) errors in the vector of covariates. Recommendations for researchers are provided.

The purpose of this paper is to propose an innovative method to extend the operating range of the laser tracking system and improve the accuracy and automation of boresighting by designing a measurement instrument. Boresighting is a process that aligns the direction of special equipment with the aircraft reference axis. Sometimes the accurate measurement and adjustment of the equipment and the aircraft are hard to achieve.

The aircraft is moved by an automatic adjustment system which consists of three numerical control positioners. For obtaining the position of the bore axis, an instrument with two measurement points is designed. Based on the multivariate normal distribution hypothesis, an uncertainty evaluation method for the aiming points is introduced. The accuracy of the measurement point is described by an uncertainty ellipsoid. A compensation and calibration method is proposed to decrease the effect of manufacturing error and deflection error by the finite element analysis.

The experimental results of the boresighting measurement prove that the proposed method is effective and reliable in digital assembly. The measurement accuracy of the angle between the bore axis and the reference axis is about ±0.004°. In addition, the measurement result is mainly influenced by the position error of the instrument.

The results of this study will provide a new way to obtain and control the installation deviation of part in aircraft digital assembly and will help to improve the precision and efficiency. This measurement method can be applied to obtain the axis of a deep blind hole.

A multi-laser sensors-based measurement instrument is proposed for the measurement of geometry errors of a differential body and quality evaluation. This paper aims to discuss the aforementioned idea.

First, the differential body is set on a rotation platform before measuring. Then one laser sensor called as “primary sensor”, is installed on the intern of the differential body. The spherical surface and four holes on the differential body are sampled by the primary sensor when the rotation platform rotates one revolution. Another sensor called as “secondary sensor”, is installed above to sample the external cylinder surface and the planar surface on the top of the differential body, and the external cylinder surface and the planar surface are high in manufacturing precision, which are used as datum surfaces to compute the errors caused by the motion of the rotation platform. Finally, the sampled points from the primary sensor are compensated to improve the measurement accuracy.

A multi-laser sensors-based measurement instrument is proposed for the measurement of geometry errors of a differential body. Based on the characteristics of the measurement data, a gradient image-based method is proposed to distinguish different objects from laser measurement data. A case study is presented to validate the measurement principle and data processing approach.

The study investigates the possibility of correction of sensor data by the measurement results of multiple sensors to improving measurement accuracy. The proposed technique enables the error analysis and compensation by the geometric correlation relationship of various features on the measurand.

The proposed error compensation principle by using multiple sensors proved to be useful for the design of new measurement device for special part inspection. The proposed approach to describe the measuring data by image also is proved to be useful to simplify the measurement data processing.

The purpose of this paper is to propose a method for selecting the position and attitude trajectory of error measurement to improve the kinematic calibration efficiency of a one translational and two rotational (1T2R) parallel power head and to improve the error compensation effect by improving the properties of the error identification matrix.

First, a general mapping model between the endpoint synthesis error is established and each geometric error source. Second, a model for optimizing the position and attitude trajectory of error measurement based on sensitivity analysis results is proposed, providing a basis for optimizing the error measurement trajectory of the mechanism in the working space. Finally, distance error measurement information and principal component analysis (PCA) ideas are used to construct an error identification matrix. The robustness and compensation effect of the identification algorithm were verified by simulation and through experiments.

Through sensitivity analysis, it is found that the distribution of the sensitivity coefficient of each error source in the plane of the workspace can approximately represent its distribution in the workspace, and when the end of the mechanism moves in a circle with a large nutation angle, the comprehensive influence coefficient of each sensitivity is the largest. Residual analysis shows that the robustness of the identification algorithm with the idea of PCA is improved. Through experiments, it is found that the compensation effect is improved.

A model for optimizing the position and attitude trajectory of error measurement is proposed, which can effectively improve the error measurement efficiency of the 1T2R parallel mechanism. In addition, the PCA idea is introduced. A least-squares PCA error identification algorithm that improves the robustness of the identification algorithm by improving the property of the identification matrix is proposed, and the compensation effect is improved. This method has been verified by experiments on 1T2R parallel mechanism and can be extended to other similar parallel mechanisms.

This paper aims to present a novel transfer alignment method based on combined double-time observations with velocity and attitude for ships’ poor maneuverability to address the system errors introduced by flexural deformation and installing which are difficult to calibrate.

Based on velocity and attitude matching, redesigning and deducing Kalman filter model by combining double-time observation. By introducing the sampling of the previous update cycle of the strapdown inertial navigation system (SINS), current observation subtracts previous observation are used as measurements for transfer alignment filter, system error in measurement introduced by deformation and installing can be effectively removed.

The results of simulations and turntable tests show that when there is a system error, the proposed method can improve alignment accuracy, shorten the alignment process and not require any active maneuvers or additional sensor equipment.

Calibrating those deformations and installing errors during transfer alignment need special maneuvers along different axes, which is difficult to fulfill for ships’ poor maneuverability. Without additional sensor equipment and active maneuvers, the system errors in attitude measurement can be eliminated by the proposed algorithms, meanwhile improving the accuracy of the shipboard SINS transfer alignment.

To clarify the nature of the error term in formative measurement models, as it had been misinterpreted in prior research.

The error term in formative measurement models is analytically contrasted with the measurement errors typically found in reflective measurement models.

It is demonstrated that, unlike in reflective measurement, the error term in formative models is not measurement error but rather a disturbance representing non‐modeled causes. It is also shown that, under certain circumstances, the inclusion of an error term is not necessary/appropriate.

Focus is only on first‐order measurement models; higher‐order specifications are not considered.

The paper helps researchers in their initial specification of formative measurement models as well as their evaluation of the subsequent model estimates, leading to better specifications for formative constructs.

Revealed preference axioms provide a simple way of testing data from consumers or firms for consistency with optimizing behavior. The resulting non-parametric tests are very attractive, since they do not require any ad hoc functional form assumptions. A weakness of such tests, however, is that they are non-stochastic. In this paper, we provide a detailed analysis of two non-parametric approaches that can be used to derive statistical tests for utility maximization, which account for random measurement errors in the observed data. These same approaches can also be used to derive tests for separability of the utility function.

This chapter presents a model of distribution dynamics in the presence of measurement error in the underlying data. Studies of international growth convergence generally ignore the fact that per capita income data from the Penn World Table (PWT) are not only continuous variables but also measured with error. Together with short-time scale fluctuations, measurement error makes inferences potentially unreliable. When first-order, time-homogeneous Markov models are fitted to continuous data with measurement error, a bias towards excess mobility is introduced into the estimated transition probability matrix. This chapter evaluates different methods of accounting for this error. An EM algorithm is used for parameter estimation, and the methods are illustrated using data from the PWT Mark 6.1. Measurement error in income data is found to have quantitatively important effects on distribution dynamics. For instance, purging the data of measurement error reduces estimated transition intensities by between one- and four-fifths and more than halves the observed mobility of countries.

Large size of aircraft assembly tooling structure and complex measurement environment exist. The laid enhanced reference points (ERS) are subject to a combination of nonuniform temperature fields and measurement errors, resulting in increased measurement registration errors. In view of the nonuniform temperature field and measurement errors affecting the ERS point registration problem, the purpose of this paper is to propose a neural network-based ERS point registration compensation method for large-size measurement fields under a nonuniform temperature field.

The approach is to collect ERS point information and temperature data, normalize the collected data to complete the data structure design and complete the construction of the neural network prediction model by data training. The data learning is performed to complete the prediction model construction, and the prediction model is used to complete the compensation analysis of ERS points. Finally, the algorithm is verified through experiments and engineering practice.

Experimental results show that the proposed neural network-based ERS point prediction and compensation method for nonuniform temperature fields effectively predicts ERS point deformation under nonuniform temperature fields compared with the conventional method. After the compensation analysis, the registration error is effectively reduced to improve registration accuracy. Reducing the combined effect of environmental nonuniform temperature field and measurement error has apparent advantages.

The method reduces the registration error caused by combining a nonuniform temperature field and measurement error. It can be used for aircraft assembly site prediction and registration error compensation analysis, which is essential to improve measurement accuracy further.