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Effect of Correlation Between Abilities Under Between-Item Dimensionality
Issue:
Volume 11, Issue 4, July 2022
Pages:
109-113
Received:
16 June 2022
Accepted:
22 July 2022
Published:
29 July 2022
DOI:
10.11648/j.ajtas.20221104.11
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Abstract: The Item Response Theory (IRT) evaluates the relationship between people’s ability and test items, and it includes unidimensional and multidimensional models. One key assumption for the unidimensional IRT model is that only one dimension of ability should be tested. However, since people’s abilities are latent, many datasets fitted with the unidimensional IRT model reflect abilities from more than one dimension in fact. To identify the consequence of fitting the unidimensional IRT model on correlated abilities, this research focuses on when the correlated abilities can be treated as a single ability, the possible pattern of misfit, and if it is reduced by higher correlated abilities. In the research, the misfits are evaluated by applying unidimensional 2-parameter logistic (2PL) IRT model while the datasets are simulated with items testing two different correlated. The dimensionalities are examined with abilities correlated to different degrees, and the misfit of using the unidimensional IRT model is tested by comparing the item difficulties and item discriminations from the fitted model and the true parameters. The results show that when the correlation between abilities is higher than 0.95, the unidimensional model can be fit without bias. But for all simulated datasets with correlated abilities below 0.95, the estimated item parameters using the unidimensional model are biased and the biases are not reduced with increasing correlation if multiple factors are identified for abilities.
Abstract: The Item Response Theory (IRT) evaluates the relationship between people’s ability and test items, and it includes unidimensional and multidimensional models. One key assumption for the unidimensional IRT model is that only one dimension of ability should be tested. However, since people’s abilities are latent, many datasets fitted with the unidime...
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Adaptive Survey Design for the Dutch Labour Force Survey
Issue:
Volume 11, Issue 4, July 2022
Pages:
114-121
Received:
19 July 2022
Accepted:
23 August 2022
Published:
31 August 2022
DOI:
10.11648/j.ajtas.20221104.12
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Abstract: A challenge for the National Statistical Institutes is to produce reliable statistics with a limited budget for data collection. During the past years, many surveys at Statistics Netherlands were redesigned to reduce costs and to increase or maintain response rates. From 2018 onwards, adaptive survey design has been applied in several social surveys to produce more accurate statistics within the same budget. In previous years, research has been done on the impact on quality and costs of reducing the use of interviewers in mixed-mode surveys that start with Internet observation, followed by telephone or face-to-face observation of Internet nonrespondents. Reducing follow-ups can be done in different ways. By using stratified selection of people eligible for follow-up, nonresponse bias may be reduced. The main decisions to be made are how to divide the population into strata and how to compute the allocation probabilities for face-to-face and telephone observation in the different strata. For this purpose, a methodology has been developed in this paper. The methodology is applied in the development of an adaptive survey design for the Dutch Labour Force Survey. Attention is paid to the survey design, in particular the sampling design, the data collection constraints, the choice of the strata for the adaptive design, the calculation of follow-up fractions by mode of observation and stratum, the practical implementation of the adaptive design, and some response and survey results.
Abstract: A challenge for the National Statistical Institutes is to produce reliable statistics with a limited budget for data collection. During the past years, many surveys at Statistics Netherlands were redesigned to reduce costs and to increase or maintain response rates. From 2018 onwards, adaptive survey design has been applied in several social survey...
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Principal Component Analysis of Standard and Spherical Covariances from the Population and Random Samples to Real and Simulated Data
Inge Koch,
Lyron Winderbaum,
Kanta Naito
Issue:
Volume 11, Issue 4, July 2022
Pages:
122-139
Received:
12 August 2022
Accepted:
5 September 2022
Published:
26 September 2022
DOI:
10.11648/j.ajtas.20221104.13
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Views:
Abstract: Principal component analysis (PCA) is the tool of choice for summarising multivariate and high-dimensional data as features in a lower-dimensional space. PCA works well for Gaussian data, but may not do so well for high-dimensional, skewed or heavy-tailed data or data with outliers as encountered in practice. The availability of complex data has enhanced these shortcomings and increased the demand for PC approaches that perform well for such data. The purpose of this paper is to critically appraise a class of interpretable PC candidates which can respond to this demand and to compare their performance to that of standard PCA. Among the large variety of nonlinear PCA, we concentrate on the subclass that is based on spherical covariance matrices. This subclass includes the spatial sign, spatial rank, and Kendall’s τ covariance matrix. We focus on three key aspects: population concepts and their properties; sample-based estimators; and actual practice based on the analysis of real and simulated data. At the population level we consider relationships between the standard covariance matrix and spherical covariance matrices. For the random sample we consider natural estimators of the population eigenvectors, look at appropriate distributional models, highlight relationships between different estimators and relate properties of estimators and their population analogues. We complement the theory we present with new analyses of multivariate and high-dimensional real data as well as simulated data from diverse distributions which elucidates behaviour patterns of spherical PCA for elliptic and non-elliptic distributions. The latter are not captured in the theoretical framework, and their inclusion therefore offers fresh insight into the performance of spherical PCA. The combination of the theory and the new analysis evidence that PCA of rank-based covariances severely outperforms that based on the potentially unstable spatial sign covariance matrix. Further, the overall good performance of rank-based PCA and its superior properties for data for which the sample covariance matrix has been known to perform poorly make rank-based PCA not only a desirable addition to standard PCA, but render it a serious competitor for dimension reduction and feature selection while retaining features valued in PCA.
Abstract: Principal component analysis (PCA) is the tool of choice for summarising multivariate and high-dimensional data as features in a lower-dimensional space. PCA works well for Gaussian data, but may not do so well for high-dimensional, skewed or heavy-tailed data or data with outliers as encountered in practice. The availability of complex data has en...
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