Biomedical subjects

K H Yuan

Publications and source records attributed to K H Yuan.

5 recordsLinked to original sources

PubMed2000

Robust transformation with applications to structural equation modelling.

Data sets in social and behavioural sciences are seldom normal. Influential cases or outliers can lead to inappropriate solutions and problematic conclusions in structural equation modelling. By giving a proper weight to each case, the influence of outliers on a robust procedure can be minimized. We propose using a robust procedure as a transformation technique, generating a new data matrix that can be analysed by a variety of multivariate methods. Mardia's multivariate skewness and kurtosis statistics are used to measure the effect of the transformation in achieving approximate normality. Since the transformation makes the data approximately normal, applying a classical normal theory based procedure to the transformed data gives more efficient parameter estimates. Three procedures for parameter evaluation and model testing are discussed. Six examples illustrate the various aspects with the robust transformation.

Humans↗

PubMed1998

Robust mean and covariance structure analysis.

Covariance structure analysis is used to evaluate hypothesized influences among unmeasured latent and observed variables. As implemented, it is not robust to outliers and bad data. Several robust methods in model fitting and testing are proposed. These include direct estimation of M-estimators of structured parameters and a two-stage procedure based on robust M- and S-estimators of population covariances. The large sample properties of these estimators are obtained. The equivalence between a direct M-estimator and a two-stage estimator based on an M-estimator of population covariance is established when sampling from an elliptical distribution. Two test statistics are presented in judging the adequacy of a hypothesized model; both are asymptotically distribution free if using distribution free weight matrices. So these test statistics possess both finite sample and large sample robustness. The two-stage procedures can be easily adapted into standard software packages by modifying existing asymptotically distribution free procedures. To demonstrate the two-stage procedure, S-estimator and M-estimators under different weight functions are calculated for some real data sets.

Analysis of Variance↗

PubMed1998

Normal theory based test statistics in structural equation modelling.

Even though data sets in psychology are seldom normal, the statistics used to evaluate covariance structure models are typically based on the assumption of multivariate normality. Consequently, many conclusions based on normal theory methods are suspect. In this paper, we develop test statistics that can be correctly applied to the normal theory maximum likelihood estimator. We propose three new asymptotically distribution-free (ADF) test statistics that technically must yield improved behaviour in samples of realistic size, and use Monte Carlo methods to study their actual finite sample behaviour. Results indicate that there exists an ADF test statistic that also performs quite well in finite sample situations. Our analysis shows that various forms of ADF test statistics are sensitive to model degrees of freedom rather than to model complexity. A new index is proposed for evaluating whether a rescaled statistic will be robust. Recommendations are given regarding the application of each test statistic.

Humans↗

PubMed1996

Test of linear trend in eigenvalues of a covariance matrix with application to data analysis.

Principal component analysis and factor analysis are the most widely used tools for dimension reduction in data analysis. Both methods require some good criterion to judge the number of dimensions to be kept. The classical method focuses on testing the equality of eigenvalues. As real data hardly have this property, practitioners turn to some ad hoc criterion in judging the dimensionality of their data. One such popular method, the 'scree test' or 'scree plot' as described in many texts and statistical programs, is based on the trend in eigenvalues of sample covariance (correlation) matrix. The principal components or common factors corresponding to eigenvalues which exhibit a slow linear decrease are discarded in further data analysis. This paper develops a formal statistical test for the 'scree plot'. A special case of this test is the classical test for equality of eigenvalues which has been suggested in several texts as the criterion to decide the number of principal components to retain. Comparisons between equality of eigenvalues and the slow linear decrease in eigenvalues on some classical examples support the hypothesis of slow linear decrease. A physical background to such a phenomenon is also suggested.

Analysis of Variance↗

PubMed1968

[Nursing in Libya].

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Africa, Northern↗