The Implementation of Factor Analysis for Stratified Data

10.29973/JCSA.200609.0005

Chong-Yau Fu；Jeng-Hsiu Hung；Shih-Hua Liu；Hui-Chu Lin

factor analysis ； stratified data ； stratum mean-corrected ； normal subgroup mean-corrected ； binary discrimination

中國統計學報

44卷3期（2006 / 09 / 01）

296 - 315

英文

Stratification of data may be formed in design stage or post hoc stage. In model review, conditional logistic models and stratified Cox models are built for stratified data. In this study, stratified data in factor analysis is investigated; the stratum mean-corrected method is proposed. And, an alternative normal-subgroup mean-corrected method is used for extracted factors result connecting with binary outcome. Two corrected methods with uncorrected method are compared from the centered value of data deviated from. The stratum mean-corrected method completely removes the effect in the analyzed data in an additive form. In an example of fetal data, in which the extracted factors were combined with binary outcome variables for model tree built, the classified accuracy rate was 95% for normal subgroup mean-corrected data comparing 92% for uncorrected data when based on the same number of cutting points in their trees. Two corrected methods provide two adjusted algorithms separately for binary outcome involved or not. Their contribution is worth noting when the analyzed data are varied with an extra variable and the factor analysis is applied.

1. Altman, D. G.(1993).Construction of age-related reference centiles using absolute residuals.Statistics in Medicine,12,917-924.
2. Bland, J. M.,Peacock, J. L.,Anderson, H. R.,Brooke, O. G.,De Curtis, M.(1990).The adjustment of birth weight for very early gestational ages: Two related problems in statistical analysis.Applied Statistics,39,229-239.
3. Breiman, L.,Friedman, J. H.,Olshen, R. A.,Stone, C. J.(1984).Classification and Regression Trees.Boca Raton:Chapman & Hall.
4. Breslow, N. E.,Day, N. E.(1980).Statistical Methods in Cancer Research Vol 1: The Analysis of Case-Control Studies.Lyon, France:International Agency on Cancer.
5. Cochran, W. G.(1968).The effectiveness of adjustment by subclassification in removing bias in observational studies.Biometrics,24,295-313.
6. Cochran, W.G.(1977).Sampling Techniques.New York:Wiely.
7. Doherty, A. D.,James, I. R.,Newnham, J. P.(2002).Estimation of the Doppler Ultrasound Umblical Maximal Waveform Envelope: II. Prediction of Fetal Distress.Ultrasound in Medicine and Biology,28(10),1261-1270.
8. Fu, C. Y.,Hung, J. H.,Liu, S. H.,Chien, Y. L.(2005).A new algorithm for solving binary discrimination in conditional logistic regression, with two choices of strata.Computational Statistics and Data Analysis,49,85-97.
9. Hosmer, D. W.,Lemshow, S.(1999).Applied Survival Analysis.New York:Wiely.
10. Hung, J. H.,Fu, C. Y.,Yuan, C. C.,Chen, C. L.,Yang, M. L.,Shu, L. P.,Wu, C. C.(2003).Nuchal translucence incorporated into a one-stage multifactorial screening model for Down Syndrome prediction at second-trimester pregnancy.Ultrasound in medicine and biology,29(12),1667-1674.
11. Johnson, R. A.,Wichern, D. W.(2002).Applied Multivariate Statistical Analysis.NJ:Prentice-Hall, Inc.
12. Mari, G.,Deter, R. L.,Uerpairojkit, B.(1996).Flow velocity Waveforms of the Ductus Arteriosus in Appropriate and Small-for-Gestational-Age Fetuses.Clinical Ultrasound,24,185-196.
13. Sharma, S.(1996).Applied Multivariate Techniques.New York:Wiley.
14. Spearman, C.(1904).General intelligence objectively determined and measured.American Journal of Psychology,15,201-293.

1. Tsai Min-Hsun,Fu Chong-Yau(2007).REMOVING AN EXTRANEOUS EFFECT IN MEASURING CORRELATION COEFFICIENT.中國統計學報,45(4),386-401.