Bulletin Spring‧Summer 1996

extension to cope with more complex situations. Recently however it has been realized that there are three important types of non-standard data that violate the above-mentioned assumptions, and hence cannot be satisfactorily handled by the existing theory and programs. The first type of non-standard data are obtained from variables whose manifestations are only observable in a discrete (i.e. separate and distinct) polytomous (divided into more than two secondary parts of branches) form. Due to the nature of questionnaires involved, these polytomous variables are most common in behavioural and social research, as for instance in attitude items, performances items, rating scales, etc. A typical case is to ask a subject to report some attitude on a scale like: Disagree, No opinion, Agree. The assumption of continuity is obviously not valid for such data. The second type refers to data that are multilevel in nature, for example those obtained by samples of randomly drawn students from randomly drawn schools, or randomly drawn workmen from randomly drawn factories. As these individuals are drawn from the same group, they are expected to be influenced by certain common factors and hence produce observations that are correlated rather than independent. The last type refers to censored data that are frequently encountered in medical, industrial and economic studies. Such data consist of times to the occurrence of an event, such as the death of an experimental animal, the birth of a child, and the failure of a light bulb. For some units in the sample, time to occurrence is censored because the event has not occurred before the termination of the experiment. If only the time of censorship is recorded, information about the situation becomes incomplete — we only know that the event has failed to occur by the censorship time. While analysing the data relating to these situations, information needs to be handled carefully i f incorrect results are to be avoided. Successful Research Ef f or ts a t CUHK t o I nc l ude Such Data The aforementioned problems that structural equation models encounter with non-standard data have been investigated by Dr. S.Y. Lee and Dr. W.Y. Poon of the Department of Statistics, with the support of a grant of HK$440,000 awarded by the UGC Research Grants Council in 1991. They have successfully developed some efficient procedures and computer programs to solve the problems, and elucidated the associated statistical properties for model analysis. Studies in Monte Carlo indicate that the results obtained are satisfactory, and hence some of them have been adapted by the well-known EQS program. Thanks to the good work of CUHK researchers, structural equation models can now be applied to situations that involve the three major types of non-standard data. The researchers will continue to improve and refine the statistical methodologies so that such models can be applied to problems and situations that are even more complex. • References Bentler, Structural Equation Program Manual, Los Angeles: BMDP Statistical Software, 1992. Jöreskog, K.G. & Sörbom, D., LISREL VII: A guide to the Program and Applications, Chicago: SPSS Inc., 1989. 25