不完整資料對共變數矩陣估計正確性的探討：實徵性研究

The Estimation of Covariance Matrices on Incomplete Data: An Empirical Study

吳鐵雄(Tieh-Hsiung Wu)

《教育心理學報》 14期 (1981/06) Pp. 189-204

https://doi.org/10.6251/BEP.19810601.13

摘要

本研究以電腦模擬資料方式，探討變數取樣各種因素對共變數矩陣估計之影響。這些因素包括：變數數目，變數間平均相關係數、樣本數、變數取樣比率、設計型態等，全部探討的設計組合共有56種。並以槪化變異數、軌跡、和最大根做為探討估計正確性之數量。一般地說，估計偏差相當大，尤以槪化變異數為甚。在所有因素中，以變數間平均相關係數估計影響最大，變數數目則無甚作用，其他如取樣比率、設計型態則結果不甚一致。意外地，樣本數的大小對估計之正確性並無明顯影響。

並列摘要

This Monte Carlo study, utilizing variable sampling approach, is to systematically investigatethe estimation of covariance matrices from incomplete data. The parametersstudied were generalized variance, trace of a matrix, and the largest root. Five factors which related to sampling plan were included: number of variables, average correlationamong variables, sample size, proportion of variable sampling, pattern of design. The sampling plans were organized by balanced incomplete block design (BIBD) and partially balanced incomplete block design (PBIBD). There were 56 conditions studied.
The results of estimates were quite biased, especially those of generalized variance. Some negative-definite matrices occured for high correlation matrices, small sample. Among the factors studied, average correlation among variables seems to be the most importantone. There were no consistent pattern for the rest of the factors in terms of accuracy of estimation. Surprisely, the estimation from the large sample size was not substantially better than those from the small sample size.