以ML檢定統計量評估結構方程模型足夠樣本人數之決定

Determination of Sufficient Sample Sizes in SEM via ML-based Test Statistics

劉心筠(Hsin-Yun Liu)

指導教授 ： 翁儷禎

國立臺灣大學/理學院/心理學研究所/博士(2011年)

https://doi.org/10.6342/NTU.2011.02952

摘要

結構方程模型奠基於大樣本理論，需要具有足夠的樣本人數，方能避免影響檢定統計量與參數估計值之統計特性而誤導研究推論，故足夠樣本人數為實徵研究者關切的議題。樣本人數取決方法主要有三種取向，絕對樣本人數、樣本人數與參數數目的比值（N:q）、與檢定力分析法，直至目前尚未有三種取向的比較研究，對於樣本人數議題也尚未有定論。本模擬研究在假設模式為真與假設模式錯誤情境下，操弄模式規模、樣本人數、因素負荷量與變項分配，以檢定統計量與適合度指標的表現，比較絕對樣本人數200人、N:q比、與RMSEA檢定力法，並提出樣本人數取決之適宜準則，做為研究者決定樣本人數之參考。結果顯示，當變項為常態分配，絕對樣本人數200人與RMSEA檢定力法建議的樣本人數，因未能適當地反映模式規模，對於規模較大的模式（以參數數目為定義），建議的樣本人數可能會有不適宜的情形。相較之下，可以反映模式規模的N:q比值為較適當之樣本人數取決方法，N:q≧10為可行的樣本人數取決原則。當變項為輕微偏離常態分配，以SBS統計量分析，N:q≧10為可行的樣本人數取決原則，但隨著變項越偏離常態分配，需要更多的樣本人數方能有穩定的分析結果。在適合度指標方面，當N:q≧5，即使變項為非常態分配，仍有可接受的表現。

關鍵字

結構方程模式 ； 樣本人數 ； 參數數目 ； 卡方統計量 ； 適合度指標

並列摘要

The statistical theory of structural equation modeling (SEM) is based on large sample theory. Thus, determining a sufficient sample size is an important issue for application of the method. The commonly adopted approaches to the issue include absolute sample size, ratio of sample size to number of parameters, and power analysis via RMSEA (root mean squared error of approximation). Yet, there have been no comparative studies of these three approaches and no consensus concerning the optimal sample size determination with SEM has been reached. The present Monte Carlo study is designed to explore the appropriateness of the sample sizes suggested by these three approaches by examining the performance of maximum likelihood-based test statistics and fit indices. Distributions of variables, sample sizes, models of various sizes, and factor loadings were systematically manipulated. For variables of normal distribution, results showed that absolute minimum sample size and sample size suggested by power analysis via RMSEA were insufficient against large models (operationally defined by the number of estimated parameters). This, therefore, implicitly highlights the importance of considering sample size in relation to the number of parameters estimated (q). The findings suggested that N:q ≧ 10 seemed a plausible rule of thumb for sample size determination in SEM. For slightly nonnormally-distributed data, the results suggested that N:q ≧ 10 might also be a plausible rule of thumb. Moreover, the optimal N:q ratios needed to be larger in order to yield trustworthy test statistics as the degree of non-normality in the data increased. In addition, the behavior of fit indices could be considered acceptable with N:q ≧ 5, even for non-normally distributed variables.

並列關鍵字

structural equation modeling ； sample size ； number of estimated parameters ； test statistics ； fit indices

參考文獻

翁儷禎、鄭中平(1996)。結構方程模型增益性適合度指標與估計方法之關係。「調查研究」，2，89-109。

Satorra, A. & Bentler, P. M. (1988). Scaling corrections for chi-square statistics in covariance structure analysis. American Statistical Association 1988 proceedings of the Business and Economics Sections (pp. 308-313). Alexandria, VA: American Statistical Association.

Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factory analysis. Psychometrika, 49, 155-173.

Barrett, P. (2007). Structural equation modeling: Adjudging model fit. Personality and Individual Differences, 42, 815-824.

Bentler, P. M., & Chou, C. -P. (1987). Practical issues in structural modeling, Sociological Methods and Research, 16, 78-117.