: On 18 Jun 2003 15:08:24 -0700, [EMAIL PROTECTED] (Dianne Worth) : wrote: :> My next question is this: :> Rather than multiple regression, I want to use structural equation :> modeling. The sample is < 250, which I've been told is not large :> enough for LISREL. The alternative software uses partial least
The issue of sample size for SEM is rather confusing (to me, at least). The number 200 (or 250?) gets thrown around a lot, I think, because of an early paper by Boomsma which showed that there are convergence problems in a certain type of model when N < 200. There are many more things to consider, however, when determining the appropriate sample size for SEM, not the least of which include the distribution of the observed variables, the number of indicators per latent variable, power considerations. Below I've reproduced an excellent brief summary of the literature that a PhD student in Norway posted to the SEM listserv some time back. I'm sure you'll find more than this if you search the SEMNET archives at http://bama.ua.edu/archives/semnet.html Mike Babyak >>> Joar Vittersx <[EMAIL PROTECTED]> 01/29/98 08:34am >>> SEMNETTERS Bentler & Chou (1987) suggested that a ratio as low as 5 subjects per parameter would be sufficient if the data are normally distributed: "The ratio of sample size to the number of free parameters may be able to go as low as 5:1 under normal and elliptical theory, especially when there are many indicators of the latent variable and the associated loadings are large." (p.173). If the data are not normally distributed, on the other hand, a sample size of 5000 subjects may sometimes be needed (Hu & Bentler, 1995) In general, Anderson and Gerbing argues that a sample size of 150 or more typically will be needed to obtain parameter estimates that have standard errors small enough to be of practical use (Anderson & Gerbing, 1988, p. 415). Boomsma (1982) found that sample sizes of 100 to be accurate under ML estimation with normal data. In a series of Monte Carlos studies with sample sizes between 150 and 1000, Finch, West & MacKinnon (1997) found that estimates of model parameters were generally unaffected by sample size. Barrett & Kline (1981), using real data, reported that a minimum of 50 subjects were the minimum needed to reproduce the factor pattern of the Sixteen Personality Factor Questionnaire. Finally, sample size as a function of the number of variables was not found to be an important factor in determining stability in structural equation modeling in a study by Guadagnoli & Velicer (1988). In this study, the sample sizes varied from 50 to 1000 and the number of variables ranged from 36 to 144. Component saturation and absolute sample size were found to be the most important factors, and with high component saturation (i.e. factor loadings of .80) solutions were stable across replicated samples regardless of the number of indicators, even with as few as 50 participants. With factor loadings of .60, a sample size of 150 should be sufficient to obtain an accurate solution. References Anderson, J. C., & Gerbing, D. W. (1988). Structural Equation modeling in practice : A review and recommended two-step approach. Psychological Bulletin, 103(3), 411-423. Barrett, P. T., & Kline, P. (1981). The observation to variable ratio in factor analysis. Personality Study and Group Behavior, 1, 23-33. Bentler, P. M., & Chou, C. (1987). Practical issues in structural modelling. Socialogocal Methods and Research, 16, 78-117. Boomsma, A. (1982). The robustness of LISREL against smal sample size in factor analysis models. In K. G. J�reskog & H. Wold (Eds.), Systems under indirect observaion, Part 1 (pp. 149-173). Amsterdam: North-Holland. Finch, J. F., West, S. G., & MacKinnon, D. P. (1997). Effects of sample size and nonnormality on the estimation of mediated effects in latent variable models. Structural Equation Modeling, 4(2), 87-107. Guadagnoli, E., & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103(2), 265-275. Hu, L.-T., & Bentler, P. (1995). Evaluating model fit. In R. H. Hoyle (Ed.), Structural Equation Modeling. Concepts, Issues, and Applications . London: Sage. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
