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| From | W Robert Long <W.R.Long@leeds.ac.uk> |
| To | "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |
| Subject | Re: st: Hierarchical CFA problem |
| Date | Mon, 22 Apr 2013 12:54:19 +0100 |
Hi John and thanks for your replyYes, I forgot to include the SDs in my post - I am working with raw data and it was an oversight - apologies for that, here they are:
ssd set sd 1.167432 1.177451 1.130979 1.164116 1.290472 1.095603 1.089534 1.012615 1.009152
FWIW, here are the means:ssd set means 4.93577 6.08804 2.250415 3.060908 4.340532 2.185572 4.185902 5.527076 5.374123
Regarding your second point, I was aware of the equivalence of models. Nevertheless I still wanted to fit the hierarchical model, as outlined in Kline. Actually the issue came up because one of my students tried to fit the model in class: it wouldn't converge and she wanted to know why. So far I haven't been able to find a reason - only the work-around of changing the unit loading variable (or to fit it in R)
Thanks again Robert Long On 22/04/2013 12:21, John Antonakis wrote:
Hi Robert: There is one issues to deal with before trying to reproduce the results and another issue about the estimation per se. First issue is that you have not set the means and standard deviations; was that an oversight? There is not much point in estimating the model with a correlation matrix: Bentler, P. M., & Savalei, V. (2010). Analysis of correlation structures: Current status and open problems. In S. Kolenikov, L. Thombs & D. Steinley (Eds.), Recent Methodological Developments in Social Science Statistics (pp. 1-36). Hoboken, NJ Wiley. Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83. Cudeck, R. (1989). Analysis of correlation matrices using covariance structure models. Psychological Bulletin, 105(2), 317-327. Steiger, J. H. (2001). Driving fast in reverse - The relationship between software development, theory, and education in structural equation modeling. Journal of the American Statistical Association, 96(453), 331-338. Second issue about the esestimation. A model with three first order factors is equivalent to the model with a higher order factor predicting the three factors (if you work out the DF by hand you'll see that they are the same). So, you are not testing anything with the hierarchical CFA beyond a first-order three factor theory. Rindskopf, D. & Rose, T. 1988. Some Theory and Applications of Confirmatory Second-Order Factor Analysis. Multivariate Behavioral Research, 23: 51-67. Best, J. __________________________________________ John Antonakis Professor of Organizational Behavior Director, Ph.D. Program in Management Faculty of Business and Economics University of Lausanne Internef #618 CH-1015 Lausanne-Dorigny Switzerland Tel ++41 (0)21 692-3438 Fax ++41 (0)21 692-3305 http://www.hec.unil.ch/people/jantonakis Associate Editor The Leadership Quarterly __________________________________________ On 22.04.2013 11:31, W Robert Long wrote:Hi all I'm working with the hierarchical CFA model of cognitive ability described on p199 of Kline "Principles and Practice of Structural Equation Modeling", 2nd edition - or p249 in the 3rd edition. I have reproduced summary statistics so that people who don't have access to the data will be able to follow: clear all ssd init x1 x2 x3 x4 x5 x6 x7 x8 x9 ssd set correlations /// 1.0000 \ /// 0.2973 1.0000 \ /// 0.4407 0.3398 1.0000 \ /// 0.3727 0.1529 0.1586 1.0000 \ /// 0.2934 0.1394 0.0772 0.7332 1.0000 \ /// 0.3568 0.1925 0.1977 0.7045 0.7200 1.0000 \ /// 0.0669 -0.0757 0.0719 0.1738 0.1020 0.1211 1.0000 \ /// 0.2239 0.0923 0.1860 0.1069 0.1387 0.1496 0.4868 1.0000 \ /// 0.3903 0.2060 0.3287 0.2078 0.2275 0.2142 0.3406 0.4490 1.0000 ssd set observations 301 The model is very straight forward: sem (L1 -> x1 x2 x3) /// (L2 -> x4 x5 x6) /// (L3 -> x7 x8 x9) /// (G -> L1@1 L2 L3) However, it fails to converge. It does however, converge if the G -> L2 path is constrained to 1 instead of the G -> L1 path I am trying to figure out what the problem is. L1 is the largest loading on G , but using the iterate() option I don't see what the problem is. I have successfully fitted the model using R, with the lavaan package, and the model with the G -> L2 path constrained has identical output in Stata and R, so I believe this must be a issue with Stata, but I do not know how to track the problem down. FWIW, here is the output from R for the model which doesn't converge in Stata: Estimate Std.err Z-value P(>|z|) Latent variables: L1 =~ x1 1.000 x2 0.554 0.100 5.554 0.000 x3 0.729 0.109 6.685 0.000 L2 =~ x4 1.000 x5 1.113 0.065 17.014 0.000 x6 0.926 0.055 16.703 0.000 L3 =~ x7 1.000 x8 1.180 0.165 7.152 0.000 x9 1.082 0.151 7.155 0.000 G =~ L1 1.000 L2 0.662 0.173 3.826 0.000 L3 0.425 0.118 3.602 0.000 Variances: x1 0.549 0.114 x2 1.134 0.102 x3 0.844 0.091 x4 0.371 0.048 x5 0.446 0.058 x6 0.356 0.043 x7 0.799 0.081 x8 0.488 0.074 x9 0.566 0.071 L1 0.192 0.170 L2 0.709 0.107 L3 0.272 0.069 G 0.617 0.183 I would be grateful for any help or advice. Thanks Robert Long * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/
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