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From |
John Antonakis <John.Antonakis@unil.ch> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Hierarchical CFA problem |

Date |
Mon, 22 Apr 2013 16:33:07 +0200 |

-------------+---------------------------------------------------------------- Variance | e.x1 | .5509189 .1985341 .2718573 1.116437 e.x2 | 1.086973 .1179499 .8787249 1.344574 e.x3 | .8554162 .1292344 .6361797 1.150205 e.x4 | .345022 .0468115 .264459 .4501272 e.x5 | .4623856 .0608402 .3572761 .5984178 e.x6 | .3636892 .0440637 .2868144 .4611688 e.x7 | .5784454 .110548 .3977291 .8412739 e.x8 | .5318421 .0899317 .3818115 .7408264 e.x9 | .7004508 .0882214 .5472292 .8965738 e.L1 | -1.00e-09 .2417215 . . e.L2 | .9446486 .1340474 .7152918 1.247548 e.L3 | .5939406 .1637864 .3459504 1.0197 G | .7258514 .2259537 .3943421 1.336049 ------------------------------------------------------------------------------

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 16:11, John Antonakis wrote:

OK.There is something wrong here; if you look at your output it gives anegative variance for the e of L1. Though as I said this model makesno sense as it is equivalent to the lower-order model:sem (L1 -> x1 x2 x3) /// (L2 -> x4 x5 x6) /// (L3 -> x7 x8 x9) This is estimatable (though still fails the chi-square test):------------------------------------------------------------------------------| OIM| Coef. Std. Err. z P>|z| [95% Conf.Interval]-------------+----------------------------------------------------------------Measurement | x1 <- | L1 | 1 (constrained) _cons | 4.93577 .0671778 73.47 0.000 4.804104 5.067436-----------+----------------------------------------------------------------x2 <- | L1 | .5534029 .1092465 5.07 0.000 .3392837 .7675221 _cons | 6.08804 .0677543 89.85 0.000 5.955244 6.220836-----------+----------------------------------------------------------------x3 <- | L1 | .7293722 .1172742 6.22 0.000 .4995191 .9592254 _cons | 2.250415 .0650802 34.58 0.000 2.12286 2.37797-----------+----------------------------------------------------------------x4 <- | L2 | 1 (constrained)_cons | 3.060908 .066987 45.69 0.000 2.9296163.1922-----------+----------------------------------------------------------------x5 <- | L2 | 1.113116 .0649824 17.13 0.000 .9857527 1.240479 _cons | 4.340532 .0742579 58.45 0.000 4.194989 4.486075-----------+----------------------------------------------------------------x6 <- | L2 | .9261753 .0561917 16.48 0.000 .8160416 1.036309 _cons | 2.185572 .0630445 34.67 0.000 2.062007 2.309137-----------+----------------------------------------------------------------x7 <- | L3 | 1 (constrained) _cons | 4.185902 .0626953 66.77 0.000 4.063021 4.308783-----------+----------------------------------------------------------------x8 <- | L3 | 1.179996 .1502814 7.85 0.000 .8854496 1.474542 _cons | 5.527076 .0582691 94.85 0.000 5.412871 5.641281-----------+----------------------------------------------------------------x9 <- | L3 | 1.081178 .1949939 5.54 0.000 .6989972 1.463359 _cons | 5.374123 .0580699 92.55 0.000 5.260308 5.487938-------------+----------------------------------------------------------------Variance | e.x1 | .5490164 .1190647 .3589104 .8398168 e.x2 | 1.133917 .1042654 .9469168 1.357846 e.x3 | .8443011 .0950778 .677084 1.052815 e.x4 | .3711728 .0479585 .2881337 .4781434 e.x5 | .4461694 .0579262 .3459301 .5754549 e.x6 | .3561501 .0434357 .280428 .4523189 e.x7 | .7993025 .0875386 .6448945 .9906807 e.x8 | .4875303 .0916455 .3372823 .7047089 e.x9 | .5663183 .0905473 .4139654 .7747421 L1 | .8093532 .1497701 .5631499 1.163194 L2 | .979491 .1122085 .7825076 1.226062 L3 | .383838 .0920543 .2398876 .6141693-------------+----------------------------------------------------------------Covariance | L1 | L2 | .4082169 .0796761 5.12 0.000 .2520546 .5643792 L3 | .2621933 .0553876 4.73 0.000 .1536356 .3707511-----------+----------------------------------------------------------------L2 | L3 | .1734852 .0493172 3.52 0.000 .0768252 .2701452------------------------------------------------------------------------------LR test of model vs. saturated: chi2(24) = 85.32, Prob > chi2 =0.0000The above results are the same as the R-results for the lower orderrelations and the covariance will equal the structuralloadings.....Interestingly,using the covariance matrix I was able to fit higher-order model inMplus. Here are the estimates (which are almost the same as what Rgives):Two-Tailed Estimate S.E. Est./S.E. P-Value L1 BY X1 1.000 0.000 999.000 999.000 X2 0.553 0.100 5.553 0.000 X3 0.729 0.109 6.685 0.000 L2 BY X4 1.000 0.000 999.000 999.000 X5 1.113 0.065 17.016 0.000 X6 0.926 0.055 16.704 0.000 L3 BY X7 1.000 0.000 999.000 999.000 X8 1.180 0.165 7.152 0.000 X9 1.081 0.151 7.155 0.000 G BY L1 1.000 0.000 999.000 999.000 L2 0.662 0.173 3.825 0.000 L3 0.425 0.118 3.601 0.000 Intercepts X1 4.936 0.067 73.473 0.000 X2 6.088 0.068 89.855 0.000 X3 2.250 0.065 34.579 0.000 X4 3.061 0.067 45.694 0.000 X5 4.341 0.074 58.452 0.000 X6 2.186 0.063 34.667 0.000 X7 4.186 0.063 66.766 0.000 X8 5.527 0.058 94.853 0.000 X9 5.374 0.058 92.545 0.000 Variances G 0.617 0.183 3.371 0.001 Residual Variances X1 0.549 0.114 4.833 0.000 X2 1.134 0.102 11.146 0.000 X3 0.844 0.091 9.315 0.000 X4 0.371 0.048 7.779 0.000 X5 0.446 0.058 7.642 0.000 X6 0.356 0.043 8.276 0.000 X7 0.799 0.081 9.822 0.000 X8 0.487 0.074 6.570 0.000 X9 0.566 0.071 8.007 0.000 L1 0.192 0.170 1.129 0.259 L2 0.709 0.107 6.625 0.000 L3 0.272 0.069 3.955 0.000Perhaps technical support can chime in (or you can contact them ifthey don't--I would be interested to know what they say, by the way).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 13:34, W Robert Long wrote: > Hi John and thanks for your reply >> Yes, I forgot to include the SDs in my post - I am working with rawdata and it was an oversight - here they are:>> ssd set sd 1.167432 1.177451 1.130979 1.164116 1.290472 1.0956031.089534 1.012615 1.009152> > FWIW, here are the means: >> ssd set means 4.93577 6.08804 2.250415 3.060908 4.340532 2.1855724.185902 5.527076 5.374123>> Regarding your second point, I was aware of the equivalence ofmodels. Nevertheless I still wanted to fit the hierarchical model, asoutlined in Kline. Actually the issue came up because one of mystudents tried to fit the model in class: it wouldn't converge and shewanted 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 fitit 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 theresults>> and another issue about the estimation per se. >>>> First issue is that you have not set the means and standarddeviations;>> 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 factorpredicting>> 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 inStata:>>> >>> 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/ > s

* * 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/

**Follow-Ups**:**Re: st: Hierarchical CFA problem***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

**st: Histogramm Graph option Note***From:*"Meulemann Max" <mmeulemann@ethz.ch>

**References**:**Re: st: Hierarchical CFA problem***From:*John Antonakis <John.Antonakis@unil.ch>

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