Dear Chuck, Thanks for saving me the trouble of checking this out. When I have a chance, I'll take a look at what's going on with the RMSEA confidence interval. Though it's been awhile, I recall checking this against several examples; obviously something is wrong here.
Thanks again, John -------------------------------- John Fox Department of Sociology McMaster University Hamilton, Ontario Canada L8S 4M4 905-525-9140x23604 http://socserv.mcmaster.ca/jfox -------------------------------- -----Original Message----- From: Chuck Cleland [mailto:[EMAIL PROTECTED] Sent: Thursday, February 26, 2004 8:10 AM To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; John Fox Subject: Re: [R] Structural Equation Model Marcos Sanches wrote: > I want to estimate parameters in a MIMIC model. I have one latent > variable (ksi), four reflexive indicators (y1, y2, y3 and y4) and four > formative indicators (x1, x2, x3, x4). Is there a way to do it in R? I > know there is the SEM library, but it seems not to be possible to > specify formative indicators, that is, observed exogenous variables > which causes the latent variable. Marcos: A MIMIC model seems to work fine in sem(). Here is an example of a MIMIC model which also has 4 indicators of a single latent variable and 4 covariates: > S.sch <- var(school) > S.sch[upper.tri(var(school))] <- 0 > round(S.sch, 4) Y1 Y2 Y3 Y4 X1 X2 X3 X4 Y1 1.3586 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Y2 1.0586 1.3815 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Y3 0.6709 0.6937 1.8192 0.0000 0.0000 0.0000 0.0000 0.0000 Y4 1.0452 1.1185 0.6584 3.6370 0.0000 0.0000 0.0000 0.0000 X1 0.4891 0.4929 0.3406 0.5244 1.1984 0.0000 0.0000 0.0000 X2 0.0011 0.0246 0.0236 0.0545 0.0177 0.2500 0.0000 0.0000 X3 -0.7325 -0.8166 -0.4524 -0.8481 -0.8759 -0.0017 4.5451 0.0000 X4 0.0614 0.0644 0.0110 0.0781 0.1070 -0.0009 -0.3961 0.1605 > # n = 5198 > model.sch <- matrix(c( + 'Eta1 -> Y1', NA, 1, + 'Eta1 -> Y2', 'lambda21', NA, + 'Eta1 -> Y3', 'lambda31', NA, + 'Eta1 -> Y4', 'lambda41', NA, + 'X1 -> Eta1', 'gamma11', NA, + 'X2 -> Eta1', 'gamma12', NA, + 'X3 -> Eta1', 'gamma13', NA, + 'X4 -> Eta1', 'gamma14', NA, + 'Eta1 <-> Eta1', 'psi1', NA, + 'Y1 <-> Y1', 'theta1', NA, + 'Y2 <-> Y2', 'theta2', NA, + 'Y3 <-> Y3', 'theta3', NA, + 'Y4 <-> Y4', 'theta4', NA, + 'X1 <-> X1', 'phi11', NA, + 'X2 <-> X2', 'phi22', NA, + 'X3 <-> X3', 'phi33', NA, + 'X4 <-> X4', 'phi44', NA, + 'X1 <-> X2', 'phi12', NA, + 'X1 <-> X3', 'phi13', NA, + 'X1 <-> X4', 'phi14', NA, + 'X2 <-> X3', 'phi23', NA, + 'X2 <-> X4', 'phi24', NA, + 'X3 <-> X4', 'phi34', NA), ncol=3, byrow=TRUE) > obs.vars.sch <- c('Y1', 'Y2', 'Y3', 'Y4', 'X1', 'X2', 'X3', 'X4') > sem.sch <- sem(model.sch, S.sch, 5198) > summary(sem.sch) Model Chisquare = 77.445 Df = 14 Pr(>Chisq) = 8.4002e-11 Goodness-of-fit index = 0.99628 Adjusted goodness-of-fit index = 0.99044 RMSEA index = 0.029530 90 % CI: (0.0011724, 0.0011724) BIC = -71.451 Normalized Residuals Min. 1st Qu. Median Mean 3rd Qu. Max. -3.82e+00 -4.27e-02 1.44e-05 6.41e-02 5.52e-01 2.74e+00 Parameter Estimates Estimate Std Error z value Pr(>|z|) lambda21 1.05267671 0.0156238 67.37643 0.00000000 Y2 <--- Eta1 lambda31 0.65931621 0.0184649 35.70637 0.00000000 Y3 <--- Eta1 lambda41 1.04965996 0.0257337 40.78937 0.00000000 Y4 <--- Eta1 gamma11 0.32691518 0.0134334 24.33606 0.00000000 Eta1 <--- X1 gamma12 0.04487985 0.0263389 1.70394 0.08839245 Eta1 <--- X2 gamma13 -0.11473656 0.0073527 -15.60472 0.00000000 Eta1 <--- X3 gamma14 -0.12574905 0.0371760 -3.38253 0.00071822 Eta1 <--- X4 psi1 0.76836697 0.0218450 35.17364 0.00000000 Eta1 <--> Eta1 theta1 0.35328543 0.0131454 26.87518 0.00000000 Y1 <--> Y1 theta2 0.26742302 0.0133470 20.03617 0.00000000 Y2 <--> Y2 theta3 1.38220283 0.0282621 48.90661 0.00000000 Y3 <--> Y3 theta4 2.52933440 0.0525526 48.12959 0.00000000 Y4 <--> Y4 phi11 1.19841396 0.0235177 50.95794 0.00000000 X1 <--> X1 phi22 0.24998279 0.0049079 50.93426 0.00000000 X2 <--> X2 phi33 4.54509222 0.0891715 50.97021 0.00000000 X3 <--> X3 phi44 0.16053813 0.0031543 50.89539 0.00000000 X4 <--> X4 phi12 0.01769075 0.0075963 2.32886 0.01986650 X2 <--> X1 phi13 -0.87588544 0.0345801 -25.32916 0.00000000 X3 <--> X1 phi14 0.10701444 0.0062625 17.08800 0.00000000 X4 <--> X1 phi23 -0.00173226 0.0147860 -0.11716 0.90673658 X3 <--> X2 phi24 -0.00087825 0.0027789 -0.31604 0.75197217 X4 <--> X2 phi34 -0.39612152 0.0130628 -30.32432 0.00000000 X4 <--> X3 Iterations = 24 This example was taken from http://statmodel.com/mplus/examples/continuous/cont2.html and the results agree fairly closely. However, there does seem to be a problem with the RMSEA 90% confidence interval above. Thanks to John Fox for providing this package. hope it helps, Chuck Cleland -- Chuck Cleland, Ph.D. NDRI, Inc. 71 West 23rd Street, 8th floor New York, NY 10010 tel: (212) 845-4495 (Tu, Th) tel: (732) 452-1424 (M, W, F) fax: (917) 438-0894 ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
