Hello all! 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. Thanks, Marcos
Structural Equation Model
5 messages · Chuck Cleland, Marcos Sanches, John Fox
Dear Marcos, I don't see why you can't specify a MIMIC model using sem(), though you might have to supply your own start values. When I have a chance, but possibly not today, I'll check. Regards, John -------------------------------- John Fox Department of Sociology McMaster University Hamilton, Ontario Canada L8S 4M4 905-525-9140x23604 http://socserv.mcmaster.ca/jfox -------------------------------- -----Original Message----- From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Marcos Sanches Sent: Thursday, February 26, 2004 6:33 AM To: r-help at stat.math.ethz.ch Subject: [R] Structural Equation Model Hello all! 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. Thanks, Marcos ______________________________________________ R-help at stat.math.ethz.ch 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
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
Thanks Chuck and John, I guess the problem is that I was specifying the error terms in the 'ram' matrix. I am not familiarized with this type of model specification as I am used to work with AMOS. Now I think it will work! Thanks very much! Marcos -----Mensagem original----- De: Chuck Cleland [mailto:ccleland at optonline.net] Enviada em: quinta-feira, 26 de fevereiro de 2004 10:10 Para: marcos.sanches at ipsos-opinion.com.br Cc: r-help at stat.math.ethz.ch; John Fox Assunto: 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
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:ccleland at optonline.net] Sent: Thursday, February 26, 2004 8:10 AM To: marcos.sanches at ipsos-opinion.com.br Cc: r-help at stat.math.ethz.ch; 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