SEM model testing with identical goodness of fits (2)
Dear John, Thanks for the reply. Maybe I had used wrong terminology, as you pointed out, in fact, variables "prob*", "o*" and "v*" are indicators of three latent variables(scales): weber, tp, and tr respectively. So variables "prob*", "o*" and "v*" are exogenous variables. e.g., variable "prob_dangerous_sport" is the answers of question "how likely do you think you will engage a dangerous sport? (1-very unlikely to 5- very likely). Variables weber, tr, tp are latent variables representing risk attitudes in different domains(recreation, planned behaviour, travel choice ). Hope this make sense of the models. By exploratory analysis, it had shown consistencies(Cronbach alpha) in each scale(latent variable tr, tp, weber), and significant correlations among these three scales. The two models mentioned in previous posts are the efforts to find out if there is a more general factor that can account for the correlations and make the three scales its sub scales. In this sense, SEM is used more of a CFA (sem is the only packages I know to do so, i did not search very hard of course). And Indeed the model fit is quite bad. regards,
John Fox wrote:
Dear hyena,
-----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of hyena
Sent: March-15-09 4:25 AM
To: r-help at stat.math.ethz.ch
Subject: Re: [R] SEM model testing with identical goodness of fits (2)
Dear John,
Thanks for the prompt reply! Sorry did not supply with more detailed
information.
The target model consists of three latent factors, general risk
scale from Weber's domain risk scales, time perspective scale from
Zimbardo(only future time oriented) and a travel risk attitude scale.
Variables with "prob_" prefix are items of general risk scale, variables
of "o1" to "o12" are items of future time perspective and "v5" to "v13"
are items of travel risk scale.
The purpose is to explore or find a best fit model that "correctly"
represent the underlining relationship of three scales. So far, the
correlated model has the best fit indices, so I 'd like to check if
there is a higher level factor that govern all three factors, thus the
second model.
Both models are very odd. In the first, each of tr, weber, and tp has direct effects on different subsets of the endogenous variables. The implicit claim of these models is that, e.g., prob_* are conditionally independent of tr and tp given weber, and that the correlations among prob_* are entirely accounted for by their dependence on weber. The structural coefficients are just the simple regressions of each prob_* on weber. The second model is the same except that the variances and covariances among weber, tr, and tp are parametrized differently. I'm not sure why you set the models up in this manner, and why your research requires a structural-equation model. I would have expected that each of the prob_*, v*, and o* variables would have comprised indicators of a latent variable (risk-taking, etc.). The models that you specified seem so strange that I think that you'd do well to try to find competent local help to sort out what you're doing in relationship to the goals of the research. Of course, maybe I'm just having a failure of imagination.
The data are all 5 point Likert scale scores by respondents(N=397).
It's problematic to treat ordinal variables if they were metric (and to fit SEMs of this complexity to a small sample).
The example listed bellow did not show "prob_" variables(their names are too long). Given the following model structure, if they are indeed observationally indistinguishable, is there some possible adjustments to test the higher level factor effects?
No. Because the models necessarily fit the same, you'd have to decide between them on grounds of plausibility. Moreover both models fit very badly. Regards, John
Thanks,
###########################
#data example, partial
#########################
1 1 1 1
id o1 o2 o3 o4 o5 o6 o7 o8 o9 o10 o11 o12 o13 v5 v13 v14 v16 v17
14602 2 2 4 4 5 5 2 3 2 4 3 4 2 5 2 2 4 2
14601 2 4 5 4 5 5 2 5 3 4 5 4 5 5 3 4 4 2
14606 1 3 5 5 5 5 3 3 5 3 5 5 5 5 5 5 5 3
14610 2 1 4 5 4 5 3 4 4 2 4 2 1 5 3 5 5 5
14609 4 3 2 2 5 5 2 5 2 4 4 2 2 4 2 4 4 4
####################################
#correlated model, three scales corrlated to each other
model.correlated <- specify.model()
weber<->tp,e.webertp,NA
tp<->tr,e.tptr,NA
tr<->weber,e.trweber,NA
weber<->weber,NA,1
tp<->tp,e.tp,NA
tr <->tr,e.trv,NA
weber -> prob_wild_camp,alpha2,NA
weber -> prob_book_hotel_in_short_time,alpha3,NA
weber -> prob_safari_Kenia, alpha4, NA
weber -> prob_sail_wild_water,alpha5,NA
weber -> prob_dangerous_sport,alpha7,NA
weber -> prob_bungee_jumping,alpha8,NA
weber -> prob_tornado_tracking,alpha9,NA
weber -> prob_ski,alpha10,NA
prob_wild_camp <-> prob_wild_camp, ep2,NA
prob_book_hotel_in_short_time <->
prob_book_hotel_in_short_time,ep3,NA
prob_safari_Kenia <-> prob_safari_Kenia, ep4, NA
prob_sail_wild_water <-> prob_sail_wild_water,ep5,NA
prob_dangerous_sport <-> prob_dangerous_sport,ep7,NA
prob_bungee_jumping <-> prob_bungee_jumping,ep8,NA
prob_tornado_tracking <-> prob_tornado_tracking,ep9,NA
prob_ski <-> prob_ski,ep10,NA
tp -> o1,NA,1
tp -> o3,beta3,NA
tp -> o4,beta4,NA
tp -> o5,beta5,NA
tp -> o6,beta6,NA
tp -> o7,beta7,NA
tp -> o9,beta9,NA
tp -> o10,beta10,NA
tp -> o11,beta11,NA
tp -> o12,beta12,NA
o1 <-> o1,eo1,NA
o3 <-> o3,eo3,NA
o4 <-> o4,eo4,NA
o5 <-> o5,eo5,NA
o6 <-> o6,eo6,NA
o7 <-> o7,eo7,NA
o9 <-> o9,eo9,NA
o10 <-> o10,eo10,NA
o11 <-> o11,eo11,NA
o12 <-> o12,eo12,NA
tr -> v5, NA,1
tr -> v13, gamma2,NA
tr -> v14, gamma3,NA
tr -> v16,gamma4,NA
tr -> v17,gamma5,NA
v5 <-> v5,ev1,NA
v13 <-> v13,ev2,NA
v14 <-> v14,ev3,NA
v16 <-> v16, ev4, NA
v17 <-> v17,ev5,NA
sem.correlated <- sem(model.correlated, cov(riskninfo_s), 397)
summary(sem.correlated)
samelist = c('weber','tp','tr')
minlist=c(names(rk),names(tp))
maxlist = NULL
path.diagram(sem2,out.file =
"e:/sem2.dot",same.rank=samelist,min.rank=minlist,max.rank =
maxlist,edge.labels="values",rank.direction='LR')
#############################################
#high level latent scale, a high level factor exist
##############################################
model.rsk <- specify.model()
rsk->tp,e.rsktp,NA
rsk->tr,e.rsktr,NA
rsk->weber,e.rskweber,NA
rsk<->rsk, NA,1
weber<->weber, e.weber,NA
tp<->tp,e.tp,NA
tr <->tr,e.trv,NA
weber -> prob_wild_camp,NA,1
weber -> prob_book_hotel_in_short_time,alpha3,NA
weber -> prob_safari_Kenia, alpha4, NA
weber -> prob_sail_wild_water,alpha5,NA
weber -> prob_dangerous_sport,alpha7,NA
weber -> prob_bungee_jumping,alpha8,NA
weber -> prob_tornado_tracking,alpha9,NA
weber -> prob_ski,alpha10,NA
prob_wild_camp <-> prob_wild_camp, ep2,NA
prob_book_hotel_in_short_time <->
prob_book_hotel_in_short_time,ep3,NA
prob_safari_Kenia <-> prob_safari_Kenia, ep4, NA
prob_sail_wild_water <-> prob_sail_wild_water,ep5,NA
prob_dangerous_sport <-> prob_dangerous_sport,ep7,NA
prob_bungee_jumping <-> prob_bungee_jumping,ep8,NA
prob_tornado_tracking <-> prob_tornado_tracking,ep9,NA
prob_ski <-> prob_ski,ep10,NA
tp -> o1,NA,1
tp -> o3,beta3,NA
tp -> o4,beta4,NA
tp -> o5,beta5,NA
tp -> o6,beta6,NA
tp -> o7,beta7,NA
tp -> o9,beta9,NA
tp -> o10,beta10,NA
tp -> o11,beta11,NA
tp -> o12,beta12,NA
o1 <-> o1,eo1,NA
o3 <-> o3,eo3,NA
o4 <-> o4,eo4,NA
o5 <-> o5,eo5,NA
o6 <-> o6,eo6,NA
o7 <-> o7,eo7,NA
o9 <-> o9,eo9,NA
o10 <-> o10,eo10,NA
o11 <-> o11,eo11,NA
o12 <-> o12,eo12,NA
tr -> v5, NA,1
tr -> v13, gamma2,NA
tr -> v14, gamma3,NA
tr -> v16,gamma4,NA
tr -> v17,gamma5,NA
v5 <-> v5,ev1,NA
v13 <-> v13,ev2,NA
v14 <-> v14,ev3,NA
v16 <-> v16, ev4, NA
v17 <-> v17,ev5,NA
sem.rsk <- sem(model.rsk, cov(riskninfo_s), 397)
summary(sem.rsk)
##############
#model one results
###############
Model Chisquare = 680.79 Df = 227 Pr(>Chisq) = 0
Chisquare (null model) = 2443.4 Df = 253
Goodness-of-fit index = 0.86163
Adjusted goodness-of-fit index = 0.83176
RMSEA index = 0.07105 90% CI: (NA, NA)
Bentler-Bonnett NFI = 0.72137
Tucker-Lewis NNFI = 0.7691
Bentler CFI = 0.79282
SRMR = 0.069628
BIC = -677.56
Normalized Residuals
Min. 1st Qu. Median Mean 3rd Qu. Max.
-3.4800 -0.8490 -0.0959 -0.0186 0.6540 8.8500
Parameter Estimates
Estimate Std Error z value Pr(>|z|)
e.webertp -0.058847 0.023473 -2.5070 1.2175e-02
e.tptrl 0.151913 0.031072 4.8890 1.0134e-06
e.trweber -0.255449 0.044469 -5.7444 9.2264e-09
e.tp 0.114260 0.038652 2.9562 3.1149e-03
e.trv 0.464741 0.068395 6.7950 1.0832e-11
alpha2 0.488106 0.051868 9.4105 0.0000e+00
alpha3 0.446255 0.052422 8.5127 0.0000e+00
alpha4 0.517707 0.050863 10.1784 0.0000e+00
alpha5 0.772128 0.045863 16.8356 0.0000e+00
alpha7 0.782098 0.045754 17.0934 0.0000e+00
alpha8 0.668936 0.048092 13.9095 0.0000e+00
alpha9 0.376798 0.052977 7.1124 1.1400e-12
alpha10 0.449507 0.051885 8.6635 0.0000e+00
ep2 0.761752 0.058103 13.1104 0.0000e+00
ep3 0.800857 0.060154 13.3134 0.0000e+00
ep4 0.731980 0.056002 13.0705 0.0000e+00
ep5 0.403819 0.040155 10.0565 0.0000e+00
ep7 0.388322 0.039930 9.7250 0.0000e+00
ep8 0.552524 0.046619 11.8519 0.0000e+00
ep9 0.858023 0.063098 13.5982 0.0000e+00
ep10 0.797945 0.059651 13.3770 0.0000e+00
beta3 1.670861 0.312656 5.3441 9.0871e-08
beta4 1.536421 0.292725 5.2487 1.5319e-07
beta5 1.530081 0.294266 5.1997 1.9966e-07
beta6 1.767803 0.329486 5.3653 8.0801e-08
beta7 0.870601 0.200366 4.3451 1.3924e-05
beta9 1.692284 0.312799 5.4101 6.2975e-08
beta10 1.009742 0.224155 4.5047 6.6480e-06
beta11 1.723416 0.324593 5.3095 1.0995e-07
beta12 1.452796 0.286857 5.0645 4.0940e-07
eo1 0.885742 0.065529 13.5168 0.0000e+00
eo3 0.681004 0.055626 12.2425 0.0000e+00
eo4 0.730277 0.057682 12.6603 0.0000e+00
eo5 0.732500 0.059305 12.3514 0.0000e+00
eo6 0.642921 0.055797 11.5226 0.0000e+00
eo7 0.913393 0.066903 13.6526 0.0000e+00
eo9 0.672777 0.054994 12.2336 0.0000e+00
eo10 0.883505 0.065198 13.5512 0.0000e+00
eo11 0.660627 0.055399 11.9249 0.0000e+00
eo12 0.758847 0.059582 12.7361 0.0000e+00
gamma2 0.689244 0.089575 7.6946 1.4211e-14
gamma3 0.880574 0.093002 9.4684 0.0000e+00
gamma4 1.083443 0.092856 11.6680 0.0000e+00
gamma5 0.589127 0.087252 6.7520 1.4584e-11
ev1 0.535257 0.050039 10.6968 0.0000e+00
ev2 0.779221 0.060274 12.9280 0.0000e+00
ev3 0.639632 0.054097 11.8239 0.0000e+00
ev4 0.454467 0.048438 9.3824 0.0000e+00
ev5 0.838702 0.062929 13.3277 0.0000e+00
#####################################
#model two results
##################################
Model Chisquare = 680.79 Df = 227 Pr(>Chisq) = 0
Chisquare (null model) = 2443.4 Df = 253
Goodness-of-fit index = 0.86163
Adjusted goodness-of-fit index = 0.83176
RMSEA index = 0.07105 90% CI: (NA, NA)
Bentler-Bonnett NFI = 0.72137
Tucker-Lewis NNFI = 0.7691
Bentler CFI = 0.79282
SRMR = 0.069627
BIC = -677.56
Normalized Residuals
Min. 1st Qu. Median Mean 3rd Qu. Max.
-3.4800 -0.8490 -0.0959 -0.0186 0.6540 8.8500
Parameter Estimates
Estimate Std Error z value Pr(>|z|)
e.rsktp 0.187069 0.045642 4.09859 4.1567e-05
e.rsktrl 0.812070 0.131731 6.16462 7.0652e-10
e.rskweber -0.153542 0.038132 -4.02660 5.6589e-05
e.weber 0.214671 0.046260 4.64056 3.4746e-06
e.tp 0.079263 0.028484 2.78270 5.3909e-03
e.trv -0.194712 0.197101 -0.98788 3.2321e-01
alpha3 0.914263 0.131132 6.97206 3.1233e-12
alpha4 1.060649 0.143622 7.38499 1.5254e-13
alpha5 1.581889 0.177961 8.88898 0.0000e+00
alpha7 1.602316 0.182893 8.76095 0.0000e+00
alpha8 1.370476 0.164966 8.30764 0.0000e+00
alpha9 0.771961 0.128670 5.99955 1.9787e-09
alpha10 0.920922 0.136148 6.76413 1.3411e-11
ep2 0.761752 0.058109 13.10909 0.0000e+00
ep3 0.800856 0.060155 13.31314 0.0000e+00
ep4 0.731979 0.056003 13.07044 0.0000e+00
ep5 0.403818 0.040155 10.05643 0.0000e+00
ep7 0.388322 0.039932 9.72459 0.0000e+00
ep8 0.552523 0.046620 11.85175 0.0000e+00
ep9 0.858024 0.063099 13.59811 0.0000e+00
ep10 0.797943 0.059651 13.37694 0.0000e+00
beta3 1.670904 0.310681 5.37820 7.5234e-08
beta4 1.536444 0.290968 5.28045 1.2887e-07
beta5 1.530096 0.292603 5.22926 1.7019e-07
beta6 1.767838 0.327427 5.39918 6.6945e-08
beta7 0.870626 0.199814 4.35718 1.3175e-05
beta9 1.692309 0.310816 5.44473 5.1885e-08
beta10 1.009760 0.223270 4.52259 6.1088e-06
beta11 1.723432 0.322488 5.34417 9.0830e-08
beta12 1.452761 0.285172 5.09434 3.4997e-07
eo1 0.885741 0.065519 13.51880 0.0000e+00
eo3 0.681003 0.055625 12.24265 0.0000e+00
eo4 0.730278 0.057683 12.66029 0.0000e+00
eo5 0.732501 0.059307 12.35108 0.0000e+00
eo6 0.642919 0.055799 11.52215 0.0000e+00
eo7 0.913394 0.066900 13.65310 0.0000e+00
eo9 0.672778 0.054994 12.23360 0.0000e+00
eo10 0.883503 0.065197 13.55124 0.0000e+00
eo11 0.660630 0.055397 11.92534 0.0000e+00
eo12 0.758852 0.059582 12.73619 0.0000e+00
gamma2 0.689244 0.089545 7.69720 1.3989e-14
gamma3 0.880580 0.092955 9.47317 0.0000e+00
gamma4 1.083430 0.092789 11.67631 0.0000e+00
gamma5 0.589119 0.087233 6.75338 1.4444e-11
ev1 0.535258 0.050034 10.69783 0.0000e+00
ev2 0.779219 0.060273 12.92808 0.0000e+00
ev3 0.639627 0.054096 11.82402 0.0000e+00
ev4 0.454472 0.048437 9.38269 0.0000e+00
ev5 0.838705 0.062929 13.32769 0.0000e+00
John Fox wrote:
Dear hyena, Actually, looking at this a bit more closely, the first models dedicate
6
parameters to the correlational and variational structure of the three variables that you mention -- 3 variances and 3 covariances; the second model also dedicates 6 parameters -- 3 factor loadings and 3 error
variances
(with the variance of the factor fixed as a normalization). You don't
show
the remaining structure of the models, but a good guess is that they are observationally indistinguishable. John
-----Original Message----- From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org]
On
Behalf Of hyena Sent: March-14-09 5:07 PM To: r-help at stat.math.ethz.ch Subject: [R] SEM model testing with identical goodness of fits HI, I am testing several models about three latent constructs that measure risk attitudes. Two models with different structure obtained identical of fit measures from chisqure to BIC. Model1 assumes three factors are correlated with each other and model two assumes a higher order factor exist and three factors related to this higher factor instead of to each other. Model1: model.one <- specify.model() tr<->tp,e.trtp,NA tp<->weber,e.tpweber,NA weber<->tr,e.webertr,NA weber<->weber, e.weber,NA tp<->tp,e.tp,NA tr <->tr,e.trv,NA .... Model two model.two <- specify.model() rsk->tp,e.rsktp,NA rsk->tr,e.rsktr,NA rsk->weber,e.rskweber,NA rsk<->rsk, NA,1 weber<->weber, e.weber,NA tp<->tp,e.tp,NA tr <->tr,e.trv,NA .... the summary of both sem model gives identical fit indices, using same data set. is there some thing wrong with this mode specification? Thanks
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-
guide.html
and provide commented, minimal, self-contained, reproducible code.
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.