SEM model testing with identical goodness of fits (2)
The purpose of carrying this CFA is to test the validity of a new developed scale "tr" with "v*" items, other two scales "weber" and "tp" are existing scales that measures specific risk attitudes. I am not sure if a simple correlation analysis is adequate to this purpose or not, thus the CFA test. Further, although a PCA has tested the dimensionality of all items, they are not divided as PCA result suggested, rather, their original grouping remains. The indicators are indeed not very well divided in PCA, mainly, "o*" items are located in two components. Originally, the EFA has been carried out on the first half of the sample and CFA on the second half. Due to the low fit indices from CFA of the partial sample, the full sample is tested in CFA to see if sample size affects much, and the results is as poor as before. It seems the time to read more about scale developing. And thanks for all these inputs. regards,
John Fox wrote:
Dear Hyena, OK -- I see that what you're trying to do is simply to fit a confirmatory factor-analysis model. The two models that you're considering aren't really different -- they are, as I said, observationally equivalent, and fit the data poorly. You can *assume* a common higher-level factor and estimate the three loadings on it for the lower-level factors, but you can't test this model against the first model. I'm not sure what you gain from the CFA beyond what you learned from an exploratory factor analysis. Using the same data first in an EFA and then for a CFA essentially invalidates the CFA, which is no longer confirmatory. One would, then, expect a CFA following an EFA to fit the data well, since the CFA was presumably specified to do so, but I suspect that a closer examination of the EFA will show that the items don't divide so neatly into the three sets. Regards, 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-15-09 12:00 PM 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 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
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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. ______________________________________________ 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.