Re: [R] SEM model testing with identical goodness of fits (2)

hyena Sun, 15 Mar 2009 12:15:35 -0700

The purpose of carrying this CFA is to test the validity of a newdeveloped scale "tr" with "v*" items, other two scales "weber" and "tp"are existing scales that measures specific risk attitudes. I am not sureif 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, theyare not divided as PCA result suggested, rather, their original groupingremains. 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 sampleand CFA on the second half. Due to the low fit indices from CFA of thepartial sample, the full sample is tested in CFA to see if sample sizeaffects much, and the results is as poor as before.

It seems the time to read more about scale developing. And thanks forall 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-boun...@r-project.org [mailto:r-help-boun...@r-project.org]

On

Behalf Of hyena
Sent: March-15-09 12:00 PM
To: r-h...@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-boun...@r-project.org

[mailto:r-help-boun...@r-project.org]

On

Behalf Of hyena
Sent: March-15-09 4:25 AM
To: r-h...@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

  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

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-boun...@r-project.org

[mailto:r-help-boun...@r-project.org]

On

Behalf Of hyena
Sent: March-14-09 5:07 PM
To: r-h...@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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PLEASE do read the posting guide

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______________________________________________
R-help@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.

______________________________________________
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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.


______________________________________________
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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.


______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Re: [R] SEM model testing with identical goodness of fits (2)

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