Andrew Kiselica
May 22, 2019, 10:41:51 AM5/22/19
to lavaan
Hello,
I am attempting to run a bifactor model in lavaan. I have successfully run one-factor, four-factor correlated, and higher order models without any problems. However, the bifactor model continually comes up with a message that the model is not identified when I am almost positive that it is identified. I've pasted the relevant output from R below. Any suggestions on how to fix the problem would be greatly appreciated!
> BifC <- ' G =~ ZUDSBENTC + zTRAILBr + zTRAILAr + ZUDSVERTN + ZDIGFORCT + ZDIGBACCT + ZVEG + ZANIMALS + ZMINTTOTS + ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD
+ VisExec =~ zTRAILBr + ZUDSBENTC + zTRAILAr + ZUDSVERTN
+ Attn =~ ZDIGFORCT + ZDIGBACCT
+ Lang =~ ZVEG + ZANIMALS + ZMINTTOTS
+ Mem =~ ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD
+ G ~~ 0*VisExec
+ G ~~ 0*Attn
+ G ~~ 0*Mem
+ G ~~ 0*Lang
+ VisExec ~~ Attn
+ VisExec ~~ Lang
+ VisExec ~~ Mem
+ Attn ~~ Mem
+ Attn ~~ Lang
+ Lang ~~ Mem'
> fitBifC <- cfa(BifC, data=Half1)
Warning messages:
1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, :
lavaan WARNING:
Could not compute standard errors! The information matrix could
not be inverted. This may be a symptom that the model is not
identified.
2: In lav_object_post_check(object) :
lavaan WARNING: some estimated ov variances are negative
3: In lav_object_post_check(object) :
lavaan WARNING: some estimated lv variances are negative
> summary(fitBifC, fit.measures=TRUE, standardized=TRUE)
lavaan 0.6-3 ended normally after 942 iterations
Optimization method NLMINB
Number of free parameters 42
Number of observations 3123
Estimator ML
Model Fit Test Statistic 2791.712
Degrees of freedom 36
P-value (Chi-square) 0.000
Model test baseline model:
Minimum Function Test Statistic 50215.496
Degrees of freedom 66
P-value 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.945
Tucker-Lewis Index (TLI) 0.899
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -233167.370
Loglikelihood unrestricted model (H1) -231771.514
Number of free parameters 42
Akaike (AIC) 466418.739
Bayesian (BIC) 466672.694
Sample-size adjusted Bayesian (BIC) 466539.243
Root Mean Square Error of Approximation:
RMSEA 0.157
90 Percent Confidence Interval 0.152 0.162
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.051
Parameter Estimates:
Information Expected
Information saturated (h1) model Structured
Standard Errors Standard
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
G =~
ZUDSBENTC 1.000 208.506 0.945
zTRAILBr 0.921 NA 192.009 0.538
zTRAILAr 0.922 NA 192.232 0.768
ZUDSVERTN 0.915 NA 190.881 0.850
ZDIGFORCT 0.841 NA 175.285 0.834
ZDIGBACCT 0.843 NA 175.847 0.826
ZVEG 0.865 NA 180.303 0.854
ZANIMALS 0.827 NA 172.435 0.869
ZMINTTOTS 0.879 NA 183.236 0.820
ZCRAFTVRS 0.859 NA 179.124 0.790
ZCRAFTDVR 0.903 NA 188.328 0.799
ZUDSBENTD 1.027 NA 214.052 0.901
VisExec =~
zTRAILBr 1.000 0.137 0.000
ZUDSBENTC 492.629 NA 67.634 0.307
zTRAILAr -394.182 NA -54.118 -0.216
ZUDSVERTN -545.508 NA -74.894 -0.333
Attn =~
ZDIGFORCT 1.000 98.523 0.469
ZDIGBACCT 1.339 NA 131.935 0.619
Lang =~
ZVEG 1.000 99.807 0.473
ZANIMALS 0.604 NA 60.281 0.304
ZMINTTOTS 0.386 NA 38.525 0.172
Mem =~
ZCRAFTVRS 1.000 NaN NaN
ZCRAFTDVR -1.531 NA NaN NaN
ZUDSBENTD 0.080 NA NaN NaN
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
G ~~
VisExec 0.000 0.000 0.000
Attn 0.000 0.000 0.000
Mem 0.000 0.000 0.000
Lang 0.000 0.000 0.000
VisExec ~~
Attn -0.049 NA -0.004 -0.004
Lang -9.082 NA -0.663 -0.663
Mem 0.931 NA 0.065 0.065
Attn ~~
Mem 93.157 NA 0.009 0.009
Lang 1482.231 NA 0.151 0.151
Lang ~~
Mem -569.790 NA -0.055 -0.055
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.ZUDSBENTC 630.804 NA 630.804 0.013
.zTRAILBr 90498.369 NA 90498.369 0.711
.zTRAILAr 22782.298 NA 22782.298 0.364
.ZUDSVERTN 8418.791 NA 8418.791 0.167
.ZDIGFORCT 3781.443 NA 3781.443 0.086
.ZDIGBACCT -2968.082 NA -2968.082 -0.065
.ZVEG 2083.574 NA 2083.574 0.047
.ZANIMALS 6005.720 NA 6005.720 0.153
.ZMINTTOTS 14928.663 NA 14928.663 0.299
.ZCRAFTVRS 30094.630 NA 30094.630 0.586
.ZCRAFTDVR 45472.594 NA 45472.594 0.818
.ZUDSBENTD 10678.225 NA 10678.225 0.189
G 43474.919 NA 1.000 1.000
VisExec 0.019 NA 1.000 1.000
Attn 9706.708 NA 1.000 1.000
Lang 9961.493 NA 1.000 1.000
Mem -10818.394 NA NaN NaN
PD
May 22, 2019, 10:44:33 AM5/22/19
to lavaan
Group factors must be uncorrelated otherwise you have linear dependence in the model. orthogonal = TRUE or change your code
Nickname
May 23, 2019, 11:35:38 AM5/23/19
to lavaan
If 'group' means 'specific' I am not sure that it is true that these must be orthogonal. I believe that it is only required that the general factor be orthogonal to the specific factors.
Bifactor models are finicky. You are pressing your luck with only two indicators for one of your factors. You might try omitting that factor and its indicators.
I generally have better luck fitting bifactor models fixing the variances of the latent variables rather than using index variables. This is illustrated below. For me, the first model fails but the second converges and has reasonable standard errors in most samples.
Caveat: I do not have much experience with the convenience wrappers like the cfa() function and was unsuccessful in overriding the auto.fix.first default. That is why I fit the second model using the lavaan() function. In principle, I think that it should be possible to fit the model using the cfa() function.
Finally, I could not help but notice that all your observed variable names begin with 'Z'. If this indicates that you are analyzing z scores, be aware that this is comparable to analyzing a correlation matrix. Analyzing a correlation matrix as if it were a covariance matrix misrepresents the degrees of freedom and thus can produce inaccurate inferential statistics.
Bifactor models are finicky. You are pressing your luck with only two indicators for one of your factors. You might try omitting that factor and its indicators.
I generally have better luck fitting bifactor models fixing the variances of the latent variables rather than using index variables. This is illustrated below. For me, the first model fails but the second converges and has reasonable standard errors in most samples.
Caveat: I do not have much experience with the convenience wrappers like the cfa() function and was unsuccessful in overriding the auto.fix.first default. That is why I fit the second model using the lavaan() function. In principle, I think that it should be possible to fit the model using the cfa() function.
Finally, I could not help but notice that all your observed variable names begin with 'Z'. If this indicates that you are analyzing z scores, be aware that this is comparable to analyzing a correlation matrix. Analyzing a correlation matrix as if it were a covariance matrix misrepresents the degrees of freedom and thus can produce inaccurate inferential statistics.
Enter code here...
# Bifactor Model
require(lavaan)
BifCSim <- '
G =~ ZUDSBENTC + zTRAILBr + zTRAILAr + ZUDSVERTN + ZDIGFORCT + ZDIGBACCT + ZVEG + ZANIMALS + ZMINTTOTS + ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD + extraIndicator
VisExec =~ zTRAILBr + ZUDSBENTC + zTRAILAr + ZUDSVERTN
Attn =~ ZDIGFORCT + ZDIGBACCT + extraIndicator
Lang =~ ZVEG + ZANIMALS + ZMINTTOTS
Mem =~ ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD
G ~~ 0*VisExec
G ~~ 0*Attn
G ~~ 0*Mem
G ~~ 0*Lang
VisExec ~~ .5 * Attn
VisExec ~~ .5 * Lang
VisExec ~~ .5 * Mem
Attn ~~ .5 * Mem
Attn ~~ .5 * Lang
Lang ~~ .5 * Mem
' # end BifCSim model
BifC <- '
G =~ ZUDSBENTC + zTRAILBr + zTRAILAr + ZUDSVERTN + ZDIGFORCT + ZDIGBACCT + ZVEG + ZANIMALS + ZMINTTOTS + ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD + extraIndicator
VisExec =~ zTRAILBr + ZUDSBENTC + zTRAILAr + ZUDSVERTN
Attn =~ ZDIGFORCT + ZDIGBACCT + extraIndicator
Lang =~ ZVEG + ZANIMALS + ZMINTTOTS
Mem =~ ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD
G ~~ 0*VisExec
G ~~ 0*Attn
G ~~ 0*Mem
G ~~ 0*Lang
VisExec ~~ Attn
VisExec ~~ Lang
VisExec ~~ Mem
Attn ~~ Mem
Attn ~~ Lang
Lang ~~ Mem
' # end BifC model
BifC2 <- '
G =~ ZUDSBENTC + zTRAILBr + zTRAILAr + ZUDSVERTN + ZDIGFORCT + ZDIGBACCT + ZVEG + ZANIMALS + ZMINTTOTS + ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD + extraIndicator
VisExec =~ zTRAILBr + ZUDSBENTC + zTRAILAr + ZUDSVERTN
Attn =~ ZDIGFORCT + ZDIGBACCT + extraIndicator
Lang =~ ZVEG + ZANIMALS + ZMINTTOTS
Mem =~ ZCRAFTVRS + ZCRAFTDVR + ZUDSBENTD
G ~~ 0*VisExec
G ~~ 0*Attn
G ~~ 0*Mem
G ~~ 0*Lang
VisExec ~~ Attn
VisExec ~~ Lang
VisExec ~~ Mem
Attn ~~ Mem
Attn ~~ Lang
Lang ~~ Mem
G ~~ 1*G
VisExec ~~ 1*VisExec
Attn ~~ 1*Attn
Lang ~~ 1*Lang
Mem ~~ 1*Mem
' # end BifC2 model
foo <- simulateData(model=BifCSim, sample.nobs=1000) #This is admittedly a hack relying on default values of one.
summary(cov(foo)[lower.tri(cov(foo))]) # Quick peek
summary(cor(foo)[lower.tri(cor(foo))])
det(cov(foo))
fitBifC <- cfa(BifC, data=foo) # Fixed index variable loadings, free latent variances
summary(fitBifC)
fitBifC2 <- lavaan(BifC2, data=foo, auto.var=TRUE) # Fixed latent variances, free loadings
summary(fitBifC2)
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/
Andrew Kiselica
May 24, 2019, 10:10:32 AM5/24/19
to lavaan
Thanks for the very helpful reply, Keith! Fixing the factor variances did the trick.
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