Factor loading greater than 1 in a bifactor model for CFA

[Ecenaz Alemdağ]

Hi everyone,

I am obtaining a very high standardized factor loading (21.826) and negative variance for one item in my bi-factor model while conducting CFA with orthogonal factors. In the factor (f3) where there is a problematic item (R13), other factor loadings are also too small. 

Here is my R code:

-----------------

model3<-'
g=~R4+R8+R9+R12+R13+R1+R5+R10+R14+R2+R3+R6+R7
f1=~R1+R5+R10+R14
f2=~R2+R3+R6+R7
f3=~R4+R8+R9+R12+R13
'
fit.model3<-cfa(model3, data=firstdata, orthogonal= TRUE, std.lv=T, estimator="MLR")
summary(fit.model3, fit.measures=T, standardized=T, rsquare=T)

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The results including factor loadings and variance:

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Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  g =~                                                                  
    R4                0.897    0.077   11.623    0.000    0.897    0.808
    R8                0.784    0.074   10.555    0.000    0.784    0.832
    R9                0.751    0.064   11.811    0.000    0.751    0.727
    R12               0.666    0.076    8.783    0.000    0.666    0.564
    R13               0.853    0.076   11.274    0.000    0.853    0.788
    R1                0.940    0.082   11.445    0.000    0.940    0.722
    R5                0.926    0.088   10.565    0.000    0.926    0.699
    R10               0.891    0.092    9.687    0.000    0.891    0.637
    R14               0.805    0.091    8.801    0.000    0.805    0.541
    R2                0.760    0.075   10.096    0.000    0.760    0.766
    R3                0.726    0.076    9.573    0.000    0.726    0.788
    R6                0.649    0.091    7.142    0.000    0.649    0.632
    R7                0.762    0.086    8.830    0.000    0.762    0.791
  f1 =~                                                                
    R1                0.709    0.123    5.778    0.000    0.709    0.544
    R5                0.783    0.119    6.587    0.000    0.783    0.591
    R10               0.911    0.102    8.924    0.000    0.911    0.652
    R14               0.762    0.099    7.670    0.000    0.762    0.512
  f2 =~                                                                
    R2                0.390    0.105    3.727    0.000    0.390    0.393
    R3                0.349    0.111    3.147    0.002    0.349    0.379
    R6                0.263    0.124    2.132    0.033    0.263    0.257
    R7                0.056    0.104    0.537    0.591    0.056    0.058
  f3 =~                                                                
    R4                0.003    0.003    1.233    0.218    0.003    0.003
    R8                0.005    0.002    2.391    0.017    0.005    0.005
    R9               -0.003    0.002   -1.462    0.144   -0.003   -0.003
    R12               0.006    0.003    2.377    0.017    0.006    0.005
    R13              23.644    0.169  139.672    0.000   23.644   21.826

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .R4                0.427    0.106    4.013    0.000    0.427    0.347
   .R8                0.273    0.057    4.765    0.000    0.273    0.307
   .R9                0.503    0.091    5.534    0.000    0.503    0.472
   .R12               0.950    0.124    7.661    0.000    0.950    0.682
   .R13            -558.576    7.988  -69.929    0.000 -558.576 -476.016
   .R1                0.311    0.051    6.098    0.000    0.311    0.183
   .R5                0.285    0.059    4.860    0.000    0.285    0.162
   .R10               0.331    0.075    4.403    0.000    0.331    0.169
   .R14               0.986    0.166    5.938    0.000    0.986    0.445
   .R2                0.255    0.078    3.286    0.001    0.255    0.259
   .R3                0.200    0.073    2.735    0.006    0.200    0.236
   .R6                0.563    0.080    7.047    0.000    0.563    0.534
   .R7                0.344    0.054    6.313    0.000    0.344    0.371
    g                 1.000                               1.000    1.000
    f1                1.000                               1.000    1.000
    f2                1.000                               1.000    1.000
    f3                1.000                               1.000    1.000

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What causes such a problem? What do I need to do?

Thank you for your help in advance.

[Nickname]

Ecenaz,

The thing that stands out to me is that the other indicators on F3 have extremely small loadings.  This seems to suggest that R13 is not related to the other indicators on that factor.  I would try fixing the R13 loading to zero to see what happens to F3 when it reflects only common variance between the other indicators exclusive of R13.  I would also look at the correlation residuals to see what correlations between the indicators are not being fit well.  It could be that R13 is associated with one or more indicators on another factor in a way that is not accounted for by the general factor.  You may have to either remove R13 from the model or free some unique variance covariances.  It can be helpful to compare the correlation residuals to the correlations side by side (or in each triangle of a square matrix).  My guess is that the F13 loading estimate reflects misspecification somewhere else in the model.

Keith

------------------------
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/

[Daniel Morillo Cuadrado]

My understanding is that the estimation algorithm is not converging. You may try increasing the maximum number of iterations, or try a different estimator (WLSMV?).

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[balal izanloo]

Greeting

also look to your data in R13 variable may be there are some "Error in entering numbers" for that variable.HTH

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[Edward Rigdon]

If you did not get an error message about statistical identification, this looks like a model that at least "nearly not identified." With only one indicator having a substantial loading, the model for factor f3 would fail identification tests if this were a conventional model. I'm not sure you can salvage this model without better indicators for f3.

Daniel's suggestion of nonconvergence is also a possibility. To overcome that problem, you might try setting plausible starting values for loadings on f3 in particular--probably values around 0.3 for all of those loadings and values of 0.10 for those observed variables' residual variances.

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