Negative Covariance Matrix

[Joan Chan]

Hi, 

I am running a multi-group CFA  (N1 = 489, N2 = 434) using this model: 

pers_model1 <- ' 

    neg_act =~ PERS_2 + PERS_8 + PERS_14 + PERS_20 + PERS_26

    neg_int =~ PERS_6 + PERS_12 + PERS_18 + PERS_24 + PERS_30

    neg_dur =~ PERS_4 + PERS_10 + PERS_16 + PERS_22 + PERS_28

    pos_act =~ PERS_1 + PERS_7 + PERS_13 + PERS_19 + PERS_25

    pos_int =~ PERS_5 + PERS_11 + PERS_17 + PERS_23 + PERS_29

    pos_dur =~ PERS_3 + PERS_9 + PERS_15 + PERS_21 + PERS_27'

And I received this error for both groups:

lavaan WARNING: covariance matrix of latent variables is not positive definite in group 1; use lavInspect(fit, "cov.lv") to investigate.

lavaan WARNING: covariance matrix of latent variables is not positive definite in group 2; use lavInspect(fit, "cov.lv") to investigate.

Here are the results of the lavInspect:

> lavInspect(pers.residual.p,"cov.lv")

$Australia

        neg_ct neg_nt neg_dr pos_ct pos_nt pos_dr

neg_act  0.884                                   

neg_int  0.805  0.817                            

neg_dur  0.798  0.747  0.828                     

pos_act -0.216 -0.143 -0.298  0.713              

pos_int -0.108  0.016 -0.186  0.612  0.611       

pos_dur -0.349 -0.270 -0.399  0.679  0.532  0.717

$Singapore

        neg_ct neg_nt neg_dr pos_ct pos_nt pos_dr

neg_act  0.788                                   

neg_int  0.709  0.761                            

neg_dur  0.707  0.687  0.738                     

pos_act -0.176 -0.153 -0.204  0.537              

pos_int -0.126 -0.029 -0.102  0.505  0.542       

pos_dur -0.197 -0.142 -0.172  0.459  0.444  0.439

Is there cause for concern here and what is the remedy?

Thank you.

Kind Regards,

Joan Chan 

[Prof. Gavin Brown]

Yes this is cause for concern. not positive definite usually suggests you have too many factors for your data. looking at the titles it seems that there may only be a negative and positive factor. look at the correlation values--if any are close to or more than 1.00 that will cause this result.

good advice on this problem in

Chen, F., Bollen, K. A., Paxton, P., Curran, P. J., & Kirby, J. B. (2001). Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological Methods & Research, 29(4), 468-508. doi:doi:10.1177/0049124101029004003

you may succeed with a bifactor model: valence on one side and act, int, dur on the other side as 2 sets of predictors for each item

[Terrence Jorgensen]

look at the correlation values--if any are close to or more than 1.00 that will cause this result.

And you can do so with lavInspect(fit, "cor.lv")

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

 

[Joan Chan]

Hi Prof Gavin and Dr Jorgensen, 

Thank you for both your replies. I had a look at lavInspect(fit, "cor.lv")and found that a few of the correlation values were about 0.950. However, when I tested a three-factor model (ACT, INT, DUR), the model fit worsened (CFI = 0.50). 

pers_3factor <- '
      gen_act =~ PERS_2 + PERS_8 + PERS_14 + PERS_20 + PERS_26 + # neg_act
                 PERS_1 + PERS_7 + PERS_13 + PERS_19 + PERS_25  #pos_act
                 
      gen_int =~ PERS_6 + PERS_12 + PERS_18 + PERS_24 + PERS_30 + #neg_int
                 PERS_5 + PERS_11 + PERS_17 + PERS_23 + PERS_29   #pos_int
                 
      gen_dur =~ PERS_4 + PERS_10 + PERS_16 + PERS_22 + PERS_28 + #neg_dur
                 PERS_3 + PERS_9 + PERS_15 + PERS_21 + PERS_27'    #pos_dur

When I tested a bi-factor and the three-factor model combined, the model fit was marginally acceptable.

pers_bifactor.3factor <- 'gen_act =~ PERS_2 + PERS_8 + PERS_14 + PERS_20 + PERS_26 + # neg_act
                                     PERS_1 + PERS_7 + PERS_13 + PERS_19 + PERS_25  #pos_act
                 
                          gen_int =~ PERS_6 + PERS_12 + PERS_18 + PERS_24 + PERS_30 + #neg_int
                                     PERS_5 + PERS_11 + PERS_17 + PERS_23 + PERS_29   #pos_int
                 
                          gen_dur =~ PERS_4 + PERS_10 + PERS_16 + PERS_22 + PERS_28 + #neg_dur
                                     PERS_3 + PERS_9 + PERS_15 + PERS_21 + PERS_27    #pos_dur
                 
                          gen_e_react =~ PERS_2 + PERS_8 + PERS_14 + PERS_20 + PERS_26 +   #neg_act
                                         PERS_6 + PERS_12 + PERS_18 + PERS_24 + PERS_30 +  #neg_int
                                         PERS_4 + PERS_10 + PERS_16 + PERS_22 + PERS_28 +  #neg_dur
                                         PERS_1 + PERS_7 + PERS_13 + PERS_19 + PERS_25 +   #pos_act
                                         PERS_5 + PERS_11 + PERS_17 + PERS_23 + PERS_29 +  #pos_int
                                         PERS_3 + PERS_9 + PERS_15 + PERS_21 + PERS_27'     #pos_dur

Model	SBX2	df	CFI	TLI	RMSEA (90% Confidence Intervals)	SRMR	AIC
Six-factor model
Singapore	725.763	390	0.940	0.933	0.050 (0.045 – 0.056)	0.054	31578.647
Australia	1094.397	390	0.905	0.894	0.68 (0.063 – 0.073)	0.069	36664.089
Three-factor model
Singapore	2830.600	402	0.577	0.543	0.131(0.127 – 0.136)	0.195	34136.035
Australia	3889.106	402	0.539	0.501	0.147 (0.142 – 0.151)	0.210	39994.469
Bi-factor + Three-factor model
Singapore	1180.821	375	0.855	0.832	0.080 (0.074 -0.085)	0.146	32190.076
Australia	1603.487	375	0.834	0.808	0.091 (0.087 – 0.096)	0.150	37318.915

 

Would you take that the bi-factor + three-factor model is the best fitting model for both countries although it has poorer model fit than the six-factor model?

Thank you so much for your help.

Kind Regards,

Joan Chan  

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[Prof. Gavin Brown]

the bifactor model is somewhat better than the 3-factor model insofar as the fit indices are concerned; but the fit is at best marginal to non-acceptable for the bifactor.

assuming the result is admissible, i would suggest rejecting all these models and try exploratory techniques to determine if there is a better model that works equally well in both locations.

In any case it seems to me that a Singapore model may never be made to fit well with the Australia data.

Given the differences in populations (culture, policy, practices) that the current models are not equally robust in each jurisdiction and a model that works for one may not work for the other.