Convergence issue: same model works in two samples, not in a third

[christophe...@nicholls.edu]

Hi folks,

I'm trying to diagnose the source of a convergence problem in my data. Essentially, I have a model that works in two separate samples (where data were collected at a single point in time), but in a third sample (where data were collected at two points in time), there is a convergence issue. I've tried specifying starting values to levels that make sense, but this has not resolved my issue. 

Any advice? 

Chris

[Terrence Jorgensen]

in a third sample (where data were collected at two points in time), there is a convergence issue.

So this model is a longitudinal model, different from the cross-sectional model for the first 2 groups?  Have you tried fitting the cross-sectional model to each occasion separately for the third group, to see if it converges on each?  If you post your syntax, it might show whether there is an identification issue.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[christophe...@nicholls.edu]

Thanks for responding, Terrence.

It might help you if you think of the model as exactly the same, but the data are gathered in such a way as to cause a temporal separation in measurement. In this data, here are the details: There are two conditions: (1) All data on the predictor and criterion are gathered simultaneously and (2) data on the predictor are gathered at time 1 and one week later data on the criterion are gathered. 

My syntax is below:

methodu.cfa <- '

##Substantive factors

PP =~ c(pp1a, pp1b)*PP1 + c(pp2a, pp2b)*PP2 + c(pp3a,pp3b)*PP3 + c(pp4a,pp4b)*PP4 + c(pp5a,pp5b)*PP5 + c(pp6a,pp6b)*PP6 + c(pp7a,pp7b)*PP7 + c(pp8a,pp8b)*PP8 + c(pp9a,pp9b)*PP9 + c(pp10a,pp10b)*PP10

IRB =~ c(irb1a,irb1b)*IRB1 + c(irb2a,irb2b)*IRB2 + c(irb3a,irb3b)*IRB3 + c(irb4a,irb4b)*IRB4 + c(irb5a,irb5b)*IRB5 + c(irb6a,irb6b)*IRB6 + c(irb7a,irb7b)*IRB7

OCBI =~ c(ocbi1a,ocbi1b)*OCBI1 + c(ocbi2a,ocbi2b)*OCBI2 + c(ocbi3a,ocbi3b)*OCBI3 + c(ocbi4a,ocbi4b)*OCBI4 + c(ocbi5a,ocbi5b)*OCBI5 + c(ocbi6a,ocbi6b)*OCBI6 + c(ocbi7a,ocbi7b)*OCBI7

OCBO =~ c(ocbo1a,ocbo1b)*OCBO1 + c(ocbo2a,ocbo2b)*OCBO2 + c(ocbo3a,ocbo3b)*OCBO3 + c(ocbo4a,ocbo4b)*OCBO4 + c(ocbo5a,ocbo5b)*OCBO5 + c(ocbo6a,ocbo6b)*OCBO6 + c(ocbo7a,ocbo7b)*OCBO7

##Method factors

PosAff =~ c(1,1)*PA + c(papp1a, papp1b)*PP1 + c(papp2a, papp2b)*PP2 + c(papp3a,papp3b)*PP3 + c(papp4a,papp4b)*PP4 + c(papp5a,papp5b)*PP5 + c(papp6a,papp6b)*PP6 + c(papp7a,papp7b)*PP7 + c(papp8a,papp8b)*PP8 + c(papp9a,papp9b)*PP9 + c(papp10a,papp10b)*PP10 + c(pairb1a,pairb1b)*IRB1 + c(pairb2a,pairb2b)*IRB2 + c(pairb3a,pairb3b)*IRB3 + c(pairb4a,pairb4b)*IRB4 + c(pairb5a,pairb5b)*IRB5 + c(pairb6a,pairb6b)*IRB6 + c(pairb7a,pairb7b)*IRB7 + c(paocbi1a,paocbi1b)*OCBI1 + c(paocbi2a,paocbi2b)*OCBI2 + c(paocbi3a,paocbi3b)*OCBI3 + c(paocbi4a,paocbi4b)*OCBI4 + c(paocbi5a,paocbi5b)*OCBI5 + c(paocbi6a,paocbi6b)*OCBI6 + c(paocbi7a,paocbi7b)*OCBI7 + c(paocbo1a,paocbo1b)*OCBO1 + c(paocbo2a,paocbo2b)*OCBO2 + c(paocbo3a,paocbo3b)*OCBO3 + c(paocbo4a,paocbo4b)*OCBO4 + c(paocbo5a,paocbo5b)*OCBO5 + c(paocbo6a,paocbo6b)*OCBO6 + c(paocbo7a,paocbo7b)*OCBO7

PA ~~ ((1-.921)*0.824)*PA

#Compute factor loading differences 

pp1c := pp1a-pp1b

pp2c := pp2a-pp2b

pp3c := pp3a-pp3b

pp4c := pp4a-pp4b

pp5c := pp5a-pp5b

pp6c := pp6a-pp6b

pp7c := pp7a-pp7b

pp8c := pp8a-pp8b

pp9c := pp9a-pp9b

pp10c := pp10a-pp10b

irb1c := irb1a-irb1b

irb2c := irb2a-irb2b

irb3c := irb3a-irb3b

irb4c := irb4a-irb4b

irb5c := irb5a-irb5b

irb6c := irb6a-irb6b

irb7c := irb7a-irb7b

ocbi1c := ocbi1a-ocbi1b

ocbi2c := ocbi2a-ocbi2b

ocbi3c := ocbi3a-ocbi3b

ocbi4c := ocbi4a-ocbi4b

ocbi5c := ocbi5a-ocbi5b

ocbi6c := ocbi6a-ocbi6b

ocbi7c := ocbi7a-ocbi7b

ocbo1c := ocbo1a-ocbo1b

ocbo2c := ocbo2a-ocbo2b

ocbo3c := ocbo3a-ocbo3b

ocbo4c := ocbo4a-ocbo4b

ocbo5c := ocbo5a-ocbo5b

ocbo6c := ocbo6a-ocbo6b

ocbo7c := ocbo7a-ocbo7b

papp1c := papp1a-papp1b

papp2c := papp2a-papp2b

papp3c := papp3a-papp3b

papp4c := papp4a-papp4b

papp5c := papp5a-papp5b

papp6c := papp6a-papp6b

papp7c := papp7a-papp7b

papp8c := papp8a-papp8b

papp9c := papp9a-papp9b

papp10c := papp10a-papp10b

pairb1c := pairb1a-pairb1b

pairb2c := pairb2a-pairb2b

pairb3c := pairb3a-pairb3b

pairb4c := pairb4a-pairb4b

pairb5c := pairb5a-pairb5b

pairb6c := pairb6a-pairb6b

pairb7c := pairb7a-pairb7b

paocbi1c := paocbi1a-paocbi1b

paocbi2c := paocbi2a-paocbi2b

paocbi3c:= paocbi3a-paocbi3b

paocbi4c := paocbi4a-paocbi4b

paocbi5c := paocbi5a-paocbi5b

paocbi6c := paocbi6a-paocbi6b

paocbi7c := paocbi7a-paocbi7b

paocbo1c := paocbo1a-paocbo1b

paocbo2c := paocbo2a-paocbo2b

paocbo3c := paocbo3a-paocbo3b

paocbo4c := paocbo4a-paocbo4b

paocbo5c := paocbo5a-paocbo5b

paocbo6c := paocbo6a-paocbo6b

paocbo7c := paocbo7a-paocbo7b

#Factor variances are fixed to 1 to allow estimation.

###Substantive factors

PP ~~ c(1,1)*PP

IRB ~~ c(1,1)*IRB

OCBI ~~ c(1,1)*OCBI

OCBO ~~ c(1,1)*OCBO

##Factor covariances freely estimated (with the exception being the bifactors). However, correlations with the method factors are fixed to zero. Method factors are also constrained to zero.

PP ~~ c(PPIRB1,PPIRB2)*IRB

PP ~~ c(PPOCBI1,PPOCBI2)*OCBI

PP ~~ c(PPOCBO1,PPOCBO2)*OCBO

PP ~~ c(0,0)*PosAff

IRB ~~ c(IRBOCBI1,IRBOCBI2)*OCBI

IRB ~~ c(IRBOCBO1,IRBOCBO2)*OCBO

IRB ~~ c(0,0)*PosAff

OCBI ~~ c(OCBIO1,OCBIO2)*OCBO

OCBI ~~ c(0,0)*PosAff

OCBO ~~ c(0,0)*PosAff

#Compute factor covariances differences.

PPIRB3 := PPIRB1-PPIRB2

PPOCBI3 := PPOCBI1-PPOCBI2

PPOCBO13 := PPOCBO1-PPOCBO2

IRBOCBI3 := IRBOCBI1-IRBOCBI2

IRBOCBO3 := IRBOCBO1-IRBOCBO2

OCBIO3 := OCBIO1-OCBIO2

#Factor means of the both groups are fixed at zero to allow identification.

##Substantive factors

PP ~ c(0, 0)*1

IRB ~ c(0, 0)*1

OCBI ~ c(0, 0)*1

OCBO ~ c(0, 0)*1

'

methodu <- cfa(methodu.cfa, ordered = c("PP1", "PP2", "PP3", 

                                              "PP4", "PP5", "PP6", "PP7", "PP8", "PP9", "PP10", 

                                              "IRB1", "IRB2", "IRB3", "IRB4", "IRB5", "IRB6", "IRB7", "OCBI1",

                                              "OCBI2", "OCBI3", "OCBI4", "OCBI5", "OCBI6", "OCBI7", "OCBO1", 

                                              "OCBO2", "OCBO3", "OCBO4", "OCBO5", "OCBO6", "OCBO7"),

                  group = "COND", data = data3, estimator = "DWLS", parameterization = "theta", information = "expected", std.lv=TRUE)

anova(baseline,methodu) 

[Terrence Jorgensen]

I've seen convergence issues with bifactor and especially MTMM models before, when factors were allowed to correlate.  Does the model converge if all factors are orthogonal?

Also, this is not really a bifactor model as it is traditionally applied.  The factor on which all items load is typically the general substantive factor, whereas each item also loads on one method factor (orthogonal to the substantive factor and often to each other).  In your case, you do not have 1 substantive factor, you have 4.  And you cannot partition out any method variance if you only have a single method that was used to measure all indicators.  The whole point is that there are systematic differences between different methods, which you model by specifying different method factors to explain those.  You might want to ask about this issue on SEMNET, where there are several people with more experience fitting bifactor models who might understand something helpful to you.

[Yves Rosseel]

Another things you may try out:

- use the argument optim.init_nelder_mead = TRUE
- switch to another optimizer, eg optim.method = "bfgs" (or "l-bfgs-b")

I would also suggest to start with a much smaller model, and than expand
the model bit by bit.

Yves.