# convergence not achieved in CFA

#### hund

##### New Member
Dear forum

I am doing factor analysis on a small quality of life questionnaire. It contains only 6 items. I did EFA with parallel analysis in STATA. This revealed a possible 2 factor structure with 4 items in factor 1 and the last two items in factor 2. When I do CFA (SEM) to test this new model I run into trouble. I get 16000 iterations and afterward STATA tells me that convergence is not achieved. However, when I look at the goodness of fit statistics I get a very good fit.
What does "convergence not achieved" mean? Should I worry about this? I know it has to do with validity, but that all I know.
Thanks
Christian

#### noetsi

##### Fortran must die
6 items seems way to small for EFA and a problem for identification in CFA with two factors depending on how the items loaded.

That correct parameters can not be calculated by the method used (or none at all in some cases). It can mean many things in practice, but likely causes of this are bad starting values (if you are using maximum likelihood especially) and too few cases. There are a vast number of other special cases that can cause it. Note that CFA requires that your model be identified (did you do that?) but I don't know if that influences convergence of the model or not.

I don't understand how you get a goodness of fit statistic if the model did not converge although I know some software does that. I would find any such result doubtful without convergence regardless of what it says.

Last edited:

#### hund

##### New Member
Why is 6 items to short for EFA. I thought EFA (and CFA) was primarily dependent on the number of observations. I have more almost 500 observations.
Factorloadings exceed 0.75 on the 4 item factor and 0.65 on the 2 item factor which should be more than acceptable. furthermore, dividing in two factors makes good sense (face validity).
when doing CFA in STATA I have to identify the model as a 2 factor model, otherwise STATA would assume a one factor structure.
I get an output from STATA after 16000 iterations (log likelihood does not change after 10 iterations though). From this output I can easily obtain fit statistics. Only problem is that the output is accompanied by a warning telling me that convergence is not achieved.

#### Lazar

##### Phineas Packard
I disagree with notesi. Six items is fine and there is no reason why your model will not be identified in a sense that it has >0 degrees of freedom (assume covar only structure you have 6 loading + 6 residuals plus 1 variance = 13 meaning 8 df). Under special cases the model could be empirically under identified for various reasons see http://davidakenny.net/cm/identify.htm.

Why is it not converging? My guess from experience would be that your model is misspecified somewhere (check carefully - use Mod indices as a data detective tool). If everything is fine you could try relaxing the convergence criteria. Not sure how to do that in STATA.

Other things you could try:
1. As CFA uses maximum liklihood it is sensitive to differences in item metrics. Try z-standadizing all items before fitting the model.
2. You could try different identification procedures. i.e. identify by constraining the latent variances to 1 rather than one of the loadings per factor.
3. As a last port of call try constraining the loadings of the two item factor to be equivalent.

#### Lazar

##### Phineas Packard
I don't understand how you get a goodness of fit statistic if the model did not converge although I know some software does that. I would find any such result doubtful without convergence regardless of what it says.
You can get fit at any stage during the iteration process including from the initial start values.

#### noetsi

##### Fortran must die
I was always taught that EFA only made sense when you had a very large number of variables - otherwise there was no sense in doing it since it is primarily a data reduction method. And for CFA I was taught that you should always have a minimum of five items to measure a latent factor even though you can have fewer and be identified.

Obviously what I was taught (and read in many sources) was wrong again