Your description of the factors as essentially positive vs negative raises the possibility that you have a unidimensional construct with correlated errors on the 'negative' items. This effect, whereby a single dimension can produce two apparent factors, has been well-documented. It would be a good idea to test the competing models and compare goodness of fit.

Marsh HW: Positive and negative global self-esteem: A substantively meaningful distinction or artifactors?

J Pers Soc Psychol 1996, 70(4):810-819.

Hankins M (2008) The factor structure of the twelve item General Health Questionnaire (GHQ-12): the result of negative phrasing? Clinical Practice & Epidemiology in Mental Health 4:10

Dear Prof. Matthew Hankins

Thanks a lot for your helpful and insightful feedback. In several earlier EFA I have also noted that negatively worded items tend to cluster togather but was not aware of the method of demonstrating that this is an artifact.

Your feedback and references to some of your publication will now help me to explore this aspect. I have accessed the full text of your second JPSP article but not the first one. May I request you to kindly send this article to me on my mail id [email protected]

I am not much aware of this item-parceling approach to CFA. It will be better if you elaborate some more on this aspect. Is it customary to allow the error terms of the negatively worded items to covary with each other or it is based on the observation of the modification indices of the AMOS output?

I would highly appreciate and feel much obliged if you could spare some of your invaluable time to elaborate upon this issue.

Regards

Dear Prof. Matthew Hankins

Initially I thought that you have used item parcels for positive and negative items. But now I have gone through your GHQ-12 related paper and it is clear that rather than using item parcels you have allowed all the error terms of NP items to covary so that response bias may be included in the model.

Thanks a lot. It is really helpful. If you can provide links to some additional readings related to this it will be of much help to us.

I tested three models as suggested by Dr. Mathew and obtained the following results

Model1- unifactorial with error terms of NP items correlated

Chi squre/df = 1.704; GFI = ..946; AGFI= .869; CFI = ..952; RMSEA = .07 (CI= .036 - .101); ECVI= 1.017

Model-2: Two correlated factors

Chi squre/df = 3.727; GFI = .934; AGFI= .895; CFI = ..896; RMSEA = .081 (CI= ..068 - .093); ECVI= .574

Model-3 : Two correlated factors with error terms of NP items correlated

Chi squre/df = 2.02; GFI = .974; AGFI= .934; CFI = .971; RMSEA = .054 (CI= .036 - .071); ECVI= .387

The last model has yielded a better fit than all others.

The first model (the single factor model with errors of NP items correlated) also appears to fit the data almost similar to the last one with few exceptions.

However, the local fit (factor loadings of NP items) is not good for the single factor solution.

In this situation, should I infer the existence of two factors as genuine or an artefact of the response bias in responding to NP items.

The findings of the EFA as well as the aforesaid models with standardized weights are given in the attachment.

I invite the views of the esteemed members and hope Dr. Mathew will give some valuable suggestions.

Interesting results - my answer to the first question would have been that the correlated errors on the negative items would be an a priori hypothesis, rather than deduced from the modification indices. So the competing models would be (1) unidimensional with correlated errors on the negative terms only and (2) the two-factor model with no correlated error terms. I'm not a big fan of adding correlations between error terms on the basis of modification indices alone (i.e. post hoc).

Also, my preference for two models with similar fit would be the more parsimonious, i.e. one factor: a good example of Occam's razor.

Note also that standard estimates of reliability (e.g. Alpha) assume no correlated errors and may over-estimate the scale reliability if errors are correlated.

Thanks Dr. Hankins for your valuable comments and suggestions.

I have, however, one doubt. Though, the Global fit (indicated by GFI, CFI etc.) of the one factor model (with error terms correlated) and the two factor model (with error terms correlated) are similar, the local fit (indicated by factor loadings) of the one factor model is very poor. The negative items have a very low loadings ranging from .04 to .22 with only one item having loading of around .5.

Further, please note that in my initial post I mentioned that the one factor model is not correlating with measures of health in the predicted direction but the two factor model has shown a theoretically meaningful pattern of correlation with measures of health.

In such situation, would you still prefer or recommend the one factor model.

Your views in this regard will be very helpful to us.

I think that's reasonable, although it's best to state the criteria for differentiating models a priori. One useful indicator of whether there are two factors or one (all else being equal) if if the two factors are themselves highly correlated and have the same assoications (allowing for differences in reliability) with other variables.