Well, you have missing data and LISREL tells you that 102 different pattern of missingness were found. If it was possible, the missing data were internally replaced (not physically!) using the EM algorithm resulting in a sample size of N = 2653. The percentage of missing data is 16.78%. The likelihood values are given for the perfect fitting model, the saturated model, and your analyzed model. Your estimator is full information maximum likelihood, which is the estimator usually used for estimating parameters and simultaneously replacing the missing data.

Then you get some model fit criteria: Your overall fit is evaluated using the chi-square value. This value is 4234, and it is significant (p= .000) at least partly because of your large sample size, but most likely because of some misfit,  i.e., the model does not fit the data too well (for a good fitting model you would need a chi-square value chi-square/df

Dear Karin,

Thank you very much for your answer. I got it now. After CFA, I conduct EFA with Principle component analysis, Varimax rotation, no factor loadings less than 0.47. Five factors were extracted and the items were located into these five factors. All these things happened as I had expected. Do these results suggest anything about the validity of my instrument? Should I conduct follow-up analysis with this instrument? Should I do anything else for CFA to increase the fit of the model? Should I include EFA results in my study and skip CFA? 

I am looking forward to your answer.

Sincerely yours,

Hoa

Dear Hoa,

PCA is actually not an EFA, and varimax rotation is seldom a good idea. Why would you expect the factors to be uncorrelated? This is a very restrictive assumption that is seldom justified. If I were you, I would look at the modification indices provided by LISREL. They will tell you the reduction in the chi-square value when you estimate a parameter freely that was fixed before.

I guess that you have a very complex model, is this correct? Then I it is no wonder that a very restrictive model does not fit the data perfectly.

The best thing to do is to look for the model misfit. Start analyzing only parts of your model and check whether such a smaller model has a good model fit. And than look at other parts, one by one. Finally add all parts of your model successively.

Most likely, error variables in your CFA are actually correlated. Just check whether the wordings of the items is quite similar or whether two items measure additionally a sub-construct which means that they share variance that is not explained by the common factor.

Another problem may be the choice of the estimation method. Which method did you use? Are your items very skewed? How many levels do your rating scales have?

Choosing a different estimator may be more appropriate for your data.

Just tell me if you need more help.

Kind regards, Karin

Dear Karin,

Thank you for your nice and detailed reply.

My PhD topic is 'Students Attitude toward Chemistry Subject in Vietnam'. I first developed an instrument with 6 scales with 7 items each. The Likert format was adopted with 5 levels. After the pilot with 262 students, the instrument was reduced to 5 scales with 30 items in total. The reduction was the results of the combination of PCA with Varimax rotation and qualitative judgement.  I then conducted the CFA with the larger sample of 2676 students and the results was as I presented  in my first question. 

I will analyze smaller parts of my model as you advised me. I also send you my questionnaire and my Lisrel data results via your email. Would you please kindly have a look at it if you have time? I would much appreciate if you could give me your precious advice based on my documents.

Best Regards,

Hoa

Hoa,

I forgot that it would be advisable to request the completely standardized solution. Otherwise you may erroneously interpret the unstandardized factor loadings as being standardized.

A mail with more suggestions is on the way to you.

Kind regards, Karin