Binary CFA problems
Message/Author
 Jim Prisciandaro posted on Tuesday, October 10, 2006 - 9:45 am
Hello Dr.s Muthen,

I tested 2 CFA models with 9 binary indicators. I have encountered some problems I was hoping you could help with. What follows is a 2-part message.

Part 1

First, I constructed a 2-factor CFA model. This model produced a standardized threshold value greater than 1. Specifically the output stated:

Thresholds

SAD\$1 -1.470 0.082 -17.936 -1.470 -1.470

So, the threshold throughout is -1.47 for this item. A standardized value greater than 1 is typically a red flag. Is this the case for thresholds? Also, seemingly unrelated to this problem, another item that is on the same factor as the abovementioned item has a very large standard error (2.59) that leads to the item having a standardized loading of .92 that is not statistically significant. All of the other standard errors for this model are closer to .15. What could be leading to such a large standard error?
 Linda K. Muthen posted on Tuesday, October 10, 2006 - 9:49 am
You should send your input, data, output, and licesne number to support@statmodel.com.
 Jim Prisciandaro posted on Tuesday, October 10, 2006 - 9:52 am
Part 2
I constructed a 1-factor model with the same items. I got the following error:
THE MODEL ESTIMATION TERMINATED NORMALLY
THE CHI-SQUARE COMPUTATION COULD NOT BE COMPLETED
BECAUSE OF A SINGULAR MATRIX.

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
PROBLEM INVOLVING PARAMETER 19.

In the TECH1 output I found:
PSI
F1
________
F1 19

Assuming the problem was the variance of the latent factor, I checked TECH4:

ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
F1
________
F1 0.316

ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
F1
________
F1 1.000

It may be misinterpreting, but I don't understand why the problem would be with this parameter. Do you have any insight on this matter?

The only thing I see that may explain these problems is that the split for one of the items (the item with the -1.47 threshold) has a very high endorsement rate (93%), while the splits for the other items are much more balanced (most are 50-50, with one other being 75-25).

Jim
 Linda K. Muthen posted on Tuesday, October 10, 2006 - 10:32 am
You should send your input, data, output, and licesne number to support@statmodel.com.
 Jim Prisciandaro posted on Saturday, October 14, 2006 - 1:42 pm
Hello Linda,

Thanks again for your help. After fixing my syntax errors, I have encountered a small problem with my model.

The model consists of 2 factors and 9 binary indicators. 3 of the indicators are modeled as loading on factor 1, and the remaining 6 are modeled as loading on factor 2. The model fits well, and the parameters seem reasonable. However, one of the items has a very small R-square value (r-square = .05). One of the modification indices suggested I load this item on both of the two factors. However, this modification index was not the largest shown (it was statistically significant though). If I allow the item in question to load on both factors, the r-square for the item jumps up to .26.

My question is: Is it reasonable to make a model modification for the sole purpose of increasing the r-square of an item (that is quite low), given that the modification is theoretically plausible? Additionally, is it reasonable to make the modification for this item given that three other modifications with higher MIs that are equally theoretically plausible are being passed over?

Thanks,
Jim
 Linda K. Muthen posted on Sunday, October 15, 2006 - 11:38 am
I think it would be hard to justify this. It may be that this item should be dropped from the analysis or changed if possible given its poor behavior.