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.
First, I constructed a 2-factor CFA model. This model produced a standardized threshold value greater than 1. Specifically the output stated:
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?
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).
Any help you could provide would be greatly appreciated,
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?