If factors are showing very low cronbach alpha value (Standardized questionnaire used) but in CFA the model fit is quite good, what as a researcher shall I do? Shall I proceed to SEM?
As pointed out earlier, the number of test items, item interrelatedness and dimensionality affect the value of alpha. There are different reports about the acceptable values of alpha, ranging from 0.70 to 0.95. A low value of alpha could be due to a low number of questions, poor interrelatedness between items or eterogeneous constructs.
Example: if a low alpha is due to poor correlation between items then some should be revised or discarded. The easiest method to find them is to compute the correlation of each test item with the total score test; items with low correlations (approaching zero) are deleted. If alpha is too high it may suggest that some items are redundant as they are testing the same question but in a different guise. A maximum alpha value of 0.90 has been recommended.
I now removed some outliers and responses with very low or high SD values. Seems the reliability is OK now and the CFA is also showing good values of AGFI/GFI.