I am conducting a CFA with six factors (all indicators are from a 1-5 scale):
f1 by y1 y2 y3 y4 f2 by y5 y6 y7 f3 by y8 y9 y10 y11 y12 f4 by y13 y14 y15 f5 by y16 y17 f6 by y18 y19 y20 y21
I have good model fit, but when I look carefully at the MI's I noticed that the 2 factors (y16 and y17) on f5 load onto several other factors (esp. f1 and f2). The odd thing is that the MI's for these 2 items are identical (akin to what you would see with invariance testing among 2 groups) with each factor. Moreover, the signs of the EPC's for both items are OPPOSITE one another, even though y16 and y17 both load on positively to f5.
This only appears to be a problem when I split my overall sample. The problem arises for only females (vs. males), older (vs. younger) and Mexican American (vs. European American).
My items are coded correctly, and are moderately positively correlated with one another.
What could be a possible explanation for such MI's?