I'm doing a confirmatory factor analysis (CFA) in Mplus, testing a 5-factor PTSD model with responses (n=376) to a PTSD questionnaire (the Harvard Trauma Questionnaire). For some reason, the output includes an interfactor correlation of 1.6. How is this possible? The corresponding raw score correlation is 0.5. The involved factors have 2 and 3 variables, respectively. It seems plausible to me that correlations based on latent measures might overcompensate for measuring error (which might be estimated to be large, given that the small number of variables involved), resulting in a correlation estimate above 1. I haven't been able to find confirmation of this, but even if it's true, could it explain a correlation as high as 1.6?
From input file: DATA: FILE IS HTQdata.dat; Variable: Names ARE pt_no agegrp3 gender country6 ethnicity htq_1_1-htq_1_16 hscl1-hscl25 sdsf1_1 sdsf1_2 sdsf1_3; Usevariables are htq_1_1-htq_1_16; Missing are all (-999); Model: Intrus by htq_1_1 htq_1_2 htq_1_3 htq_1_16; Avoidan by htq_1_11 htq_1_15; Numbing by htq_1_4 htq_1_5 htq_1_12 htq_1_13 htq_1_14; DysArou by htq_1_7 htq_1_8 htq_1_10; AnxArou by htq_1_6 htq_1_9; Output: sampstat; stand; tech4; Mod(1);