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Quick question... when running a second order LGCM, the first stage is to check measurement invariance of our repeated factors... so we fix the loadings, and then the intercepts equal over time. When fitting the latter model (strong invariance) we would free up the means to differ, i.e. in Mplus code, like in the code below F1 BY V1_1 V1_2 (V_a) V1_3 (V_b); F2 BY V2_1 V2_2 (V_a) V2_3 (V_b); F3 BY V3_1 V3_2 (V_a) V3_3 (V_b); F4 BY V4_1 V4_2 (V_a) V4_3 (V_b); [V1_1 V2_1 V3_1 V4_1] (V_c); [V1_2 V2_2 V3_2 V4_2] (V_d); [V1_3 V2_3 V3_3 V4_3] (V_e); [F1@0]; [F2 F3 F4]; However, when we extend to a second order LGCM, adding i s  F1@0 F2@1 etc we then refix the means  or rather intercepts as they now become  i.e. we remove [F1@0]; [F2 F3 F4]; and allow the usual Mplus fixing of means to come back into effect as in example 6.14 in the Mplus users guide. Why are these factor intercepts refixed to equality i.e. all equalling zero, rather than just the F1 intercept equalling 0 i.e retaining [F1@0]; [F2 F3 F4]? 


These factor intercepts should all be fixed at zero because we want the growth factors to be the only source of observed outcome means changing over time. Without the growth model, the factor means themselves drive the mean changes. Fixing them at zero also makes it analogous to regular growth modeling  the factors take the role of the observed outcomes and the observed outcome intercepts are fixed at zero in regular growth modeling. 


Thanks, makes sense 


I will use a LGM (categorical indicators)). I am trying to set up a model for measurement invariance over time. 1)How do I code this in Mplus? See my input below. 2) How to write the code to impute missing data in the input below? My input: VARIABLE: NAMES u1u48; CATEGORICAL are u1u48; USEVARIABLES are u1u48; MISSING are all(999); Model: !Mesurement invariant model ! SPACS Time 1 KAP1 by u1u4; COI1 by u5u8; WTA1 by u9u12; SPACS1 by KAP1 COI1 WTA1; ! SPACS Time 2 KAP2 by u13u16; COI2 by u17u20; WTA2 by u21u24; SPACS2 by KAP2 COI2 WTA2; ! SPACS Time 3 KAP3 by u25u28; COI3 by u29u32; WTA3 by u33u36; SPACS3 by KAP3 COI3 WTA3; ! SPACS Time 4 KAP4 by u37u40; COI4 by u41u44; WTA4 by u45u48; SPACS4 by KAP4 COI4 WTA4; i s  SPACS1@0 SPACS2@1 SPACS3@2 SPACS4@3; [SPACS1@0 SPACS2@0 SPACS3@0 SPACS4@0] ________________________ Kind regards, Daniel 


See UG ex 6.15. 


Thank you! If I understand you correctly the model below should be the righ. Is that correct? Model: ! Time 1 KAP1 by u1 u2u4 (13); COI1 by u5 u6u8(13); WTA1 by u9 u10u12 (13); SPACS1 by KAP1 COI1 WTA1; ! Time 2 KAP2 by u13 u14u16 (13); COI2 by u17 u18u20(13); WTA2 by u21 u22u24 (13); SPACS2 by KAP2 COI2 WTA2; !( ! Time 3 and 4, the same pattern as in Time 1 and 2 [u1$4 u13$4 u25$4 u37$4] (4); [u2$4 u14$4 u26$4 u38$4] (5); [u3$4 u15$4 u27$4 u39$4] (6); [u4$4 u16$4 u28$4 u40$4] (7); [u5$4 u17$4 u29$4 u41$4] (8); [u6$4 u18$4 u30$4 u42$4] (9); [u7$4 u19$4 u31$4 u43$4] (10); [u8$4 u20$4 u32$4 u44$4] (11); [u9$4 u21$4 u33$4 u45$4] (12); [u10$4 u22$4 u34$4 u46$4] (13); [u11$4 u23$4 u36$4 u47$4] (14); [u12$4 u24$4 u36$4 u48$4] (15); {u1u12@1 u13u48}; i s  SPACS1@0 SPACS2@1 SPACS3@2 SPACS4@3; 


I think you need to fix the intercepts at zero for the 3 firstorder factors when they serve as indicators of the secondorder factor or the model won't be identified. 

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