2nd order LGCM - fixing of factor int...
Message/Author
 Chris Stride posted on Tuesday, July 16, 2019 - 1:48 pm
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]?
 Bengt O. Muthen posted on Tuesday, July 16, 2019 - 5:40 pm
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.
 Chris Stride posted on Wednesday, July 17, 2019 - 4:25 am
Thanks, makes sense
 Daniel Olsson posted on Tuesday, October 29, 2019 - 3:50 am
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 u1-u48;
CATEGORICAL are u1-u48;
USEVARIABLES are u1-u48;
MISSING are all(999);
Model: !Mesurement invariant model

! SPACS Time 1
KAP1 by u1-u4;
COI1 by u5-u8;
WTA1 by u9-u12;
SPACS1 by KAP1 COI1 WTA1;

! SPACS Time 2
KAP2 by u13-u16;
COI2 by u17-u20;
WTA2 by u21-u24;
SPACS2 by KAP2 COI2 WTA2;

! SPACS Time 3
KAP3 by u25-u28;
COI3 by u29-u32;
WTA3 by u33-u36;
SPACS3 by KAP3 COI3 WTA3;

! SPACS Time 4
KAP4 by u37-u40;
COI4 by u41-u44;
WTA4 by u45-u48;
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
 Bengt O. Muthen posted on Tuesday, October 29, 2019 - 3:59 pm
See UG ex 6.15.
 Daniel Olsson posted on Thursday, October 31, 2019 - 5:56 am
Thank you!
If I understand you correctly the model below should be the righ. Is that correct?

Model:
! Time 1
KAP1 by u1
u2-u4 (1-3);
COI1 by u5
u6-u8(1-3);
WTA1 by u9
u10-u12 (1-3);

SPACS1 by KAP1 COI1 WTA1;

! Time 2
KAP2 by u13
u14-u16 (1-3);
COI2 by u17
u18-u20(1-3);
WTA2 by u21
u22-u24 (1-3);

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);
{u1-u12@1 u13-u48};

i s | SPACS1@0 SPACS2@1 SPACS3@2 SPACS4@3;
 Bengt O. Muthen posted on Thursday, October 31, 2019 - 2:28 pm
I think you need to fix the intercepts at zero for the 3 first-order factors when they serve as indicators of the second-order factor or the model won't be identified.