It is for 2 waves only, with 1 indicator latents (and with measurement error estimated for both 'cause' and 'effect' sets of variables: yes, it runs!), and for observed variables only. It was posted on SEMNET, and there is a lot more on this 'change modeling' (another posting on Semnet sends to lots of materials, full texts too).
Try it on your data (no changes needed: just add your own variable names in DEFINE), and let me know what you see in your data, in one of mine I saw the SIGN of the effect flipping when using latents!!!
1. With LVs
DEFINE: X1 = YourXatTime1; X2 = YourXatTime2; Y1 = YourYatTime1; Y2 = YourYatTime2; MODEL: !X part ! first create LV behind each observed indicator: ! time 1 LX1 by X1; ! define new 1 indicator LV [X1@0] ; ! set the intercept of the X1 to 0 to identify/define the meal of its latent X1 (measerrX);! name the residual error to be set equal across time and estimated ! time 2 LX2 by X2; ! define new 1 indicator LV [X2@0] ; ! set the intercept of the X1 to 0 to identify/define the meal of its latent X2 (measerrX);! name the residual error to be set equal across time and estimated LCS21X by LX2@1; !defined by the 2nd variable LX2 @0; !residual variance of 2nd measure @0: note this is true residual, with measurement LCS21X ON LX1; !PROPORTIONAL-GROWTH estimated: can omit it too, by adding ! or adding @0: [LX2 @0] ; !intercepts of 2nd measure @0 LX2 on LX1@1; !autoregressive path set @1 !Y part ! first create LV behind each observed indicator: ! time 1 LY1 by Y1; ! define new 1 indicator LV [Y1@0] ; ! set the intercept of the X1 to 0 to identify/define the meal of its latent Y1 (measerrY);! name the residual error to be set equal across time and estimated ! time 2 LY2 by Y2; ! define new 1 indicator LV [Y2@0] ; ! set the intercept of the X1 to 0 to identify/define the meal of its latent Y2 (measerrY);! name the residual error to be set equal across time and estimated LCS21Y by LY2@1; !defined by the 2nd variable LY2 @0; !residual variance of 2nd measure @0: note this is true residual, with measurement LCS21Y ON LY1; !PROPORTIONAL-GROWTH estimated: can omit it too, by adding ! or adding @0: [LY2 @0] ; !intercepts of 2nd measure @0 LY2 on LY1@1; !autoregressive path set @1 ! bivariate section LCS21Y ON LCS21X; ! CHANGE IN X LEADING TO CHANGE IN Y ! COVARIANCES BETWEEN EXOGENOUS VARIABLES ARE ADDED BY DEFAULT: YOU MAY WANT TO DEFLECT TH ! LX1 WITH LY1@0 ; ! BE PREPARED TO MAKE THESE @0 IT MAY NOT RUN OTHERWISE LCS21X @0; LCS21Y @0; OUTPUT: TECH1 TECH4 stand ; 2. With observed variables: DEFINE: X1 = YourXatTime1; X2 = YourXatTime2; Y1 = YourYatTime1; Y2 = YourYatTime2; MODEL: !X part LCS21X by X2@1; !defined by the 2nd variable X2 @0; !residual variance of 2nd measure @0: note this is true residual, with measurement error of X1 partialled out LCS21X ON X1; !PROPORTIONAL-GROWTH estimated: can omit it too, by adding ! or adding @0: different models!!! [X2 @0] ; !intercepts of 2nd measure @0 X2 on X1@1; !autoregressive path set @1 !Y part LCS21Y by Y2@1; !defined by the 2nd variable Y2 @0; !residual variance of 2nd measure @0: note this is true residual, with measurement error of X1 partialled out LCS21Y ON Y1; !PROPORTIONAL-GROWTH estimated: can omit it too, by adding ! or adding @0: different models!!! [Y2 @0] ; !intercepts of 2nd measure @0 Y2 on Y1@1; !autoregressive path set @1 ! bivariate section LCS21Y ON LCS21X; ! CHANGE IN X LEADING TO CHANGE IN Y ! COVARIANCES BETWEEN EXOGENOUS VARIABLES ARE ADDED BY DEFAULT: YOU MAY WANT TO DEFLECT THEM INITIALLY ! X1 WITH Y1@0 ; ! BE PREPARED TO MAKE THESE @0 IT MAY NOT RUN OTHERWISE !LCS21X @0; !LCS21Y @0; OUTPUT: TECH1 TECH4 stand ;
