# ------------------------------------------------------------------------------
# 1. Cholesky Decomposition ACE Model for CONTINUOUS data
# ------------------------------------------------------------------------------


# ------------------------------------------------------------------------------
# 2. Latent Growth Curve ACE Model for CONTINUOUS data
# ------------------------------------------------------------------------------


1. Specify number of latent factors
   nf <- 2	
2. Specify total variance in the model
   Hint: GO TO # Algebra to compute total variances and standard deviations (diagonal only)
3. Fix covariance formula
4. Fix FIML objective
5. Write & run nested models AE, CE & A

# ------------
# Run CE LGC model
# ------------

LgcCeModel   		<- omxSetParameters( LgcCeModel, labels=c( AlLabs,AsLabs ), free=FALSE, values=0 )
LgcCeModel@matrices$al			# Check the C pathways are dropped to zero
LgcCeModel@matrices$as			# Check the C pathways are dropped to zero
LgcCeFit    <- mxRun(LgcCeModel)
LgcCeSumm   <- summary(LgcCeFit)
LgcCeSumm

# ------------
# Run E LGC model
# ------------


LgcEModel   		<- omxSetParameters( LgcEModel, labels=c( ClLabs,CsLabs,AlLabs,AsLabs ), free=FALSE, values=0 )
LgcEModel@matrices$cl			# Check the C pathways are dropped to zero
LgcEModel@matrices$cs			# Check the C pathways are dropped to zero
LgcEModel@matrices$al			# Check the C pathways are dropped to zero
LgcEModel@matrices$as			# Check the C pathways are dropped to zero
LgcEFit    <- mxRun(LgcEModel)
LgcESumm   <- summary(LgcEFit)
LgcESumm




# ------------------------------------------------------------------------------
# 3. Simplex ACE Model - for continuous data
# ------------------------------------------------------------------------------

1. Under 'Create labels' specify which transmission elements are free (TRUE) vs fixed (FALSE) 

tFree     <- c(F,T,F,F,T,F)			    # Specify free vs fixed transmission elements
									    # CHANGE LENGTH if CHANGING # of VARIABLES
2. Write variance formula for total C effects 
   HInt: GO TO CovC # Matrices A, C, & E to compute variance components.
   
covC      <- mxAlgebra( expression=solve(I-ct) %&% (ci %*% t(ci)), name="C" )
   
3. Write & run nested AE, & CE models

# Run CE Simplex model
# ------------

CeSimpModel   <- mxModel( SimpAceFit, name="CeSimp" )
CeSimpModel   <- omxSetParameters( CeSimpModel, labels=c( AtLabs,AiLabs ), free=FALSE, values=0 )
CeSimpModel$rA 		<- NULL
CeSimpModel$MZ.rA 	<- NULL
CeSimpModel$DZ.rA 	<- NULL
CeSimpFit     <- mxRun(CeSimpModel)
SimpCeSumm   <- summary(CeSimpFit)
SimpCeSumm



# ------------------------------------------------------------------------------
# 3. Latent Growth Curve ACE Model + Sex effects for ORDINAL data
# ------------------------------------------------------------------------------


1. Specify fixed path values for the factor loading matrix

pathFl    <- mxMatrix( type="Full", nrow=nv, ncol=nf, free=FALSE, values=c(1,1,1,0,1,2), labels=FlLabs,name="fl" )