3-level longitudinal latent growth curve model

###
#Team Level [Lv2]
###
##If you do not have a model in mind for level 2, you can specify a saturated level by adding all variances and covariances of the endogenous variables
#https://lavaan.ugent.be/tutorial/multilevel.html
##Default starting Values: Variances=1; Covariances/regressions 0.5 (or 0)... but I will try mxAutoStart
#https://openmx.ssri.psu.edu/thread/1366

#Define Lv2Data
Lv2Data<-mxData(
observed=DataIndividualForOpenMx[!duplicated(DataIndividualForOpenMx$OpenMxTeamNumber),],
type="raw",
primaryKey="OpenMxTeamNumber"
)
Lv2Data
#Define the Manifest and Latent Variables
Lv2Manifests<-c()
Lv2Manifests
Lv2AggregationsOfLv1Measures<-paste(c("At3","At4","At5","At6","At7","At8","At9"),"_Agg",sep="")
Lv2AggregationsOfLv1Measures
Lv2Latents<-c(Lv2AggregationsOfLv1Measures,"Lv2Intercept","Lv2Slope","Lv2Sqr")
Lv2Latents
#Residual Variances of aggregations from indicators on Lv1
ResVarOfAggregationsFromIndicatorsOnLv1<-mxPath(
from=Lv2AggregationsOfLv1Measures,
to=Lv2AggregationsOfLv1Measures,
arrows=2,
free=TRUE,
values=1
)
ResVarOfAggregationsFromIndicatorsOnLv1
#The Covariances between Intercept, Slope and Sqr
##This seems to be needed as per: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5875450/
##Order is: (a,b), (a,c), (b,c)
#As shown by: https://www.rdocumentation.org/packages/OpenMx/versions/2.7.9/topics/mxPath
Lv2CovBWInterceptSlopeSqr<-mxPath(
from=c("Lv2Intercept","Lv2Slope","Lv2Sqr"),
arrows=2,
connect="unique.bivariate",
free=TRUE,
values=0
)
Lv2CovBWInterceptSlopeSqr
#Var of InterceptSlopeSqr
Lv2VarOfInterceptSlopeSqr<-mxPath(
from=c("Lv2Intercept","Lv2Slope","Lv2Sqr"),
arrows=2,
connect="single",
free=TRUE,
values=1
)
Lv2VarOfInterceptSlopeSqr
#Means
Lv2MeanOfIntercepts<-mxPath(
from="one",
to="Lv2Intercept",
arrows=1,
free=TRUE,
values=0
)
Lv2MeanOfIntercepts
Lv2MeanOfSlopes<-mxPath(
from="one",
to="Lv2Slope",
arrows=1,
free=TRUE,
values=0
)
Lv2MeanOfSlopes
Lv2MeanOfSqrs<-mxPath(
from="one",
to="Lv2Sqr",
arrows=1,
free=TRUE,
values=0
)
Lv2MeanOfSqrs
#Loading Lv2AggregationsOfLv1Measures on Lv2Intercept, Lv2Slope and Lv2Sqr
Lv2OverTimeLoadingsToLv2Intercept<-mxPath(
from="Lv2Intercept",
to=Lv2AggregationsOfLv1Measures,
arrows=1,
free=FALSE,
values=c(1,1,1,1,1,1,1)
)
Lv2OverTimeLoadingsToLv2Intercept
Lv2OverTimeLoadingsToLv2Slope<-mxPath(
from="Lv2Slope",
to=Lv2AggregationsOfLv1Measures,
arrows=1,
free=TRUE,
values=c(0,1,2,3,4,5,6)
)
Lv2OverTimeLoadingsToLv2Slope
Lv2OverTimeLoadingsToLv2Sqr<-mxPath(
from="Lv2Sqr",
to=Lv2AggregationsOfLv1Measures,
arrows=1,
free=TRUE,
values=c(0,1,4,9,16,25,36)
)
Lv2OverTimeLoadingsToLv2Sqr
#Build Lv2 Model
MxModelLv2<-mxModel(
model="MxModelLv2", type="RAM",
data=Lv2Data,
manifestVars=Lv2Manifests, latentVars=Lv2Latents,
ResVarOfAggregationsFromIndicatorsOnLv1,
Lv2CovBWInterceptSlopeSqr,
Lv2VarOfInterceptSlopeSqr,
Lv2MeanOfIntercepts,
Lv2MeanOfSlopes,
Lv2MeanOfSqrs,
Lv2OverTimeLoadingsToLv2Intercept,
Lv2OverTimeLoadingsToLv2Slope,
Lv2OverTimeLoadingsToLv2Sqr
)#end MxModelLv2

###
#Individual Level [Lv1]
###

##Lv1 Data
Lv1Data<-mxData(
observed=DataIndividualForOpenMx,
type="raw",
primaryKey="PrimaryKeyInteger"
)
Lv1Data
##Define the Manifest and Latent Variables
Lv1Manifests<-c("At3","At4","At5","At6","At7","At8","At9","gender_binary")
Lv1Manifests
Lv1Latents<-c("Lv1Intercept","Lv1Slope","Lv1Sqr")
Lv1Latents
##Connect Lv1Data to Lv2Data
Lv1Links<-paste("MxModelLv2.",c("At3","At4","At5","At6","At7","At8","At9"),"_Agg",sep="")
Lv1Links
ConnectingPath<-mxPath(
from=Lv1Links,
to=c("At3","At4","At5","At6","At7","At8","At9"),
free=FALSE,
values=1,
joinKey="OpenMxTeamNumber"
)
ConnectingPath
##Vars of InterceptSlopeSqr
Lv1VarOfInterceptSlopeSqr<-mxPath(
from=c("Lv1Intercept","Lv1Slope","Lv1Sqr"),
arrows=2,
connect="single",
free=TRUE,
values=0
)
Lv1VarOfInterceptSlopeSqr
##Means of InterceptSlopeSqr
Lv1MeanOfIntercepts<-mxPath(
from="one",
to="Lv1Intercept",
arrows=1,
free=TRUE,
values=0
)
Lv1MeanOfIntercepts
Lv1MeanOfSlopes<-mxPath(
from="one",
to="Lv1Slope",
arrows=1,
free=TRUE,
values=0
)
Lv1MeanOfSlopes
Lv1MeanOfSqrs<-mxPath(
from="one",
to="Lv1Sqr",
arrows=1,
free=TRUE,
values=0
)
Lv1MeanOfSqrs
##The Covariances between Intercept, Slope and Sqr (https://www.rdocumentation.org/packages/OpenMx/versions/2.7.9/topics/mxPath)
Lv1CovBWInterceptSlopeSqr<-mxPath(
from=c("Lv1Intercept","Lv1Slope","Lv1Sqr"),
arrows=2,
connect="unique.bivariate",
free=TRUE,
values=0
)
Lv1CovBWInterceptSlopeSqr

##Loadings of Repeated Measures on Intercept (All of these are fixed to 1 in a latent Growth Curve)
Lv1OverTimeLoadingsToLv1Intercept<-mxPath(
from="Lv1Intercept",
to=c("At3","At4","At5","At6","At7","At8","At9"),
arrows=1,
free=FALSE,
values=1
)
Lv1OverTimeLoadingsToLv1Intercept
#Loadings of Repeated Measures on Slope (These start at 0 and increase in increments of 1)
Lv1OverTimeLoadingsToLv1Slope<-mxPath(
from="Lv1Slope",
to=c("At3","At4","At5","At6","At7","At8","At9"),
arrows=1,
free=FALSE,
values=c(0,1,2,3,4,5,6)
)
Lv1OverTimeLoadingsToLv1Slope
#Loadings of Repeated Measures on Sqr (These are "slope" values ^2... e.g. 0^2, 1^2, 2^2, 3^2... etc)
Lv1OverTimeLoadingsToLv1Sqr<-mxPath(
from="Lv1Sqr",
to=c("At3","At4","At5","At6","At7","At8","At9"),
arrows=1,
free=FALSE,
values=c(0,1,4,9,16,25,36)
)
Lv1OverTimeLoadingsToLv1Sqr

#ResidualVariancseOfRepeatedMeasures
Lv1ResidualVariancesOfRepeatedMeasures<-mxPath(
from=c("At3","At4","At5","At6","At7","At8","At9"),
to=c("At3","At4","At5","At6","At7","At8","At9"),
arrows=2,
free=TRUE,
values=1
)
Lv1ResidualVariancesOfRepeatedMeasures

#Covariances of Intercept, Slope and Sqr
#Order is: #(a,a), (a,b), (a,c), (b,b), (b,c), (c,c)
#As shown by: https://www.rdocumentation.org/packages/OpenMx/versions/2.7.9/topics/mxPath
Lv1CovBWInterceptSlopeAndSqr<-mxPath(
from=c("Lv1Intercept","Lv1Slope","Lv1Sqr"),
arrows=2,
free=TRUE,
values=0,
connect="unique.bivariate"
)
Lv1CovBWInterceptSlopeAndSqr

##IV (gender_binary) as a predictor for variability from quadradic trajectory
#Vars of gender_binary
Lv1VarOfGender<-mxPath(
from="gender_binary",
arrows=2,
free=TRUE,
values=1
)
Lv1VarOfGender
#Means of Gender
Lv1MeanOfGender<-mxPath(
from="one",
to="gender_binary",
arrows=1,
free=TRUE,
values=0
)
Lv1MeanOfGender
#Gender Predicting Repeated Measures
Lv1GenderToOverTime<-mxPath(
from="gender_binary",
to=c("At3","At4","At5","At6","At7","At8","At9"),
arrows=1,
free=TRUE,
values=c(0,0,0,0,0,0,0)
)
Lv1GenderToOverTime

##Building the Model
MxModelLv1<-mxModel(
model="MxModelLv1", type="RAM",
manifestVars=Lv1Manifests, latentVars=Lv1Latents,
mxModel(model=MxModelLv2),
Lv1Data,
ConnectingPath,
Lv1VarOfInterceptSlopeSqr,
Lv1MeanOfIntercepts,
Lv1MeanOfSlopes,
Lv1MeanOfSqrs,
Lv1CovBWInterceptSlopeAndSqr,
Lv1OverTimeLoadingsToLv1Intercept,
Lv1OverTimeLoadingsToLv1Slope,
Lv1OverTimeLoadingsToLv1Sqr,
Lv1ResidualVariancesOfRepeatedMeasures,
Lv1CovBWInterceptSlopeAndSqr,
Lv1VarOfGender, Lv1GenderToOverTime, Lv1GenderToOverTime
)#end StudentGrowthIntSlopeAndSqrModel