ctStanFit: ctStanFit

In ctsem: Continuous Time Structural Equation Modelling

ctStanFit

Description

Fits a ctsem model specified via ctModel with type either 'stanct' or 'standt'.

Usage

ctStanFit(
  datalong,
  ctstanmodel,
  stanmodeltext = NA,
  iter = 1000,
  intoverstates = TRUE,
  binomial = FALSE,
  fit = TRUE,
  intoverpop = "auto",
  sameInitialTimes = FALSE,
  stationary = FALSE,
  plot = FALSE,
  derrind = NA,
  optimize = TRUE,
  optimcontrol = list(),
  nlcontrol = list(),
  nopriors = NA,
  priors = FALSE,
  chains = 2,
  cores = ifelse(optimize, getOption("mc.cores", 2L), "maxneeded"),
  inits = NULL,
  compileArgs = list(),
  forcerecompile = FALSE,
  saveCompile = TRUE,
  savescores = FALSE,
  savesubjectmatrices = FALSE,
  saveComplexPars = FALSE,
  gendata = FALSE,
  control = list(),
  verbose = 0,
  vb = FALSE,
  ...
)

Arguments

datalong	long format data containing columns for subject id (numeric values, 1 to max subjects), manifest variables, any time dependent (i.e. varying within subject) predictors, and any time independent (not varying within subject) predictors.
ctstanmodel	model object as generated by ctModel with type='stanct' or 'standt', for continuous or discrete time models respectively.
stanmodeltext	already specified Stan model character string, generally leave NA unless modifying Stan model directly. (Possible after modification of output from fit=FALSE)
iter	used when optimize=FALSE. number of iterations, half of which will be devoted to warmup by default when sampling. When optimizing, this is the maximum number of iterations to allow – convergence hopefully occurs before this!
intoverstates	logical indicating whether or not to integrate over latent states using a Kalman filter. Generally recommended to set TRUE unless using non-gaussian measurement model.
binomial	Deprecated. Logical indicating the use of binary rather than Gaussian data, as with IRT analyses. This now sets intoverstates = FALSE and the manifesttype of every indicator to 1, for binary.
fit	If TRUE, fit specified model using Stan, if FALSE, return stan model object without fitting.
intoverpop	if 'auto', set to TRUE if optimizing and FALSE if using hmc. if TRUE, integrates over population distribution of parameters rather than full sampling. Allows for optimization of non-linearities and random effects.
sameInitialTimes	if TRUE, include an empty observation for every subject that has no observation at the earliest observation time of the dataset. This ensures that the T0MEANS occurs for every subject at the same time, rather than just at the earliest observation for that subject. Important when modelling trends over time, age, etc.
stationary	Logical. If TRUE, T0VAR and T0MEANS input matrices are ignored, the parameters are instead fixed to long run expectations. More control over this can be achieved by instead setting parameter names of T0MEANS and T0VAR matrices in the input model to 'stationary', for elements that should be fixed to stationarity.
plot	if TRUE, for sampling, a Shiny program is launched upon fitting to interactively plot samples. May struggle with many (e.g., > 5000) parameters. For optimizing, various optimization details are plotted – in development.
derrind	deprecated, latents involved in dynamic error calculations are determined automatically now.
optimize	if TRUE, use stanoptimis function for maximum a posteriori / importance sampling estimates, otherwise use the HMC sampler from Stan, which is (much) slower, but generally more robust, accurate, and informative.
optimcontrol	list of parameters sent to stanoptimis governing optimization / importance sampling.
nlcontrol	List of non-linear control parameters. maxtimestep must be a positive numeric, specifying the largest time span covered by the numerical integration. The large default ensures that for each observation time interval, only a single step of exponential integration is used. When maxtimestep is smaller than the observation time interval, the integration is nested within an Euler like loop. Smaller values may offer greater accuracy, but are slower and not always necessary. Given the exponential integration, linear model elements are fit exactly with only a single step.
nopriors	deprecated, use priors argument. logical. If TRUE, any priors are disabled – sometimes desirable for optimization.
priors	if TRUE, priors are included in computations, otherwise specified priors are ignored.
chains	used when optimize=FALSE. Number of chains to sample, during HMC or post-optimization importance sampling. Unless the cores argument is also set, the number of chains determines the number of cpu cores used, up to the maximum available minus one. Irrelevant when optimize=TRUE.
cores	number of cpu cores to use. Either 'maxneeded' to use as many as available minus one, up to the number of chains, or a positive integer. If optimize=TRUE, more cores are generally faster.
inits	either character string 'optimize, NULL, or vector of (unconstrained) parameter start values, as returned by the rstan function rstan::unconstrain_pars, or the parameter values found in a ctsem fit object myfit$stanfit$rawest (or $rawposterior) for instance.
compileArgs	List of arguments to pass to stan_model for compilation of the Stan model.
forcerecompile	logical. For development purposes. If TRUE, stan model is recompiled, regardless of apparent need for compilation.
saveCompile	if TRUE and compilation is needed / requested, writes the stan model to the parent frame as ctsem.compiled (unless that object already exists and is not from ctsem), to avoid unnecessary recompilation.
savescores	Logical. If TRUE, output from the Kalman filter is saved in output. For datasets with many variables or time points, will increase file size substantially.
savesubjectmatrices	Logical. If TRUE, subject specific matrices are saved – only relevant when either time dependent predictors or individual differences are used. Can increase memory usage dramatically in large models, and can be computed after fitting using ctExtract or ctStanSubjectPars .
saveComplexPars	Logical. If TRUE, also save rowwise output of any complex parameters specified, i.e. combinations of parameters, functions and states.
gendata	Logical – If TRUE, uses provided data for only covariates and a time and missingness structure, and generates random data according to the specified model / priors. Generated data is in the $Ygen subobject after running extract on the fit object. For datasets with many manifest variables or time points, file size may be large. To generate data based on the posterior of a fitted model, see ctStanGenerateFromFit.
control	Used when optimize=FALSE. List of arguments sent to stan control argument, regarding warmup / sampling behaviour. Unless specified, values used are: list(adapt_delta = .8, adapt_window=2, max_treedepth=10, adapt_init_buffer=2, stepsize = .001)
verbose	Integer from 0 to 2. Higher values print more information during model fit – for debugging.
vb	Logical. Use variational Bayes algorithm from stan? Only kind of working, not recommended.
...	additional arguments to pass to stan function.

Examples

#generate a ctStanModel relying heavily on defaults
model<-ctModel(type='stanct',
  latentNames=c('eta1','eta2'),
  manifestNames=c('Y1','Y2'),
  MANIFESTVAR=diag(.1,2),
  TDpredNames='TD1', 
  TIpredNames=c('TI1','TI2','TI3'),
  LAMBDA=diag(2)) 

fit<-ctStanFit(ctstantestdat, model,priors=TRUE)

summary(fit) 

plot(fit,wait=FALSE)

#### extended examples

library(ctsem)
set.seed(3)

#  Data generation (run this, but no need to understand!) -----------------

Tpoints <- 20
nmanifest <- 4
nlatent <- 2
nsubjects<-20

#random effects
age <- rnorm(nsubjects) #standardised
cint1<-rnorm(nsubjects,2,.3)+age*.5
cint2 <- cint1*.5+rnorm(nsubjects,1,.2)+age*.5
tdpredeffect <- rnorm(nsubjects,5,.3)+age*.5

for(i in 1:nsubjects){
  #generating model
  gm<-ctModel(Tpoints=Tpoints,n.manifest = nmanifest,n.latent = nlatent,n.TDpred = 1,
    LAMBDA = matrix(c(1,0,0,0, 0,1,.8,1.3),nrow=nmanifest,ncol=nlatent),
    DRIFT=matrix(c(-.3, .2, 0, -.5),nlatent,nlatent),
    TDPREDMEANS=matrix(c(rep(0,Tpoints-10),1,rep(0,9)),ncol=1),
    TDPREDEFFECT=matrix(c(tdpredeffect[i],0),nrow=nlatent),
    DIFFUSION = matrix(c(1, 0, 0, .5),2,2),
    CINT = matrix(c(cint1[i],cint2[i]),ncol=1),
    T0VAR=diag(2,nlatent,nlatent),
    MANIFESTVAR = diag(.5, nmanifest))

  #generate data
  newdat <- ctGenerate(ctmodelobj = gm,n.subjects = 1,burnin = 2,
    dtmat<-rbind(c(rep(.5,8),3,rep(.5,Tpoints-9))))
  newdat[,'id'] <- i #set id for each subject
  newdat <- cbind(newdat,age[i]) #include time independent predictor
  if(i ==1) {
    dat <- newdat[1:(Tpoints-10),] #pre intervention data
    dat2 <- newdat #including post intervention data
  }
  if(i > 1) {
    dat <- rbind(dat, newdat[1:(Tpoints-10),])
    dat2 <- rbind(dat2,newdat)
  }
}
colnames(dat)[ncol(dat)] <- 'age'
colnames(dat2)[ncol(dat)] <- 'age'


#plot generated data for sanity
plot(age)
matplot(dat[,gm$manifestNames],type='l',pch=1)
plotvar <- 'Y1'
plot(dat[dat[,'id']==1,'time'],dat[dat[,'id']==1,plotvar],type='l',
  ylim=range(dat[,plotvar],na.rm=TRUE))
for(i in 2:nsubjects){
  points(dat[dat[,'id']==i,'time'],dat[dat[,'id']==i,plotvar],type='l',col=i)
}


dat2[,gm$manifestNames][sample(1:length(dat2[,gm$manifestNames]),size = 100)] <- NA


#data structure
head(dat2)


# Model fitting -----------------------------------------------------------

##simple univariate default model

m <- ctModel(type = 'stanct', manifestNames = c('Y1'), LAMBDA = diag(1))
ctModelLatex(m)

#Specify univariate linear growth curve

m1 <- ctModel(type = 'stanct',
  manifestNames = c('Y1'), latentNames=c('eta1'),
  DRIFT=matrix(-.0001,nrow=1,ncol=1),
  DIFFUSION=matrix(0,nrow=1,ncol=1),
  T0VAR=matrix(0,nrow=1,ncol=1),
  CINT=matrix(c('cint1'),ncol=1),
  T0MEANS=matrix(c('t0m1'),ncol=1),
  LAMBDA = diag(1),
  MANIFESTMEANS=matrix(0,ncol=1),
  MANIFESTVAR=matrix(c('merror'),nrow=1,ncol=1))

ctModelLatex(m1)

#fit
f1 <- ctStanFit(datalong = dat2, ctstanmodel = m1, optimize=TRUE, priors=FALSE)

summary(f1)

#plots of individual subject models v data
ctKalman(f1,plot=TRUE,subjects=1,kalmanvec=c('y','yprior'),timestep=.01)
ctKalman(f1,plot=TRUE,subjects=1:3,kalmanvec=c('y','ysmooth'),timestep=.01,errorvec=NA)

ctStanPostPredict(f1, wait=FALSE) #compare randomly generated data from posterior to observed data

cf<-ctCheckFit(f1) #compare mean and covariance of randomly generated data to observed cov
plot(cf,wait=FALSE)

 ### Further example models

#Include intervention
m2 <- ctModel(type = 'stanct',
  manifestNames = c('Y1'), latentNames=c('eta1'),
  n.TDpred=1,TDpredNames = 'TD1', #this line includes the intervention
  TDPREDEFFECT=matrix(c('tdpredeffect'),nrow=1,ncol=1), #intervention effect
  DRIFT=matrix(-1e-5,nrow=1,ncol=1),
  DIFFUSION=matrix(0,nrow=1,ncol=1),
  CINT=matrix(c('cint1'),ncol=1),
  T0MEANS=matrix(c('t0m1'),ncol=1),
  T0VAR=matrix(0,nrow=1,ncol=1),
  LAMBDA = diag(1),
  MANIFESTMEANS=matrix(0,ncol=1),
  MANIFESTVAR=matrix(c('merror'),nrow=1,ncol=1))



#Individual differences in intervention, Bayesian estimation, covariates
m2i <- ctModel(type = 'stanct',
  manifestNames = c('Y1'), latentNames=c('eta1'),
  TIpredNames = 'age',
  TDpredNames = 'TD1', #this line includes the intervention
  TDPREDEFFECT=matrix(c('tdpredeffect||TRUE'),nrow=1,ncol=1), #intervention effect
  DRIFT=matrix(-1e-5,nrow=1,ncol=1),
  DIFFUSION=matrix(0,nrow=1,ncol=1),
  CINT=matrix(c('cint1'),ncol=1),
  T0MEANS=matrix(c('t0m1'),ncol=1),
  T0VAR=matrix(0,nrow=1,ncol=1),
  LAMBDA = diag(1),
  MANIFESTMEANS=matrix(0,ncol=1),
  MANIFESTVAR=matrix(c('merror'),nrow=1,ncol=1))
  
  
#Including covariate effects
m2ic <- ctModel(type = 'stanct',
  manifestNames = c('Y1'), latentNames=c('eta1'),
  n.TIpred = 1, TIpredNames = 'age',
  n.TDpred=1,TDpredNames = 'TD1', #this line includes the intervention
  TDPREDEFFECT=matrix(c('tdpredeffect'),nrow=1,ncol=1), #intervention effect
  DRIFT=matrix(-1e-5,nrow=1,ncol=1),
  DIFFUSION=matrix(0,nrow=1,ncol=1),
  CINT=matrix(c('cint1'),ncol=1),
  T0MEANS=matrix(c('t0m1'),ncol=1),
  T0VAR=matrix(0,nrow=1,ncol=1),
  LAMBDA = diag(1),
  MANIFESTMEANS=matrix(0,ncol=1),
  MANIFESTVAR=matrix(c('merror'),nrow=1,ncol=1))

m2ic$pars$indvarying[m2ic$pars$matrix %in% 'TDPREDEFFECT'] <- TRUE


#Include deterministic dynamics
m3 <- ctModel(type = 'stanct',
  manifestNames = c('Y1'), latentNames=c('eta1'),
  n.TDpred=1,TDpredNames = 'TD1', #this line includes the intervention
  TDPREDEFFECT=matrix(c('tdpredeffect'),nrow=1,ncol=1), #intervention effect
  DRIFT=matrix('drift11',nrow=1,ncol=1),
  DIFFUSION=matrix(0,nrow=1,ncol=1),
  CINT=matrix(c('cint1'),ncol=1),
  T0MEANS=matrix(c('t0m1'),ncol=1),
  T0VAR=matrix('t0var11',nrow=1,ncol=1),
  LAMBDA = diag(1),
  MANIFESTMEANS=matrix(0,ncol=1),
  MANIFESTVAR=matrix(c('merror1'),nrow=1,ncol=1))





#Add system noise to allow for fluctuations that persist in time
m3n <- ctModel(type = 'stanct',
  manifestNames = c('Y1'), latentNames=c('eta1'),
  n.TDpred=1,TDpredNames = 'TD1', #this line includes the intervention
  TDPREDEFFECT=matrix(c('tdpredeffect'),nrow=1,ncol=1), #intervention effect
  DRIFT=matrix('drift11',nrow=1,ncol=1),
  DIFFUSION=matrix('diffusion',nrow=1,ncol=1),
  CINT=matrix(c('cint1'),ncol=1),
  T0MEANS=matrix(c('t0m1'),ncol=1),
  T0VAR=matrix('t0var11',nrow=1,ncol=1),
  LAMBDA = diag(1),
  MANIFESTMEANS=matrix(0,ncol=1),
  MANIFESTVAR=matrix(c(0),nrow=1,ncol=1))



#include 2nd latent process

m4 <- ctModel(n.manifest = 2,n.latent = 2, type = 'stanct',
  manifestNames = c('Y1','Y2'), latentNames=c('L1','L2'),
  n.TDpred=1,TDpredNames = 'TD1',
  TDPREDEFFECT=matrix(c('tdpredeffect1','tdpredeffect2'),nrow=2,ncol=1),
  DRIFT=matrix(c('drift11','drift21','drift12','drift22'),nrow=2,ncol=2),
  DIFFUSION=matrix(c('diffusion11','diffusion21',0,'diffusion22'),nrow=2,ncol=2),
  CINT=matrix(c('cint1','cint2'),nrow=2,ncol=1),
  T0MEANS=matrix(c('t0m1','t0m2'),nrow=2,ncol=1),
  T0VAR=matrix(c('t0var11','t0var21',0,'t0var22'),nrow=2,ncol=2),
  LAMBDA = matrix(c(1,0,0,1),nrow=2,ncol=2),
  MANIFESTMEANS=matrix(c(0,0),nrow=2,ncol=1),
  MANIFESTVAR=matrix(c('merror1',0,0,'merror2'),nrow=2,ncol=2))

#dynamic factor model -- fixing CINT to 0 and freeing indicator level intercepts

m3df <- ctModel(type = 'stanct',
  manifestNames = c('Y2','Y3'), latentNames=c('eta1'),
  n.TDpred=1,TDpredNames = 'TD1', #this line includes the intervention
  TDPREDEFFECT=matrix(c('tdpredeffect'),nrow=1,ncol=1), #intervention effect
  DRIFT=matrix('drift11',nrow=1,ncol=1),
  DIFFUSION=matrix('diffusion',nrow=1,ncol=1),
  CINT=matrix(c(0),ncol=1),
  T0MEANS=matrix(c('t0m1'),ncol=1),
  T0VAR=matrix('t0var11',nrow=1,ncol=1),
  LAMBDA = matrix(c(1,'Y3loading'),nrow=2,ncol=1),
  MANIFESTMEANS=matrix(c('Y2_int','Y3_int'),nrow=2,ncol=1),
  MANIFESTVAR=matrix(c('Y2residual',0,0,'Y3residual'),nrow=2,ncol=2))

ctsem documentation built on Sept. 11, 2024, 9:06 p.m.