**See the NEWS file for recent updates, and below for quick
start!**

ctsem allows for easy specification and fitting of a range of continuous and discrete time dynamic models, including multiple indicators (dynamic factor analysis), multiple, potentially higher order processes, and time dependent (varying within subject) and time independent (not varying within subject) covariates. Classic longitudinal models like latent growth curves and latent change score models are also possible. Version 1 of ctsem provided SEM based functionality by linking to the OpenMx software, allowing mixed effects models (random means but fixed regression and variance parameters) for multiple subjects. For version 2 of the R package ctsem, we include a hierarchical specification and fitting routine that uses the Stan probabilistic programming language, via the rstan package in R. This allows for all parameters of the dynamic model to individually vary, using an estimated population mean and variance, and any time independent covariate effects, as a prior. Version 3 allows for state dependencies in the parameter specification (i.e. time varying parameters).

The current manual is at https://cran.r-project.org/package=ctsem/vignettes/hierarchicalmanual.pdf. The original ctsem is documented in a JSS publication (Driver, Voelkle, Oud, 2017), and in R vignette form at https://cran.r-project.org/package=ctsemOMX/vignettes/ctsem.pdf, however these OpenMx based functions have been split off into a sub package, ctsemOMX. For most use cases the newer formulation (with Kalman filtering coded in Stan) is faster, more robust, and more flexible, and both default to maximum likelihood. For cases with many subjects, few time points, and no individual differences in timing, ctsemOMX may be faster.

For questions (or to see past answers) please use https://github.com/cdriveraus/ctsem/discussions

To cite ctsem please use the citation(“ctsem”) command in R.

`::install_github('cdriveraus/ctsem', INSTALL_opts = "--no-multiarch", dependencies = c("Depends", "Imports")) remotes`

`install.packages('ctsem')`

Ensure recent version of R and Rtools is installed. If the installctsem.R code has never been run before, be sure to run that (see above).

Place this line in ~/.R/makevars.win , and if there are other lines, delete them:

`CXX14FLAGS += -mtune=native -Wno-ignored-attributes -Wno-deprecated-declarations`

see for details

In case of compile errors like `g++ not found`

, ensure the
devtools package is installed:

`install.packages('devtools')`

and include the following in your .Rprofile, replacing c:/Rtools with the appropriate path – sometimes Rbuildtools/4.0/ .

```
library(devtools)
Sys.setenv(PATH = paste("C:/Rtools/bin", Sys.getenv("PATH"), sep=";"))
Sys.setenv(PATH = paste("C:/Rtools/mingw_64/bin", Sys.getenv("PATH"), sep=";"))
Sys.setenv(BINPREF = "C:/Rtools/mingw_$(WIN)/bin/")
```

#’ The basic long data structure. Diet, (our covariate) is a categorical variable so needs dummy / ‘one hot’ encoding.

`head(ChickWeight) `

#’ Setup dummy coding

```
library(data.table)
library(mltools)
<- one_hot(as.data.table(ChickWeight),cols = 'Diet') chickdata
```

#’ Scaling of continuous variables makes for easier estimation and more sensible default priors (if used). Time intervals can also benefit

```
$weight <- scale(chickdata$weight)
chickdatahead(chickdata) #now we have the four diet categories
```

#’ Setup continuous time model – in this case we are estimating a regular first order autoregressive

```
library(ctsem)
<- ctModel(
m LAMBDA=diag(1), #Factor loading matrix of latent processes on measurements, fixed to 1
type = 'stanct', #Could specify 'standt' here for discrete time.
tipredDefault = FALSE, #limit covariate effects on parameters to those explicitly specified
manifestNames='weight', #Observed measurements of the latent processes
latentNames='Lweight', #Names here simply make parameters and plots more interpretable
TIpredNames = paste0('Diet_',2:4), #Covariates, in this case one category needs to be baseline...
DRIFT='a11 | param', #normally self feedback (diagonal drift terms) are restricted to negative
MANIFESTMEANS=0, #For identification CINT is normally zero with this freely estimated
CINT='cint ||||Diet_2,Diet_3,Diet_4', #diet covariates specified in 5th 'slot' (four '|' separators)
time='Time',
id='Chick')
```

#’ View model in pdf/ latex form

`ctModelLatex(m)`

#’ Fit model to data – here using priors because Hessian problems are reported otherwise

`<- ctStanFit(chickdata,m,nopriors=FALSE) f `

#’ Summarise fit, view covariate effects – Diets 3 and 4 seem most obviously successful

```
=summary(f)
s
print(s$tipreds )
```

#’ Predictions conditional on all earlier data

`ctKalman(f,plot=TRUE,subjects=2:4,kalmanvec=c('yprior','ysmooth')) `

#’ Predictions conditional only on covariates, showing 1 chick from each diet

```
ctKalman(f,plot=T,
subjects=as.numeric(chickdata$Chick[!duplicated(ChickWeight$Diet)]),
removeObs = T,polygonalpha=0)
```

#’ Plot temporal regression coefficients conditional on time interval – increases in this case!

`ctStanDiscretePars(f,plot=T) `

#’ Other useful functions:

#’ Compare two fits: ctChisqTest()

#’ Fit and summarise / plot a list of models: ctFitMultiModel()

#’ Add samples to fit to increase estimate precision: ctAddSamples()

#’ Return dynamic system parameters in matrix forms: ctStanContinuousPars()

#’ Compute cross validation statistics: ctLOO()

#’ Plot time independent predictor (covariate effects on parameters): ctStanTIpredEffects()

#’ Generate data from a specified model of fixed parameters: ctGenerate()

#’ Generate data from a specified model of fixed and free parameters / priors: ctStanGenerate()

#’ Generate data from a fitted model: ctStanGenerateFromFit()

#’ Get samples from the fitted object: ctExtract()

#’ In samples, pop_DRIFT refers to the population drift matrix, subj_DRIFT refers to the subject matrix. Subject matrices only computed for max likelihood / posterior mode by default, and found in the (stanfit)transformedparsfull object.