# Sparse time series chain graphical models Computes sparse vector autoregressive coefficient matrices of order 1 and 2 and precision matrix estimates for time series chain graphical models using SCAD or LASSO penalties. In time series chain graphs, `directed` edges are identified by nonzero entries of the autoregressive coefficients matrix and `undirected` edges are identified by nonzero entries of the precision matrix. ```r sparse.tscgm( data = data, lam1 = NULL, lam2 = NULL, nlambda = NULL, model = c("ar1", "ar2"), penalty = c("scad", "lasso"), optimality = c("NULL", "bic", "bic_ext", "bic_mod", "aic", "gic"), control = list() ) ``` ## Arguments - `data`: Longitudinal data format (matrix or data.frame). - `lam1`: Numeric. Scalar or vector of tuning parameter values for the precision matrix penalty. If `NULL`, the program generates a sequence based on `nlambda`. - `lam2`: Numeric. Scalar or vector of tuning parameter values for the autoregression matrix penalty. If `NULL`, a sequence is generated based on `nlambda`. - `nlambda`: Integer. Number of tuning parameter values to generate if `lam1` or `lam2` are `NULL`. Default is 10. - `model`: Character. Order of the vector autoregressive model. Choices: `"ar1"` or `"ar2"`. - `penalty`: Character. Type of penalty to use. Choices: `"scad"` (default) or `"lasso"`. - `optimality`: Character. Information criterion for model selection. Choices: `"NULL"` (no selection), `"bic"`, `"bic_ext"`, `"bic_mod"`, `"aic"`, `"gic"`. - `control`: List. Control parameters for the algorithm: - **maxit.out**: Maximum outer iterations (default 5). - **maxit.in**: Maximum inner iterations (default 50). - **tol.out**: Convergence tolerance (default 1e-4). - **silent**: TRUE/FALSE, whether to print progress messages (default TRUE). ## Returns A list containing: - **theta**: Estimated precision matrix. Nonzero entries represent undirected edges. - **gamma**: Estimated autoregressive coefficient matrix. Nonzero entries represent directed edges. - **lam1.opt**: Optimal tuning parameter for the precision matrix. - **lam2.opt**: Optimal tuning parameter for the autoregression matrix. - **min.ic**: Minimum value of the selected information criterion. - **tun.ic**: Matrix of tuning parameters and corresponding information criterion values. - **lam1.seq**: Sequence of precision matrix tuning parameters. - **lam2.seq**: Sequence of autoregression matrix tuning parameters. - **s.theta**: Sparsity level of the precision matrix. - **s.gamma**: Sparsity level of the autoregression matrix. ## Details For description of the objective functions and computational details, see Abegaz and Wit (2013). ## Examples ```r seed <- 321 datas <- sim.data(model="ar1", time=10, n.obs=10, n.var=5, seed=seed, prob0=0.35, network="random") data.fit <- datas$data1 prec_true <- datas$theta autoR_true <- datas$gamma res.tscgm <- sparse.tscgm(data=data.fit, lam1=NULL, lam2=NULL, nlambda=NULL, model="ar1", penalty="scad", optimality="bic_mod", control=list(maxit.out=10, maxit.in=100)) # Estimated sparse precision and autoregression matrices prec <- res.tscgm$theta autoR <- res.tscgm$gamma # Optimal tuning parameter values lambda1.opt <- res.tscgm$lam1.opt lambda2.opt <- res.tscgm$lam2.opt # Sparsity levels sparsity_theta <- res.tscgm$s.theta sparsity_gamma <- res.tscgm$s.gamma # Graphical visualization oldpar <- par(mfrow=c(2,2)) plot.tscgm(datas, mat="precision", main="True precision matrix") plot.tscgm(res.tscgm, mat="precision", main="Estimated precision matrix") plot.tscgm(datas, mat="autoregression", main="True autoregression coef. matrix") plot.tscgm(res.tscgm, mat="autoregression", main="Estimated autoregression coef. matrix") par(oldpar) ``` ## References Fentaw Abegaz and Ernst Wit (2013). Sparse time series chain graphical models for reconstructing genetic networks. **Biostatistics**, 14(3), 586–599. Rothman, Levina, and Zhu (2010). Sparse multivariate regression with covariance estimation. **Journal of Computational and Graphical Statistics**, 19, 947–962.

sparse.tscgm function