# Simulate Data from a Conditional Gaussian Graphical Model with Censored and/or Missing Values ‘rcggm’ function is used to produce one or more samples from a conditional Gaussian graphical model with censored and/or missing values. ```r rcggm(n, p, b0, X, B, Sigma, probl, probr, probna, ...) ``` ## Arguments - `n`: the number of samples required (optional, see below for a description). - `p`: the number of response variables (optional, see below for a description). - `b0`: a vector of length `p` used to specify the intercepts. Default is a zero vector of length `p` (optional, see below for a description). - `X`: a matrix of dimension $n x q$ used to model the expected values of the response variables (optional, see below for a description). - `B`: a matrix of dimension $q x p$ used to specify the regression coefficients. If `X` is missing then `B` is set equal to `NULL` (optional, see below for a description). - `Sigma`: a positive-definite symmetric matrix specifying the covariance matrix of the response variables. Default is the identity matrix (optional, see below for a description). - `probl`: a vector giving the probabilities that the response variables are left-censored. - `probr`: a vector giving the probabilities that the response variables are right-censored. - `probna`: the probability that a response value is missing-at-random. By default ‘probna’ is set equal to zero. - ``...``: further arguments passed to the function ‘mvrnorm’ . ## Details The ‘rcggm’ function simulates a dataset from a conditional Gaussian graphical model with censored or missing values and returns an object of class ‘datacggm’ . Censoring values are implicitly specified using arguments `probl` and `probr`, that is, `lo` and `up` are computed in such a way that the average probabilities of left and right censoring are equal to `probl` and `probr`, respectively. Missing-at-random values are simulated using a Bernoulli distribution with probability `probna`. The dataset is simulated through the following steps: 1. lower and upper censoring values (`lo` and `up`) are computed according to the arguments `probl` and `probr`; 2. The function `mvrnorm` is used to simulate one or more samples from the multivariate Gaussian distribution specified by the arguments `b0`, `X`, `B` and `Sigma`; 3. The response values that are outside of the interval `[lo, up]` are replaced with the corresponding censoring values; 4. if `probna` is greater than zero, then missing-at-random values are simulated using a Bernoulli distribution with probability `probna`. ||||||||| |:-:|:-:|:-:|:-:|:-:|:-:|:-:|:--| |Model|`n`|`p`|`b0`|`X`|`B`|`Sigma`|Gaussian distribution| |1|`x`|`x`|||||$Y ~ N(0, I)$| |2|`x`|||||`x`|$Y ~ N(0, Sigma)$| |3|`x`||`x`||||$Y ~ N(b0, I)$| |4|`x`||`x`|||`x`|$Y ~ N(b0, Sigma)$| |5||||`x`|`x`||$Y ~ N(XB, I)$| |6||||`x`|`x`|`x`|$Y ~ N(XB, Sigma)$| |7|||`x`|`x`|`x`||$Y ~ N(b0 + XB, I)$| |8|||`x`|`x`|`x`|`x`|$Y ~ N(b0 + XB, Sigma)$| The previous table sums up the default setting of the multivariate Gaussian distribution used in step 2 (specified arguments are marked by the symbol ‘x’ ). See also below for some examples. ## Returns `rcggm` returns an object of class ‘datacggm’ . See `datacggm` for further details. ## Author(s) Luigi Augugliaro (luigi.augugliaro@unipa.it ) ## References Augugliaro L., Sottile G., Wit E.C., and Vinciotti V. (2023) . cglasso: An R Package for Conditional Graphical Lasso Inference with Censored and Missing Values. **Journal of Statistical Software** 105 (1), 1--58. Augugliaro, L., Sottile, G., and Vinciotti, V. (2020a) . The conditional censored graphical lasso estimator. **Statistics and Computing** 30 , 1273--1289. Augugliaro, L., Abbruzzo, A., and Vinciotti, V. (2020b) . $l1$-Penalized censored Gaussian graphical model. **Biostatistics** 21 , e1--e16. ## See Also `datacggm`. ## Examples ```r set.seed(123) n <- 100 p <- 3 q <- 2 b0 <- rep(1, p) X <- matrix(rnorm(n * q), n, q) B <- matrix(rnorm(q * p), q, p) Sigma <- outer(1:p, 1:p, function(i, j) 0.3^abs(i - j)) probl <- 0.05 probr <- 0.05 probna <- 0.05 # Model 1: Y ~ N(0, I) Z <- rcggm(n = n, p = p, probl = probl, probr = probr, probna = probna) summary(Z) # Model 2: Y ~ N(0, Sigma) Z <- rcggm(n = n, Sigma = Sigma, probl = probl, probr = probr, probna = probna) summary(Z) # Model 3: Y ~ N(b0, I) Z <- rcggm(n = n, b0 = b0, probl = probl, probr = probr, probna = probna) summary(Z) # Model 4: Y ~ N(b0, Sigma) Z <- rcggm(n = n, b0 = b0, Sigma = Sigma, probl = probl, probr = probr, probna = probna) summary(Z) # Model 5: Y ~ N(XB, I) Z <- rcggm(X = X, B = B, probl = probl, probr = probr, probna = probna) summary(Z) # Model 6: Y ~ N(XB, Sigma) Z <- rcggm(X = X, B = B, Sigma = Sigma, probl = probl, probr = probr, probna = probna) summary(Z) # Model 7: Y ~ N(b0 + XB, I) Z <- rcggm(b0 = b0, X = X, B = B, probl = probl, probr = probr, probna = probna) summary(Z) # Model 8: Y ~ N(b0 + XB, Sigma) Z <- rcggm(b0 = b0, X = X, B = B, Sigma = Sigma, probl = probl, probr = probr, probna = probna) summary(Z) ```

rcggm function