# Simulate OLBM data It simulates an ordinal data matrix according to OLBM. ```r simu.olbm(M, P, Pi, rho, delta, mu, sd, thresh) ``` ## Arguments - `M`: The number of rows of the ordinal matrix Y. - `P`: The number of columns of the ordinal matrix Y. - `Pi`: A Q x L connectivity matrix to manage missing data (coded az zeros in Y). - `rho`: A vector of length Q, containing multinomial probabilities for row cluster assignments. - `delta`: A vector of length L, containing multinomial probabilities for column cluster assignments. - `mu`: A Q x L matrix containing the means of the latent Gaussian distributions. - `sd`: A Q x L matrix containing the standard deviations of the latent Gaussian distributions. - `thresh`: A K+1 vector containing the sorted tresholds used to simulate the ordinal entries in Y, where K is the number of ordinal modalities. The first entry in tresh must be -Inf, the last entry +Inf. ## Returns It returns a list containing: - **Y**: An M x P matrix. The observed ordinal entries are integers between 1 and K. Missing data are coded as zeros. - **Rclus**: A vector of length M containing the row cluster memberships. - **Cclus**: A vector of length P containing the column cluster memberships. ## Examples ```r M <- 150 P <- 100 Q <- 3 L <- 2 ## connectivity matrix Pi <- matrix(.7, nrow = Q, ncol = L) Pi[1,1] <- Pi[2,2] <- Pi[3,2] <- .5 ## cluster memberships proportions rho <- c(1/3, 1/3 ,1/3) delta <- c(1/2, 1/2) # Thresholds thresh <- c(-Inf, 2.37, 2.67, 3.18, 4.33, Inf) # K = 5 ## Gaussian parameters mu <- matrix(c(0, 3.4, 2.6, 0, 2.6, 3.4), nrow = Q, ncol = L) sd <- matrix(c(1.2,1.4,1.0,1.2,1.4,1.0), nrow = Q, ncol = L) ## Data simulation dat <- simu.olbm(M, P, Pi, rho, delta, mu, sd, thresh) ``` ## References Corneli M.,Bouveyron C. and Latouche P. (2019) **Co-Clustering of ordinal data via latent continuous random variables and a classification EM algorithm.**([https://hal.archives-ouvertes.fr/hal-01978174](https://hal.archives-ouvertes.fr/hal-01978174))

simu.olbm function