# Variance-covariance matrix estimation Estimates the variance-covariance matrix for model parameter estimates. ```r click.var(X, y = NULL, alpha, beta = NULL, gamma, z) ``` ## Arguments - `X`: dataset array (p x p x n) - `y`: vector of initial states (length n) - `alpha`: vector of mixing proportions (length K) - `beta`: matrix of initial state probabilities (K x p) - `gamma`: array of transition probabilities (p x p x K) - `z`: matrix of posterior probabilities (n x K) ## Details Returns an estimated variance-covariance matrix for model parameter estimates. ## References Melnykov, V. (2016) Model-Based Biclustering of Clickstream Data, Computational Statistics and Data Analysis, 93, 31-45. Melnykov, V. (2016) ClickClust: An R Package for Model-Based Clustering of Categorical Sequences, Journal of Statistical Software, 74, 1-34. ## Author(s) Melnykov, V. ## See Also click.EM ## Examples ```r set.seed(123) n.seq <- 200 p <- 5 K <- 2 mix.prop <- c(0.3, 0.7) TP1 <- matrix(c(0.20, 0.10, 0.15, 0.15, 0.40, 0.20, 0.20, 0.20, 0.20, 0.20, 0.15, 0.10, 0.20, 0.20, 0.35, 0.15, 0.10, 0.20, 0.20, 0.35, 0.30, 0.30, 0.10, 0.10, 0.20), byrow = TRUE, ncol = p) TP2 <- matrix(c(0.15, 0.15, 0.20, 0.20, 0.30, 0.20, 0.10, 0.30, 0.30, 0.10, 0.25, 0.20, 0.15, 0.15, 0.25, 0.25, 0.20, 0.15, 0.15, 0.25, 0.10, 0.30, 0.20, 0.20, 0.20), byrow = TRUE, ncol = p) TP <- array(rep(NA, p * p * K), c(p, p, K)) TP[,,1] <- TP1 TP[,,2] <- TP2 # DATA SIMULATION A <- click.sim(n = n.seq, int = c(10, 50), alpha = mix.prop, gamma = TP) C <- click.read(A$S) # EM ALGORITHM M2 <- click.EM(X = C$X, y = C$y, K = 2) # VARIANCE ESTIMATION V <- click.var(X = C$X, y = C$y, alpha = M2$alpha, beta = M2$beta, gamma = M2$gamma, z = M2$z) # 95% confidence intervals for all model parameters Estimate <- c(M2$alpha[-K], as.vector(t(M2$beta[,-p])), as.vector(apply(M2$gamma[,-p,], 3, t))) Lower <- Estimate - qnorm(0.975) * sqrt(diag(V)) Upper <- Estimate + qnorm(0.975) * sqrt(diag(V)) cbind(Estimate, Lower, Upper) ```

VarEst function