# pdf of the Gaussian additive (Markov-switching) model for hhsmm The probability density function of a Gaussian additive (Markov-switching) model for a specified observation vector, a specified state and a specified model's parameters ```r dnorm_additive_reg(x, j, model, control = list(K = 5, resp.ind = 1)) ``` ## Arguments - `x`: the observation matrix including responses and covariates - `j`: a specified state between 1 to nstate - `model`: a hhsmmspec model - `control`: the parameters to control the density function. The simillar name is chosen with that of `additive_reg_mstep`, to be used in `...` argument of the `hhsmmfit` function. Here, it contains the following items: * `K` the degrees of freedom for the B-spline, default is `K=5` * `resp.ind` a vector of the column numbers of `x` which contain response variables. The default is 1, which means that the first column of `x` is the univariate response variable ## Returns the probability density function value ## Examples ```r J <- 3 initial <- c(1, 0, 0) semi <- rep(FALSE, 3) P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, byrow = TRUE) par <- list(intercept = list(3, list(-10, -1), 14), coefficient = list(-1, list(1, 5), -7), csigma = list(1.2, list(2.3, 3.4), 1.1), mix.p = list(1, c(0.4, 0.6), 1)) model <- hhsmmspec(init = initial, transition = P, parms.emis = par, dens.emis = dmixlm, semi = semi) train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, remission = rmixlm, covar = list(mean = 0, cov = 1)) clus = initial_cluster(train = train, nstate = 3, nmix = NULL, ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE) initmodel = initialize_model(clus = clus ,mstep = additive_reg_mstep, dens.emission = dnorm_additive_reg, sojourn = NULL, semi = rep(FALSE, 3), M = max(train$N),verbose = TRUE) fit1 = hhsmmfit(x = train, model = initmodel, mstep = additive_reg_mstep, M = max(train$N)) plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = fit1$yhat, xlab = "x", ylab = "y") text(0,30, "colors are real states",col="red") text(0,28, "characters are predicted states") pred <- addreg_hhsmm_predict(fit1, train$x[, 2], 5) yhat1 <- pred[[1]] yhat2 <- pred[[2]] yhat3 <- pred[[3]] lines(yhat1[order(train$x[, 2])]~sort(train$x[, 2]),col = 2) lines(yhat2[order(train$x[, 2])]~sort(train$x[, 2]),col = 1) lines(yhat3[order(train$x[, 2])]~sort(train$x[, 2]),col = 3) ``` ## References Langrock, R., Adam, T., Leos-Barajas, V., Mews, S., Miller, D. L., and Papastamatiou, Y. P. (2018). Spline-based nonparametric inference in general state-switching models. Statistica Neerlandica, 72(3), 179-200. ## Author(s) Morteza Amini, morteza.amini@ut.ac.ir , Reza Salehian, reza.salehian@ut.ac.ir

dnorm_additive_reg function