# Simulate item response times based on Wang et al.'s (2018) joint model of response times and accuracy in learning Simulate a cube of subjects' response times across time points according to a variant of the logNormal model ```r sim_RT(alphas, Q_matrix, Design_array, RT_itempars, taus, phi, G_version) ``` ## Arguments - `alphas`: An N-by-K-by-T `array` of attribute patterns of all persons across T time points - `Q_matrix`: A J-by-K Q-matrix for the test - `Design_array`: A N-by-J-by-L array indicating whether item j is administered to examinee i at l time point. - `RT_itempars`: A J-by-2 `matrix` of item time discrimination and time intensity parameters - `taus`: A length N `vector` of latent speed of each person - `phi`: A `scalar` of slope of increase in fluency over time due to covariates (G) - `G_version`: An `int` of the type of covariate for increased fluency (1: G is dichotomous depending on whether all skills required for current item are mastered; 2: G cumulates practice effect on previous items using mastered skills; 3: G is a time block effect invariant across subjects with different attribute trajectories) ## Returns A `cube` of response times of subjects on each item across time ## Examples ```r N = dim(Design_array)[1] J = nrow(Q_matrix) K = ncol(Q_matrix) L = dim(Design_array)[3] class_0 <- sample(1:2^K, N, replace = TRUE) Alphas_0 <- matrix(0,N,K) mu_thetatau = c(0,0) Sig_thetatau = rbind(c(1.8^2,.4*.5*1.8),c(.4*.5*1.8,.25)) Z = matrix(rnorm(N*2),N,2) thetatau_true = Z%*%chol(Sig_thetatau) thetas_true = thetatau_true[,1] taus_true = thetatau_true[,2] G_version = 3 phi_true = 0.8 for(i in 1:N){ Alphas_0[i,] <- inv_bijectionvector(K,(class_0[i]-1)) } lambdas_true <- c(-2, .4, .055) Alphas <- sim_alphas(model="HO_joint", lambdas=lambdas_true, thetas=thetas_true, Q_matrix=Q_matrix, Design_array=Design_array) RT_itempars_true <- matrix(NA, nrow=J, ncol=2) RT_itempars_true[,2] <- rnorm(J,3.45,.5) RT_itempars_true[,1] <- runif(J,1.5,2) ETAs <- ETAmat(K,J,Q_matrix) L_sim <- sim_RT(Alphas,Q_matrix,Design_array,RT_itempars_true,taus_true,phi_true,G_version) ```

sim_RT function