Function for sampling parameters from full conditional distributions. The function returns a list of arrays or matrices with parameter posterior samples. Note that the output includes the posterior samples in objects.
dina(Y, Q, chain_length = 10000)
| Y | A \(N \times J\) |
|---|---|
| Q | A \(N \times K\) |
| chain_length | Number of MCMC iterations. |
A list with samples from the posterior distribution with each
entry named:
CLASSES = individual attribute profiles,
PIs = latent class proportions,
SigS = item slipping parameters, and
GamS = item guessing parameters.
if (FALSE) { #################################### # Tatsuoka Fraction Subtraction Data #################################### # This example requires data from the CDM package. if(requireNamespace("CDM")) { data(fraction.subtraction.data, package = "CDM") data(fraction.subtraction.qmatrix, package = "CDM") Y_1984 = as.matrix(fraction.subtraction.data) Q_1984 = as.matrix(fraction.subtraction.qmatrix) K_1984 = ncol(fraction.subtraction.qmatrix) J_1984 = ncol(Y_1984) # Creating matrix of possible attribute profiles As_1984 = rep(0, K_1984) for(j in 1:K_1984) { temp = combn(1:K_1984, m = j) tempmat = matrix(0, ncol(temp), K_1984) for(j in 1:ncol(temp)) tempmat[j, temp[, j]] = 1 As_1984 = rbind(As_1984, tempmat) } As_1984 = as.matrix(As_1984) # Generate samples from posterior distribution # May take 8 minutes chainLength = 5000 burnin = 1000 chain_samples = burnin:chainLength outchain_1984 = dina(Y = Y_1984, Q = Q_1984, chain_length = chainLength) # Summarize posterior samples for g and 1-s mgs_1984 = apply(outchain_1984$GamS[, chain_samples], 1, mean) sgs_1984 = apply(outchain_1984$GamS[, chain_samples], 1, sd) mss_1984 = 1 - apply(outchain_1984$SigS[, chain_samples], 1, mean) sss_1984 = apply(outchain_1984$SigS[, chain_samples], 1, sd) output_1984 = cbind(mgs_1984, sgs_1984, mss_1984, sss_1984) colnames(output_1984) = c('g Est','g SE','1-s Est','1-s SE') rownames(output_1984) = colnames(Y_1984) print(output_1984, digits = 3) # Summarize marginal skill distribution using posterior samples for latent # class proportions marg_PIs = t(As_1984) %*% outchain_1984$PIs PI_Est = apply(marg_PIs[, chain_samples], 1, mean) PI_Sd = apply(marg_PIs[, chain_samples], 1, sd) PIoutput = cbind(PI_Est, PI_Sd) colnames(PIoutput) = c('EST', 'SE') rownames(PIoutput) = paste('Skill', 1:K_1984) print(PIoutput, digits = 3) } ####################################################### # de la Torre (2009) Simulation Replication w/ N = 200 ####################################################### N = 200 K = 5 J = 30 delta0 = rep(1, 2^K) # Creating Q matrix Q = matrix(rep(diag(K), 2), 2*K, K, byrow = TRUE) for(mm in 2:K) { temp = combn(1:K, m = mm) tempmat = matrix(0, ncol(temp), K) for(j in 1:ncol(temp)) tempmat[j, temp[, j]] = 1 Q = rbind(Q, tempmat) } Q = Q[1:J,] # Setting item parameters and generating attribute profiles ss = gs = rep(.2, J) PIs = rep(1/(2^K), 2^K) CLs = c(1:(2^K)) %*% rmultinom(n = N, size = 1, prob = PIs) # Defining matrix of possible attribute profiles As = rep(0,K) for(j in 1:K) { temp = combn(1:K, m = j) tempmat = matrix(0, ncol(temp), K) for(j in 1:ncol(temp)) tempmat[j, temp[, j]] = 1 As = rbind(As, tempmat) } As = as.matrix(As) # Sample true attribute profiles Alphas = As[CLs,] # Simulate data under DINA model Y_sim = simcdm::sim_dina_items(Alphas, Q, ss, gs) ## Execute MCMC DINA routine ---- # NOTE: This example uses a small chain length to reduce # computation time to illustrate the pedagogical concept. # In a real-life scenario, increase the chain length to # at least 5,000. chainLength = 200 burnin = 100 outchain = dina(Y_sim, Q, chain_length = chainLength) ## Summarize posterior samples for g and 1-s ---- chain_samples = burnin:chainLength mGs = apply(outchain$GamS[, chain_samples], 1, mean) sGs = apply(outchain$GamS[, chain_samples], 1, sd) m1mSS = 1 - apply(outchain$SigS[, chain_samples], 1, mean) s1mSS = apply(outchain$SigS[, chain_samples], 1, sd) output = cbind(mGs, sGs, m1mSS, s1mSS) colnames(output) = c('g Est', 'g SE', '1-s Est', '1-s SE') rownames(output) = paste('Item', 1:J) print(output, digits = 3) ## Summarize marginal skill distribution ---- # Via posterior samples for latent class proportions PIoutput = cbind(apply(outchain$PIs, 1, mean), apply(outchain$PIs, 1, sd)) colnames(PIoutput) = c('EST', 'SE') rownames(PIoutput) = apply(As, 1, paste0, collapse='') print(PIoutput, digits = 3) }