HMDCM
Load the spatial rotation data
(1) Simulate responses based on the HMDCM model
class_0 <- sample(1:2^K, N, replace = L)
Alphas_0 <- matrix(0,N,K)
for(i in 1:N){
Alphas_0[i,] <- inv_bijectionvector(K,(class_0[i]-1))
}
thetas_true = rnorm(N)
lambdas_true = c(-1, 1.8, .277, .055)
Alphas <- sim_alphas(model="HO_sep",
lambdas=lambdas_true,
thetas=thetas_true,
Q_matrix=Q_matrix,
Design_array=Design_array)
table(rowSums(Alphas[,,5]) - rowSums(Alphas[,,1])) # used to see how much transition has taken place
#>
#> 0 1 2 3 4
#> 37 46 86 151 30
itempars_true <- matrix(runif(J*2,.1,.2), ncol=2)
Y_sim <- sim_hmcdm(model="DINA",Alphas,Q_matrix,Design_array,
itempars=itempars_true)(2) Run the MCMC to sample parameters from the posterior distribution
output_HMDCM = hmcdm(Y_sim,Q_matrix,"DINA_HO",Test_order = Test_order, Test_versions = Test_versions,
chain_length=100,burn_in=30,
theta_propose = 2,deltas_propose = c(.45,.35,.25,.06))
#> 0
output_HMDCM = hmcdm(Y_sim,Q_matrix,"DINA_HO",Design_array,
chain_length=100,burn_in=30,
theta_propose = 2,deltas_propose = c(.45,.35,.25,.06))
#> 0
output_HMDCM
#>
#> Model: DINA_HO
#>
#> Sample Size: 350
#> Number of Items:
#> Number of Time Points:
#>
#> Chain Length: 100, burn-in: 30
summary(output_HMDCM)
#>
#> Model: DINA_HO
#>
#> Item Parameters:
#> ss_EAP gs_EAP
#> 0.2718 0.1835
#> 0.1524 0.1541
#> 0.1427 0.1569
#> 0.2032 0.1494
#> 0.1583 0.1279
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -0.92961
#> λ1 1.73112
#> λ2 0.24180
#> λ3 0.06832
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1347
#> 0001 0.1429
#> 0010 0.1845
#> 0011 0.2826
#> 0100 0.1889
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 19045.81
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5211
#> M2: 0.49
#> total scores: 0.6252
a <- summary(output_HMDCM)
a$ss_EAP
#> [,1]
#> [1,] 0.2718115
#> [2,] 0.1523667
#> [3,] 0.1427245
#> [4,] 0.2031685
#> [5,] 0.1583040
#> [6,] 0.1602565
#> [7,] 0.1815204
#> [8,] 0.1770748
#> [9,] 0.1349393
#> [10,] 0.1354039
#> [11,] 0.1451500
#> [12,] 0.1208791
#> [13,] 0.1524734
#> [14,] 0.1287837
#> [15,] 0.2013584
#> [16,] 0.1751351
#> [17,] 0.1304720
#> [18,] 0.1857648
#> [19,] 0.1484415
#> [20,] 0.1631852
#> [21,] 0.1174927
#> [22,] 0.1525531
#> [23,] 0.1414680
#> [24,] 0.1049404
#> [25,] 0.2146924
#> [26,] 0.1517713
#> [27,] 0.1467120
#> [28,] 0.1488276
#> [29,] 0.1703580
#> [30,] 0.1204788
#> [31,] 0.1524716
#> [32,] 0.1019105
#> [33,] 0.1667775
#> [34,] 0.2383756
#> [35,] 0.1943779
#> [36,] 0.1451961
#> [37,] 0.2065169
#> [38,] 0.1352363
#> [39,] 0.1288229
#> [40,] 0.1043957
#> [41,] 0.1759679
#> [42,] 0.2236318
#> [43,] 0.1290089
#> [44,] 0.2011330
#> [45,] 0.2277559
#> [46,] 0.1692664
#> [47,] 0.2606467
#> [48,] 0.1582794
#> [49,] 0.1710168
#> [50,] 0.1862473
a$lambdas_EAP
#> [,1]
#> λ0 -0.92961404
#> λ1 1.73111576
#> λ2 0.24180050
#> λ3 0.06832165
mean(a$PPP_total_scores)
#> [1] 0.6259837
mean(upper.tri(a$PPP_item_ORs))
#> [1] 0.49
mean(a$PPP_item_means)
#> [1] 0.5137143(3) Evaluate the accuracy of estimated parameters
Attribute-wise agreement rate between true and estimated alphas
(4) Evaluate the fit of the model to the observed response
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2130.923 NA 14874.17 1226.763 18231.86
#> D(theta_bar) 1848.910 NA 14382.72 1186.281 17417.91
#> DIC 2412.937 NA 15365.63 1267.245 19045.81
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.8285714 0.7285714 1.00000000 0.9000000 1.0000000
#> [2,] 0.2714286 0.7142857 0.90000000 0.7285714 0.6285714
#> [3,] 0.6142857 0.5571429 0.38571429 0.4571429 0.5000000
#> [4,] 0.5714286 0.4285714 0.42857143 0.8714286 0.3857143
#> [5,] 0.8714286 0.5571429 0.10000000 0.9428571 0.8142857
#> [6,] 0.7000000 0.7714286 0.08571429 0.2142857 1.0000000
head(a$PPP_item_means)
#> [1] 0.6000000 0.4714286 0.4857143 0.4428571 0.6000000 0.5285714
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] NA 0.9428571 0.1000000 0.4857143 0.8285714 0.4571429 0.9142857
#> [2,] NA NA 0.7428571 0.2428571 0.1571429 0.1285714 0.8000000
#> [3,] NA NA NA 0.8428571 0.3714286 0.7857143 0.5857143
#> [4,] NA NA NA NA 0.8428571 0.9571429 0.7285714
#> [5,] NA NA NA NA NA 0.3428571 0.5428571
#> [6,] NA NA NA NA NA NA 0.4428571
#> [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 0.62857143 0.5285714 0.9285714 0.5000000 1.0000000 0.1428571 0.4142857
#> [2,] 0.97142857 0.7142857 0.5571429 0.3285714 0.9714286 0.4000000 0.4714286
#> [3,] 0.07142857 0.9571429 0.9857143 0.6285714 0.9714286 0.5714286 0.7428571
#> [4,] 0.52857143 0.6571429 0.7714286 0.6857143 0.6285714 0.7000000 0.2000000
#> [5,] 0.52857143 0.3857143 0.1857143 0.8571429 0.9714286 0.9142857 0.2285714
#> [6,] 0.35714286 0.7000000 0.4285714 0.6714286 0.3714286 0.6285714 0.3285714
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21]
#> [1,] 0.9000000 0.4142857 0.62857143 0.74285714 0.5571429 0.7000000 0.9571429
#> [2,] 0.2285714 0.6142857 0.18571429 0.01428571 0.8714286 0.7714286 0.8285714
#> [3,] 0.8571429 0.5142857 0.94285714 0.82857143 0.9142857 0.9000000 0.6428571
#> [4,] 0.4428571 0.1142857 0.81428571 0.77142857 0.6000000 0.5857143 0.8428571
#> [5,] 0.9857143 0.3000000 0.52857143 0.27142857 0.6285714 0.9142857 0.6142857
#> [6,] 0.2142857 0.2428571 0.02857143 0.22857143 0.4857143 0.2285714 0.9000000
#> [,22] [,23] [,24] [,25] [,26] [,27] [,28]
#> [1,] 0.9571429 0.68571429 0.12857143 0.3571429 0.87142857 0.1714286 0.7285714
#> [2,] 0.6571429 0.74285714 0.20000000 0.7428571 0.92857143 0.8571429 0.7000000
#> [3,] 0.5285714 0.32857143 0.45714286 0.5571429 0.32857143 0.2714286 0.3285714
#> [4,] 0.8428571 0.81428571 0.62857143 0.8857143 0.07142857 0.8285714 0.8714286
#> [5,] 0.3571429 0.05714286 0.07142857 0.8571429 0.31428571 0.5857143 0.4428571
#> [6,] 0.2714286 0.40000000 0.17142857 0.6857143 0.28571429 0.9428571 0.3857143
#> [,29] [,30] [,31] [,32] [,33] [,34] [,35]
#> [1,] 0.6714286 0.1571429 0.9000000 0.4000000 0.7857143 0.5428571 0.1000000
#> [2,] 0.1428571 0.7571429 0.3142857 0.6428571 0.4571429 0.3142857 0.4428571
#> [3,] 0.2857143 0.6285714 0.3714286 0.4000000 0.8857143 0.2000000 0.4000000
#> [4,] 0.5000000 0.9857143 0.1428571 0.8857143 0.4571429 0.8000000 0.7571429
#> [5,] 0.1000000 0.5571429 0.2571429 0.3857143 0.7142857 0.4000000 0.1714286
#> [6,] 0.2000000 0.9000000 0.1857143 0.4571429 0.8428571 0.8857143 0.3142857
#> [,36] [,37] [,38] [,39] [,40] [,41] [,42]
#> [1,] 0.7000000 0.42857143 0.8571429 0.28571429 0.6857143 0.3428571 0.7571429
#> [2,] 0.7285714 0.81428571 0.8571429 0.27142857 0.9714286 0.7428571 0.7714286
#> [3,] 0.7428571 0.00000000 0.8714286 0.02857143 0.1000000 0.5714286 0.8000000
#> [4,] 0.1428571 0.17142857 0.7000000 0.54285714 1.0000000 0.8857143 0.9142857
#> [5,] 0.5142857 0.08571429 0.3142857 0.65714286 0.4428571 0.7571429 0.1428571
#> [6,] 0.1428571 0.15714286 0.1000000 0.38571429 0.5142857 0.8714286 0.4428571
#> [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,] 0.3857143 0.5428571 0.4285714 0.7285714 0.78571429 0.5142857 0.6000000
#> [2,] 0.9285714 0.5857143 0.9571429 0.7571429 0.50000000 0.4714286 0.8714286
#> [3,] 0.6285714 0.9714286 0.7571429 0.6142857 0.31428571 0.1714286 0.7714286
#> [4,] 0.4571429 0.4428571 0.8285714 0.9285714 0.52857143 0.4857143 1.0000000
#> [5,] 0.5285714 0.2428571 0.7571429 0.4142857 0.21428571 0.1428571 0.3714286
#> [6,] 0.6000000 0.5000000 0.9857143 0.6000000 0.04285714 0.2571429 0.2000000
#> [,50]
#> [1,] 0.97142857
#> [2,] 0.54285714
#> [3,] 0.50000000
#> [4,] 1.00000000
#> [5,] 0.08571429
#> [6,] 0.74285714
library(bayesplot)
pp_check(output_HMDCM)
pp_check(output_HMDCM, plotfun="hist", type="item_OR")
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Convergence checking
Checking convergence of the two independent MCMC chains with
different initial values using coda package.
# output_HMDCM1 = hmcdm(Y_sim, Q_matrix, "DINA_HO", Design_array,
# chain_length=100, burn_in=30,
# theta_propose = 2, deltas_propose = c(.45,.35,.25,.06))
# output_HMDCM2 = hmcdm(Y_sim, Q_matrix, "DINA_HO", Design_array,
# chain_length=100, burn_in=30,
# theta_propose = 2, deltas_propose = c(.45,.35,.25,.06))
#
# library(coda)
#
# x <- mcmc.list(mcmc(t(rbind(output_HMDCM1$ss, output_HMDCM1$gs, output_HMDCM1$lambdas))),
# mcmc(t(rbind(output_HMDCM2$ss, output_HMDCM2$gs, output_HMDCM2$lambdas))))
#
# gelman.diag(x, autoburnin=F)