HMDCM

library(hmcdm)

Load the spatial rotation data

N = dim(Design_array)[1]
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = dim(Design_array)[3]

(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 
#>  34  42  83 145  46
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
#>  0.1583 0.1214
#>  0.1033 0.1939
#>  0.2095 0.1673
#>  0.1634 0.1891
#>  0.1586 0.2067
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    lambdas_EAP
#> λ0     -1.4218
#> λ1      2.3065
#> λ2      0.1990
#> λ3      0.1273
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1932
#> 0001  0.2080
#> 0010  0.1540
#> 0011  0.2187
#> 0100  0.1493
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 18662.77 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5051
#> M2:  0.49
#> total scores:  0.6271
a <- summary(output_HMDCM)
a$ss_EAP
#>             [,1]
#>  [1,] 0.15825283
#>  [2,] 0.10334640
#>  [3,] 0.20948117
#>  [4,] 0.16339135
#>  [5,] 0.15862398
#>  [6,] 0.18991916
#>  [7,] 0.15445880
#>  [8,] 0.10103082
#>  [9,] 0.16882064
#> [10,] 0.15113708
#> [11,] 0.20433357
#> [12,] 0.19807978
#> [13,] 0.20800023
#> [14,] 0.09660672
#> [15,] 0.16522923
#> [16,] 0.18308455
#> [17,] 0.09583899
#> [18,] 0.13756038
#> [19,] 0.11376633
#> [20,] 0.14134252
#> [21,] 0.15827191
#> [22,] 0.22390574
#> [23,] 0.16612060
#> [24,] 0.23959900
#> [25,] 0.13678979
#> [26,] 0.14653933
#> [27,] 0.12716318
#> [28,] 0.24993782
#> [29,] 0.15482670
#> [30,] 0.10495696
#> [31,] 0.13307867
#> [32,] 0.16903655
#> [33,] 0.20043167
#> [34,] 0.16831519
#> [35,] 0.13242000
#> [36,] 0.13125061
#> [37,] 0.28603996
#> [38,] 0.14735152
#> [39,] 0.11615620
#> [40,] 0.16212220
#> [41,] 0.12047219
#> [42,] 0.13108897
#> [43,] 0.25809179
#> [44,] 0.15365442
#> [45,] 0.15914937
#> [46,] 0.14922763
#> [47,] 0.15424291
#> [48,] 0.08147976
#> [49,] 0.13937486
#> [50,] 0.06673718
a$lambdas_EAP
#>          [,1]
#> λ0 -1.4218310
#> λ1  2.3064813
#> λ2  0.1990276
#> λ3  0.1272570
mean(a$PPP_total_scores)
#> [1] 0.6277714
mean(upper.tri(a$PPP_item_ORs))
#> [1] 0.49
mean(a$PPP_item_means)
#> [1] 0.5245714

(3) Evaluate the accuracy of estimated parameters

Attribute-wise agreement rate between true and estimated alphas

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9192857 0.9407143 0.9564286 0.9678571 0.9685714

Pattern-wise agreement rate between true and estimated alphas

PAR_vec <- numeric(L)
for(t in 1:L){
  PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.7228571 0.7857143 0.8485714 0.8828571 0.8914286

(4) Evaluate the fit of the model to the observed response

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2041.133            NA 14541.86 1265.925 17848.92
#> D(theta_bar)   1726.881            NA 14083.72 1224.472 17035.08
#> DIC            2355.386            NA 15000.01 1307.378 18662.77

head(a$PPP_total_scores)
#>           [,1]      [,2]      [,3]      [,4]       [,5]
#> [1,] 0.1285714 0.5285714 0.8285714 0.8000000 0.80000000
#> [2,] 0.4571429 0.5857143 0.6000000 0.8000000 0.05714286
#> [3,] 0.2857143 0.5142857 0.7571429 0.8428571 0.40000000
#> [4,] 0.6285714 0.9428571 0.3285714 1.0000000 0.80000000
#> [5,] 0.4714286 0.1142857 0.3428571 0.3000000 0.80000000
#> [6,] 0.5857143 0.7857143 0.8000000 0.8000000 0.41428571
head(a$PPP_item_means)
#> [1] 0.4142857 0.4714286 0.4714286 0.5714286 0.4571429 0.5857143
head(a$PPP_item_ORs)
#>      [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]
#> [1,]   NA 0.7857143 0.7857143 0.4428571 0.7857143 0.4000000 0.7428571 0.5285714
#> [2,]   NA        NA 0.9571429 0.5571429 0.7428571 0.7571429 0.3142857 0.5285714
#> [3,]   NA        NA        NA 0.2857143 0.8285714 0.8571429 0.8714286 0.6571429
#> [4,]   NA        NA        NA        NA 0.3428571 0.5571429 0.7142857 0.8285714
#> [5,]   NA        NA        NA        NA        NA 0.7000000 0.5142857 0.9285714
#> [6,]   NA        NA        NA        NA        NA        NA 0.5285714 0.3714286
#>           [,9]     [,10]      [,11]     [,12]     [,13]      [,14]     [,15]
#> [1,] 0.5142857 0.3714286 0.40000000 0.4428571 0.9714286 0.90000000 0.9285714
#> [2,] 0.7571429 0.4714286 0.08571429 0.8428571 1.0000000 0.80000000 0.8000000
#> [3,] 0.7285714 0.9428571 0.91428571 0.4285714 0.8714286 0.72857143 0.9000000
#> [4,] 0.8285714 0.7857143 0.71428571 0.1571429 0.8428571 0.34285714 0.7142857
#> [5,] 0.9285714 0.8142857 0.68571429 0.7000000 1.0000000 0.97142857 0.9142857
#> [6,] 0.2000000 0.3000000 0.08571429 0.3285714 0.7571429 0.02857143 0.2857143
#>           [,16]     [,17]     [,18]      [,19]      [,20]     [,21]     [,22]
#> [1,] 0.88571429 0.4714286 0.9285714 0.85714286 0.97142857 0.6428571 0.7285714
#> [2,] 0.74285714 0.7857143 0.6571429 0.54285714 1.00000000 0.6571429 0.5714286
#> [3,] 0.78571429 0.7428571 0.1714286 0.88571429 0.47142857 0.3857143 0.3142857
#> [4,] 0.31428571 0.2857143 0.2000000 0.48571429 0.21428571 1.0000000 0.6142857
#> [5,] 0.95714286 1.0000000 0.8428571 1.00000000 0.98571429 0.7285714 0.4571429
#> [6,] 0.08571429 0.2000000 0.2428571 0.05714286 0.04285714 0.9857143 0.1000000
#>          [,23]     [,24]     [,25]     [,26]     [,27]     [,28]     [,29]
#> [1,] 0.6857143 0.6428571 0.9000000 0.4142857 0.7428571 0.8285714 0.4000000
#> [2,] 0.7428571 0.3857143 0.9714286 0.3428571 0.4142857 0.9142857 0.9714286
#> [3,] 0.3142857 0.3142857 0.5000000 0.5285714 0.4857143 0.7857143 0.7571429
#> [4,] 0.7142857 0.9428571 0.5000000 0.5000000 0.9857143 1.0000000 1.0000000
#> [5,] 0.6857143 0.8285714 0.7857143 0.8714286 0.8714286 0.7857143 0.9857143
#> [6,] 0.1428571 0.6142857 0.6571429 0.8142857 0.2571429 0.9857143 0.9857143
#>          [,30]      [,31]     [,32]     [,33]     [,34]     [,35]      [,36]
#> [1,] 0.8285714 0.15714286 0.1000000 0.4428571 0.6857143 0.6714286 0.07142857
#> [2,] 0.8428571 0.70000000 0.1857143 0.1714286 0.6000000 0.5857143 0.27142857
#> [3,] 0.1142857 0.74285714 0.9285714 0.6142857 0.4857143 0.4857143 0.40000000
#> [4,] 0.4428571 0.07142857 0.9142857 0.3571429 0.7142857 0.3000000 0.25714286
#> [5,] 0.6428571 0.72857143 0.5285714 0.8714286 0.1857143 0.7428571 0.77142857
#> [6,] 0.5714286 0.27142857 0.2142857 0.3000000 0.0000000 0.1428571 0.04285714
#>          [,37]     [,38]      [,39]     [,40]     [,41]     [,42]     [,43]
#> [1,] 0.5142857 0.0000000 0.84285714 0.2428571 1.0000000 0.7714286 0.5428571
#> [2,] 0.4428571 0.4285714 0.75714286 0.4428571 0.8714286 0.9000000 0.7571429
#> [3,] 0.9142857 0.6857143 0.62857143 0.9714286 0.4428571 0.2571429 0.3428571
#> [4,] 0.8571429 0.6285714 0.31428571 0.9285714 0.9428571 0.8714286 0.9714286
#> [5,] 0.7857143 0.4571429 1.00000000 0.6571429 0.9857143 0.8428571 0.6000000
#> [6,] 0.1142857 0.3285714 0.05714286 0.1571429 0.3000000 0.4428571 0.1142857
#>          [,44]     [,45]     [,46]     [,47]     [,48]     [,49]     [,50]
#> [1,] 0.3714286 0.7571429 0.4571429 0.3857143 0.1571429 0.5285714 0.2571429
#> [2,] 0.8285714 0.9714286 0.9571429 0.9285714 0.7714286 0.9857143 0.9428571
#> [3,] 0.9428571 0.6428571 0.5000000 0.5285714 0.7714286 0.8571429 0.3000000
#> [4,] 0.4571429 0.7428571 0.3285714 0.7857143 0.8857143 0.7428571 0.7000000
#> [5,] 0.6857143 0.9857143 0.2285714 0.5571429 0.3000000 0.3571429 0.2857143
#> [6,] 0.5714286 0.2571429 0.2000000 0.1000000 0.2142857 0.4571429 0.4285714
library(bayesplot)
pp_check(output_HMDCM)

pp_check(output_HMDCM, plotfun="dens_overlay", type="item_mean")

pp_check(output_HMDCM, plotfun="hist", type="item_OR")
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

pp_check(output_HMDCM, plotfun="stat_2d", type="item_mean")

pp_check(output_HMDCM, plotfun="scatter_avg", type="total_score")

pp_check(output_HMDCM, plotfun="error_scatter_avg", type="total_score")

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)