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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 
#>  36  28  91 161  34
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
#>  0.1698 0.1651
#>  0.1680 0.1600
#>  0.1493 0.1269
#>  0.1329 0.1430
#>  0.1139 0.1124
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    lambdas_EAP
#> λ0     -1.4473
#> λ1      1.9931
#> λ2      0.1998
#> λ3      0.1391
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1429
#> 0001  0.1706
#> 0010  0.1868
#> 0011  0.2530
#> 0100  0.1556
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 19275.41 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.4937
#> M2:  0.49
#> total scores:  0.623
a <- summary(output_HMDCM)
a$ss_EAP
#>            [,1]
#>  [1,] 0.1697906
#>  [2,] 0.1680309
#>  [3,] 0.1492832
#>  [4,] 0.1329068
#>  [5,] 0.1138727
#>  [6,] 0.1661326
#>  [7,] 0.1705610
#>  [8,] 0.1246988
#>  [9,] 0.2354335
#> [10,] 0.1794307
#> [11,] 0.1431058
#> [12,] 0.1529385
#> [13,] 0.1331102
#> [14,] 0.1267657
#> [15,] 0.1497950
#> [16,] 0.1769501
#> [17,] 0.1744780
#> [18,] 0.1824385
#> [19,] 0.2135706
#> [20,] 0.1727740
#> [21,] 0.1837538
#> [22,] 0.1474389
#> [23,] 0.2108857
#> [24,] 0.1130164
#> [25,] 0.1082945
#> [26,] 0.1829056
#> [27,] 0.2060486
#> [28,] 0.1929764
#> [29,] 0.1876752
#> [30,] 0.1507918
#> [31,] 0.1301102
#> [32,] 0.1945162
#> [33,] 0.2057871
#> [34,] 0.1923413
#> [35,] 0.1234793
#> [36,] 0.2201181
#> [37,] 0.2065649
#> [38,] 0.1702183
#> [39,] 0.1853408
#> [40,] 0.1845450
#> [41,] 0.1679590
#> [42,] 0.1603618
#> [43,] 0.1931209
#> [44,] 0.1568479
#> [45,] 0.2033812
#> [46,] 0.1286860
#> [47,] 0.1235941
#> [48,] 0.2308971
#> [49,] 0.1723194
#> [50,] 0.1458139
a$lambdas_EAP
#>          [,1]
#> λ0 -1.4473139
#> λ1  1.9930927
#> λ2  0.1997842
#> λ3  0.1390890
mean(a$PPP_total_scores)
#> [1] 0.6246612
mean(upper.tri(a$PPP_item_ORs))
#> [1] 0.49
mean(a$PPP_item_means)
#> [1] 0.506

(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] 0.9171429 0.9385714 0.9592857 0.9742857 0.9785714

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] 0.7200000 0.7800000 0.8514286 0.9142857 0.9200000

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2082.864            NA 15064.31 1289.583 18436.75
#> D(theta_bar)   1811.729            NA 14528.49 1257.873 17598.09
#> DIC            2353.999            NA 15600.12 1321.292 19275.41

head(a$PPP_total_scores)
#>           [,1]      [,2]      [,3]      [,4]      [,5]
#> [1,] 0.2714286 0.8714286 1.0000000 0.5000000 1.0000000
#> [2,] 0.5428571 0.4000000 1.0000000 1.0000000 0.5285714
#> [3,] 0.2714286 0.5857143 0.4571429 0.5714286 0.8714286
#> [4,] 0.3285714 0.5285714 0.5571429 0.5857143 1.0000000
#> [5,] 0.5428571 0.5285714 0.9285714 0.4571429 0.7714286
#> [6,] 0.7571429 0.8142857 1.0000000 1.0000000 0.2428571
head(a$PPP_item_means)
#> [1] 0.5000000 0.4571429 0.5857143 0.5285714 0.5000000 0.4285714
head(a$PPP_item_ORs)
#>      [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]
#> [1,]   NA 0.7714286 0.7285714 0.5285714 0.5571429 0.7142857 0.6000000 0.6714286
#> [2,]   NA        NA 0.8714286 0.6571429 0.8571429 0.5428571 0.8857143 0.9571429
#> [3,]   NA        NA        NA 0.9714286 0.4428571 0.8142857 0.3142857 0.9857143
#> [4,]   NA        NA        NA        NA 0.8285714 0.7714286 0.9142857 0.6428571
#> [5,]   NA        NA        NA        NA        NA 0.7571429 0.8285714 0.5857143
#> [6,]   NA        NA        NA        NA        NA        NA 0.2857143 0.6285714
#>           [,9]     [,10]      [,11]     [,12]     [,13]     [,14]      [,15]
#> [1,] 0.9142857 0.6142857 0.71428571 0.9428571 0.9857143 0.6857143 0.35714286
#> [2,] 0.5428571 0.2714286 0.05714286 0.7571429 0.8714286 0.4571429 0.54285714
#> [3,] 0.2285714 0.3857143 0.27142857 0.1714286 0.7857143 0.1857143 0.35714286
#> [4,] 0.6714286 0.6428571 0.91428571 0.7571429 0.5571429 0.5857143 0.48571429
#> [5,] 0.2571429 0.4000000 0.11428571 0.4714286 0.8142857 0.2857143 0.04285714
#> [6,] 0.8714286 0.4714286 0.42857143 0.1571429 0.4142857 0.2714286 0.17142857
#>          [,16]      [,17]     [,18]      [,19]     [,20]      [,21]      [,22]
#> [1,] 0.9714286 0.37142857 0.2285714 0.41428571 0.7000000 0.70000000 0.57142857
#> [2,] 0.6142857 0.42857143 0.6857143 0.15714286 0.4571429 0.72857143 0.11428571
#> [3,] 0.1857143 0.58571429 0.9714286 0.02857143 0.4285714 0.05714286 0.10000000
#> [4,] 0.7857143 0.47142857 0.9285714 0.35714286 0.5714286 0.31428571 0.32857143
#> [5,] 0.3285714 0.04285714 0.0000000 0.12857143 0.2142857 0.50000000 0.55714286
#> [6,] 0.8285714 0.48571429 0.3571429 0.38571429 0.8428571 0.58571429 0.07142857
#>          [,23]     [,24]     [,25]      [,26]     [,27]     [,28]     [,29]
#> [1,] 0.1000000 0.8714286 0.7571429 0.17142857 0.1285714 0.6142857 0.6714286
#> [2,] 0.6000000 0.6857143 0.5142857 0.48571429 0.1000000 0.6571429 0.6571429
#> [3,] 0.4571429 0.8000000 0.7142857 0.04285714 0.5000000 0.4714286 0.2571429
#> [4,] 0.3285714 0.9571429 0.9571429 0.30000000 0.9142857 0.6571429 0.1000000
#> [5,] 0.2000000 1.0000000 0.6000000 0.64285714 0.4000000 0.6285714 0.7714286
#> [6,] 0.2571429 0.9000000 0.4428571 0.65714286 0.1285714 0.3000000 0.4142857
#>          [,30]     [,31]     [,32]     [,33]     [,34]      [,35]      [,36]
#> [1,] 0.6428571 0.3285714 0.6714286 0.8714286 0.6428571 0.81428571 0.80000000
#> [2,] 0.6428571 0.8714286 0.2857143 0.6142857 0.4428571 0.01428571 0.05714286
#> [3,] 0.2571429 0.9142857 0.3000000 0.4714286 0.8857143 0.91428571 0.91428571
#> [4,] 0.3285714 0.4571429 0.2571429 0.8571429 0.2571429 0.27142857 0.21428571
#> [5,] 1.0000000 0.4142857 0.3857143 0.4571429 0.7285714 0.42857143 0.42857143
#> [6,] 0.1000000 0.4571429 0.2285714 0.6714286 0.5571429 0.12857143 0.20000000
#>          [,37]     [,38]     [,39]     [,40]     [,41]     [,42]      [,43]
#> [1,] 0.8857143 0.9428571 0.9857143 0.9285714 0.5571429 0.1714286 0.11428571
#> [2,] 0.6000000 0.3428571 0.1285714 0.7000000 0.1714286 0.7285714 0.38571429
#> [3,] 0.8285714 0.6285714 0.8142857 0.4428571 0.7571429 0.9142857 0.22857143
#> [4,] 0.7142857 0.2714286 0.9714286 0.1428571 0.8857143 0.9428571 0.07142857
#> [5,] 0.5428571 0.3857143 0.9714286 0.5857143 0.6000000 0.5857143 0.18571429
#> [6,] 0.8142857 0.3571429 0.7857143 0.9571429 0.1857143 0.9714286 0.10000000
#>           [,44]      [,45]     [,46]      [,47]      [,48]     [,49]     [,50]
#> [1,] 0.01428571 0.00000000 0.2714286 0.04285714 0.44285714 0.1571429 0.1142857
#> [2,] 0.37142857 0.02857143 0.6000000 0.40000000 0.35714286 0.3285714 0.2857143
#> [3,] 0.82857143 0.51428571 0.9857143 0.91428571 0.52857143 0.2571429 0.9428571
#> [4,] 0.20000000 0.67142857 0.5714286 0.54285714 0.70000000 0.6285714 0.1000000
#> [5,] 0.32857143 0.01428571 0.9000000 0.65714286 0.04285714 0.6714286 0.2571429
#> [6,] 0.08571429 0.18571429 0.4571429 0.57142857 0.12857143 0.2571429 0.3000000
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)

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