This function can provide the Hull plot. The point suggested by the Hull method is marked in red.

# S3 method for class 'validation'
plot(x, i, ...)

Arguments

x

A validation in which method = "Hull".

i

A numeric, which represents the item you want to plot Hull curve.

...

Additional arguments.

Value

None. This function is used for side effects (plotting).

Examples

set.seed(123)
library(Qval)

## generate Q-matrix and data
K <- 4
I <- 20
IQ <- list(
  P0 = runif(I, 0.2, 0.4),
  P1 = runif(I, 0.6, 0.8)
)

# \donttest{
Q <- sim.Q(K, I)
data <- sim.data(Q = Q, N = 500, IQ = IQ, model = "GDINA", distribute = "horder")
#> distribute =  horder 
#>  model =  GDINA 
#>  number of attributes:  4 
#>  number of items:  20 
#>  num of examinees:  500 
#>  average of P0 =  0.31 
#>  average of P1 =  0.715 
#> theta_mean =  0.03 , theta_sd = 0.969 
#>  a =  1.5 1.5 1.5 1.5 
#>  b =  1.5 -1.5 0.5 -0.5 
MQ <- sim.MQ(Q, 0.1)
#> rate of mis-specifications =  0.1 
#>  rate of  over-specifications =  0.05 
#>  rate of under-specifications =  0.05 

CDM.obj <- CDM(data$dat, MQ)
#> 
Iter = 1  Max. abs. change = 0.38821  Deviance  = 15020.27                                                                                  
Iter = 2  Max. abs. change = 0.07103  Deviance  = 13317.06                                                                                  
Iter = 3  Max. abs. change = 0.04349  Deviance  = 13237.85                                                                                  
Iter = 4  Max. abs. change = 0.03598  Deviance  = 13212.53                                                                                  
Iter = 5  Max. abs. change = 0.02092  Deviance  = 13199.34                                                                                  
Iter = 6  Max. abs. change = 0.02010  Deviance  = 13190.65                                                                                  
Iter = 7  Max. abs. change = 0.02132  Deviance  = 13184.38                                                                                  
Iter = 8  Max. abs. change = 0.02181  Deviance  = 13180.06                                                                                  
Iter = 9  Max. abs. change = 0.02135  Deviance  = 13176.81                                                                                  
Iter = 10  Max. abs. change = 0.02017  Deviance  = 13174.33                                                                                  
Iter = 11  Max. abs. change = 0.01851  Deviance  = 13172.51                                                                                  
Iter = 12  Max. abs. change = 0.01461  Deviance  = 13171.09                                                                                  
Iter = 13  Max. abs. change = 0.00775  Deviance  = 13170.01                                                                                  
Iter = 14  Max. abs. change = 0.00629  Deviance  = 13169.19                                                                                  
Iter = 15  Max. abs. change = 0.00590  Deviance  = 13168.51                                                                                  
Iter = 16  Max. abs. change = 0.00539  Deviance  = 13167.94                                                                                  
Iter = 17  Max. abs. change = 0.00486  Deviance  = 13167.45                                                                                  
Iter = 18  Max. abs. change = 0.00447  Deviance  = 13166.99                                                                                  
Iter = 19  Max. abs. change = 0.00421  Deviance  = 13166.57                                                                                  
Iter = 20  Max. abs. change = 0.00404  Deviance  = 13166.15                                                                                  
Iter = 21  Max. abs. change = 0.00406  Deviance  = 13165.74                                                                                  
Iter = 22  Max. abs. change = 0.00410  Deviance  = 13165.33                                                                                  
Iter = 23  Max. abs. change = 0.00412  Deviance  = 13164.92                                                                                  
Iter = 24  Max. abs. change = 0.00414  Deviance  = 13164.50                                                                                  
Iter = 25  Max. abs. change = 0.00420  Deviance  = 13164.08                                                                                  
Iter = 26  Max. abs. change = 0.00430  Deviance  = 13163.64                                                                                  
Iter = 27  Max. abs. change = 0.00439  Deviance  = 13163.20                                                                                  
Iter = 28  Max. abs. change = 0.00447  Deviance  = 13162.74                                                                                  
Iter = 29  Max. abs. change = 0.00454  Deviance  = 13162.28                                                                                  
Iter = 30  Max. abs. change = 0.00460  Deviance  = 13161.80                                                                                  
Iter = 31  Max. abs. change = 0.00464  Deviance  = 13161.31                                                                                  
Iter = 32  Max. abs. change = 0.00465  Deviance  = 13160.82                                                                                  
Iter = 33  Max. abs. change = 0.00464  Deviance  = 13160.31                                                                                  
Iter = 34  Max. abs. change = 0.00473  Deviance  = 13159.81                                                                                  
Iter = 35  Max. abs. change = 0.00485  Deviance  = 13159.29                                                                                  
Iter = 36  Max. abs. change = 0.00489  Deviance  = 13158.81                                                                                  
Iter = 37  Max. abs. change = 0.00493  Deviance  = 13158.34                                                                                  
Iter = 38  Max. abs. change = 0.00495  Deviance  = 13157.89                                                                                  
Iter = 39  Max. abs. change = 0.00497  Deviance  = 13157.46                                                                                  
Iter = 40  Max. abs. change = 0.00496  Deviance  = 13157.06                                                                                  
Iter = 41  Max. abs. change = 0.00494  Deviance  = 13156.68                                                                                  
Iter = 42  Max. abs. change = 0.00492  Deviance  = 13156.33                                                                                  
Iter = 43  Max. abs. change = 0.00486  Deviance  = 13156.01                                                                                  
Iter = 44  Max. abs. change = 0.00480  Deviance  = 13155.72                                                                                  
Iter = 45  Max. abs. change = 0.00473  Deviance  = 13155.45                                                                                  
Iter = 46  Max. abs. change = 0.00465  Deviance  = 13155.22                                                                                  
Iter = 47  Max. abs. change = 0.00457  Deviance  = 13155.01                                                                                  
Iter = 48  Max. abs. change = 0.00448  Deviance  = 13154.82                                                                                  
Iter = 49  Max. abs. change = 0.00441  Deviance  = 13154.65                                                                                  
Iter = 50  Max. abs. change = 0.00431  Deviance  = 13154.50                                                                                  
Iter = 51  Max. abs. change = 0.00424  Deviance  = 13154.37                                                                                  
Iter = 52  Max. abs. change = 0.00413  Deviance  = 13154.25                                                                                  
Iter = 53  Max. abs. change = 0.00405  Deviance  = 13154.14                                                                                  
Iter = 54  Max. abs. change = 0.00397  Deviance  = 13154.04                                                                                  
Iter = 55  Max. abs. change = 0.00390  Deviance  = 13153.95                                                                                  
Iter = 56  Max. abs. change = 0.00385  Deviance  = 13153.87                                                                                  
Iter = 57  Max. abs. change = 0.00380  Deviance  = 13153.79                                                                                  
Iter = 58  Max. abs. change = 0.00375  Deviance  = 13153.72                                                                                  
Iter = 59  Max. abs. change = 0.00371  Deviance  = 13153.65                                                                                  
Iter = 60  Max. abs. change = 0.00367  Deviance  = 13153.59                                                                                  
Iter = 61  Max. abs. change = 0.00222  Deviance  = 13153.52                                                                                  
Iter = 62  Max. abs. change = 0.00178  Deviance  = 13153.47                                                                                  
Iter = 63  Max. abs. change = 0.00170  Deviance  = 13153.41                                                                                  
Iter = 64  Max. abs. change = 0.00164  Deviance  = 13153.36                                                                                  
Iter = 65  Max. abs. change = 0.00157  Deviance  = 13153.31                                                                                  
Iter = 66  Max. abs. change = 0.00150  Deviance  = 13153.27                                                                                  
Iter = 67  Max. abs. change = 0.00144  Deviance  = 13153.22                                                                                  
Iter = 68  Max. abs. change = 0.00138  Deviance  = 13153.18                                                                                  
Iter = 69  Max. abs. change = 0.00133  Deviance  = 13153.14                                                                                  
Iter = 70  Max. abs. change = 0.00128  Deviance  = 13153.10                                                                                  
Iter = 71  Max. abs. change = 0.00123  Deviance  = 13153.06                                                                                  
Iter = 72  Max. abs. change = 0.00119  Deviance  = 13153.03                                                                                  
Iter = 73  Max. abs. change = 0.00117  Deviance  = 13152.99                                                                                  
Iter = 74  Max. abs. change = 0.00117  Deviance  = 13152.95                                                                                  
Iter = 75  Max. abs. change = 0.00117  Deviance  = 13152.92                                                                                  
Iter = 76  Max. abs. change = 0.00117  Deviance  = 13152.88                                                                                  
Iter = 77  Max. abs. change = 0.00119  Deviance  = 13152.85                                                                                  
Iter = 78  Max. abs. change = 0.00125  Deviance  = 13152.81                                                                                  
Iter = 79  Max. abs. change = 0.00132  Deviance  = 13152.78                                                                                  
Iter = 80  Max. abs. change = 0.00138  Deviance  = 13152.75                                                                                  
Iter = 81  Max. abs. change = 0.00144  Deviance  = 13152.71                                                                                  
Iter = 82  Max. abs. change = 0.00151  Deviance  = 13152.68                                                                                  
Iter = 83  Max. abs. change = 0.00157  Deviance  = 13152.64                                                                                  
Iter = 84  Max. abs. change = 0.00163  Deviance  = 13152.61                                                                                  
Iter = 85  Max. abs. change = 0.00169  Deviance  = 13152.58                                                                                  
Iter = 86  Max. abs. change = 0.00175  Deviance  = 13152.54                                                                                  
Iter = 87  Max. abs. change = 0.00181  Deviance  = 13152.51                                                                                  
Iter = 88  Max. abs. change = 0.00187  Deviance  = 13152.48                                                                                  
Iter = 89  Max. abs. change = 0.00192  Deviance  = 13152.44                                                                                  
Iter = 90  Max. abs. change = 0.00198  Deviance  = 13152.41                                                                                  
Iter = 91  Max. abs. change = 0.00204  Deviance  = 13152.37                                                                                  
Iter = 92  Max. abs. change = 0.00210  Deviance  = 13152.34                                                                                  
Iter = 93  Max. abs. change = 0.00216  Deviance  = 13152.30                                                                                  
Iter = 94  Max. abs. change = 0.00221  Deviance  = 13152.27                                                                                  
Iter = 95  Max. abs. change = 0.00226  Deviance  = 13152.23                                                                                  
Iter = 96  Max. abs. change = 0.00232  Deviance  = 13152.20                                                                                  
Iter = 97  Max. abs. change = 0.00237  Deviance  = 13152.16                                                                                  
Iter = 98  Max. abs. change = 0.00243  Deviance  = 13152.13                                                                                  
Iter = 99  Max. abs. change = 0.00249  Deviance  = 13152.09                                                                                  
Iter = 100  Max. abs. change = 0.00254  Deviance  = 13152.06                                                                                  
Iter = 101  Max. abs. change = 0.00260  Deviance  = 13152.02                                                                                  
Iter = 102  Max. abs. change = 0.00265  Deviance  = 13151.98                                                                                  
Iter = 103  Max. abs. change = 0.00271  Deviance  = 13151.95                                                                                  
Iter = 104  Max. abs. change = 0.00276  Deviance  = 13151.91                                                                                  
Iter = 105  Max. abs. change = 0.00282  Deviance  = 13151.87                                                                                  
Iter = 106  Max. abs. change = 0.00287  Deviance  = 13151.83                                                                                  
Iter = 107  Max. abs. change = 0.00293  Deviance  = 13151.80                                                                                  
Iter = 108  Max. abs. change = 0.00298  Deviance  = 13151.76                                                                                  
Iter = 109  Max. abs. change = 0.00304  Deviance  = 13151.72                                                                                  
Iter = 110  Max. abs. change = 0.00309  Deviance  = 13151.68                                                                                  
Iter = 111  Max. abs. change = 0.00315  Deviance  = 13151.64                                                                                  
Iter = 112  Max. abs. change = 0.00320  Deviance  = 13151.60                                                                                  
Iter = 113  Max. abs. change = 0.00325  Deviance  = 13151.56                                                                                  
Iter = 114  Max. abs. change = 0.00331  Deviance  = 13151.52                                                                                  
Iter = 115  Max. abs. change = 0.00335  Deviance  = 13151.48                                                                                  
Iter = 116  Max. abs. change = 0.00340  Deviance  = 13151.44                                                                                  
Iter = 117  Max. abs. change = 0.00345  Deviance  = 13151.40                                                                                  
Iter = 118  Max. abs. change = 0.00349  Deviance  = 13151.36                                                                                  
Iter = 119  Max. abs. change = 0.00354  Deviance  = 13151.32                                                                                  
Iter = 120  Max. abs. change = 0.00359  Deviance  = 13151.28                                                                                  
Iter = 121  Max. abs. change = 0.00365  Deviance  = 13151.24                                                                                  
Iter = 122  Max. abs. change = 0.00371  Deviance  = 13151.19                                                                                  
Iter = 123  Max. abs. change = 0.00377  Deviance  = 13151.15                                                                                  
Iter = 124  Max. abs. change = 0.00384  Deviance  = 13151.11                                                                                  
Iter = 125  Max. abs. change = 0.00390  Deviance  = 13151.06                                                                                  
Iter = 126  Max. abs. change = 0.00396  Deviance  = 13151.02                                                                                  
Iter = 127  Max. abs. change = 0.00402  Deviance  = 13150.98                                                                                  
Iter = 128  Max. abs. change = 0.00407  Deviance  = 13150.93                                                                                  
Iter = 129  Max. abs. change = 0.00413  Deviance  = 13150.89                                                                                  
Iter = 130  Max. abs. change = 0.00418  Deviance  = 13150.84                                                                                  
Iter = 131  Max. abs. change = 0.00423  Deviance  = 13150.79                                                                                  
Iter = 132  Max. abs. change = 0.00427  Deviance  = 13150.75                                                                                  
Iter = 133  Max. abs. change = 0.00430  Deviance  = 13150.70                                                                                  
Iter = 134  Max. abs. change = 0.00433  Deviance  = 13150.65                                                                                  
Iter = 135  Max. abs. change = 0.00436  Deviance  = 13150.60                                                                                  
Iter = 136  Max. abs. change = 0.00437  Deviance  = 13150.55                                                                                  
Iter = 137  Max. abs. change = 0.00439  Deviance  = 13150.51                                                                                  
Iter = 138  Max. abs. change = 0.00439  Deviance  = 13150.46                                                                                  
Iter = 139  Max. abs. change = 0.00438  Deviance  = 13150.41                                                                                  
Iter = 140  Max. abs. change = 0.00437  Deviance  = 13150.36                                                                                  
Iter = 141  Max. abs. change = 0.00435  Deviance  = 13150.31                                                                                  
Iter = 142  Max. abs. change = 0.00322  Deviance  = 13150.26                                                                                  
Iter = 143  Max. abs. change = 0.00261  Deviance  = 13150.21                                                                                  
Iter = 144  Max. abs. change = 0.00237  Deviance  = 13150.17                                                                                  
Iter = 145  Max. abs. change = 0.00217  Deviance  = 13150.14                                                                                  
Iter = 146  Max. abs. change = 0.00200  Deviance  = 13150.10                                                                                  
Iter = 147  Max. abs. change = 0.00185  Deviance  = 13150.06                                                                                  
Iter = 148  Max. abs. change = 0.00172  Deviance  = 13150.03                                                                                  
Iter = 149  Max. abs. change = 0.00160  Deviance  = 13150.00                                                                                  
Iter = 150  Max. abs. change = 0.00149  Deviance  = 13149.96                                                                                  
Iter = 151  Max. abs. change = 0.00145  Deviance  = 13149.93                                                                                  
Iter = 152  Max. abs. change = 0.00140  Deviance  = 13149.90                                                                                  
Iter = 153  Max. abs. change = 0.00136  Deviance  = 13149.87                                                                                  
Iter = 154  Max. abs. change = 0.00133  Deviance  = 13149.84                                                                                  
Iter = 155  Max. abs. change = 0.00133  Deviance  = 13149.80                                                                                  
Iter = 156  Max. abs. change = 0.00137  Deviance  = 13149.77                                                                                  
Iter = 157  Max. abs. change = 0.00141  Deviance  = 13149.75                                                                                  
Iter = 158  Max. abs. change = 0.00144  Deviance  = 13149.72                                                                                  
Iter = 159  Max. abs. change = 0.00148  Deviance  = 13149.69                                                                                  
Iter = 160  Max. abs. change = 0.00151  Deviance  = 13149.66                                                                                  
Iter = 161  Max. abs. change = 0.00155  Deviance  = 13149.63                                                                                  
Iter = 162  Max. abs. change = 0.00159  Deviance  = 13149.60                                                                                  
Iter = 163  Max. abs. change = 0.00162  Deviance  = 13149.58                                                                                  
Iter = 164  Max. abs. change = 0.00166  Deviance  = 13149.55                                                                                  
Iter = 165  Max. abs. change = 0.00168  Deviance  = 13149.52                                                                                  
Iter = 166  Max. abs. change = 0.00172  Deviance  = 13149.49                                                                                  
Iter = 167  Max. abs. change = 0.00176  Deviance  = 13149.47                                                                                  
Iter = 168  Max. abs. change = 0.00178  Deviance  = 13149.44                                                                                  
Iter = 169  Max. abs. change = 0.00181  Deviance  = 13149.42                                                                                  
Iter = 170  Max. abs. change = 0.00184  Deviance  = 13149.39                                                                                  
Iter = 171  Max. abs. change = 0.00187  Deviance  = 13149.37                                                                                  
Iter = 172  Max. abs. change = 0.00190  Deviance  = 13149.34                                                                                  
Iter = 173  Max. abs. change = 0.00192  Deviance  = 13149.32                                                                                  
Iter = 174  Max. abs. change = 0.00195  Deviance  = 13149.30                                                                                  
Iter = 175  Max. abs. change = 0.00196  Deviance  = 13149.28                                                                                  
Iter = 176  Max. abs. change = 0.00199  Deviance  = 13149.25                                                                                  
Iter = 177  Max. abs. change = 0.00200  Deviance  = 13149.23                                                                                  
Iter = 178  Max. abs. change = 0.00202  Deviance  = 13149.21                                                                                  
Iter = 179  Max. abs. change = 0.00205  Deviance  = 13149.19                                                                                  
Iter = 180  Max. abs. change = 0.00206  Deviance  = 13149.17                                                                                  
Iter = 181  Max. abs. change = 0.00208  Deviance  = 13149.15                                                                                  
Iter = 182  Max. abs. change = 0.00210  Deviance  = 13149.13                                                                                  
Iter = 183  Max. abs. change = 0.00212  Deviance  = 13149.10                                                                                  
Iter = 184  Max. abs. change = 0.00214  Deviance  = 13149.08                                                                                  
Iter = 185  Max. abs. change = 0.00216  Deviance  = 13149.06                                                                                  
Iter = 186  Max. abs. change = 0.00218  Deviance  = 13149.04                                                                                  
Iter = 187  Max. abs. change = 0.00220  Deviance  = 13149.02                                                                                  
Iter = 188  Max. abs. change = 0.00222  Deviance  = 13149.00                                                                                  
Iter = 189  Max. abs. change = 0.00224  Deviance  = 13148.98                                                                                  
Iter = 190  Max. abs. change = 0.00225  Deviance  = 13148.95                                                                                  
Iter = 191  Max. abs. change = 0.00227  Deviance  = 13148.93                                                                                  
Iter = 192  Max. abs. change = 0.00229  Deviance  = 13148.91                                                                                  
Iter = 193  Max. abs. change = 0.00230  Deviance  = 13148.89                                                                                  
Iter = 194  Max. abs. change = 0.00232  Deviance  = 13148.86                                                                                  
Iter = 195  Max. abs. change = 0.00233  Deviance  = 13148.84                                                                                  
Iter = 196  Max. abs. change = 0.00234  Deviance  = 13148.82                                                                                  
Iter = 197  Max. abs. change = 0.00236  Deviance  = 13148.79                                                                                  
Iter = 198  Max. abs. change = 0.00237  Deviance  = 13148.77                                                                                  
Iter = 199  Max. abs. change = 0.00238  Deviance  = 13148.75                                                                                  
Iter = 200  Max. abs. change = 0.00239  Deviance  = 13148.72                                                                                  
Iter = 201  Max. abs. change = 0.00239  Deviance  = 13148.70                                                                                  
Iter = 202  Max. abs. change = 0.00240  Deviance  = 13148.67                                                                                  
Iter = 203  Max. abs. change = 0.00241  Deviance  = 13148.65                                                                                  
Iter = 204  Max. abs. change = 0.00241  Deviance  = 13148.62                                                                                  
Iter = 205  Max. abs. change = 0.00241  Deviance  = 13148.60                                                                                  
Iter = 206  Max. abs. change = 0.00242  Deviance  = 13148.57                                                                                  
Iter = 207  Max. abs. change = 0.00242  Deviance  = 13148.54                                                                                  
Iter = 208  Max. abs. change = 0.00242  Deviance  = 13148.52                                                                                  
Iter = 209  Max. abs. change = 0.00248  Deviance  = 13148.49                                                                                  
Iter = 210  Max. abs. change = 0.00253  Deviance  = 13148.47                                                                                  
Iter = 211  Max. abs. change = 0.00258  Deviance  = 13148.44                                                                                  
Iter = 212  Max. abs. change = 0.00263  Deviance  = 13148.41                                                                                  
Iter = 213  Max. abs. change = 0.00268  Deviance  = 13148.39                                                                                  
Iter = 214  Max. abs. change = 0.00273  Deviance  = 13148.36                                                                                  
Iter = 215  Max. abs. change = 0.00278  Deviance  = 13148.34                                                                                  
Iter = 216  Max. abs. change = 0.00282  Deviance  = 13148.31                                                                                  
Iter = 217  Max. abs. change = 0.00287  Deviance  = 13148.28                                                                                  
Iter = 218  Max. abs. change = 0.00291  Deviance  = 13148.26                                                                                  
Iter = 219  Max. abs. change = 0.00295  Deviance  = 13148.23                                                                                  
Iter = 220  Max. abs. change = 0.00299  Deviance  = 13148.21                                                                                  
Iter = 221  Max. abs. change = 0.00302  Deviance  = 13148.18                                                                                  
Iter = 222  Max. abs. change = 0.00306  Deviance  = 13148.16                                                                                  
Iter = 223  Max. abs. change = 0.00309  Deviance  = 13148.13                                                                                  
Iter = 224  Max. abs. change = 0.00311  Deviance  = 13148.11                                                                                  
Iter = 225  Max. abs. change = 0.00314  Deviance  = 13148.09                                                                                  
Iter = 226  Max. abs. change = 0.00317  Deviance  = 13148.06                                                                                  
Iter = 227  Max. abs. change = 0.00319  Deviance  = 13148.04                                                                                  
Iter = 228  Max. abs. change = 0.00322  Deviance  = 13148.02                                                                                  
Iter = 229  Max. abs. change = 0.00324  Deviance  = 13147.99                                                                                  
Iter = 230  Max. abs. change = 0.00326  Deviance  = 13147.97                                                                                  
Iter = 231  Max. abs. change = 0.00328  Deviance  = 13147.95                                                                                  
Iter = 232  Max. abs. change = 0.00329  Deviance  = 13147.93                                                                                  
Iter = 233  Max. abs. change = 0.00331  Deviance  = 13147.91                                                                                  
Iter = 234  Max. abs. change = 0.00332  Deviance  = 13147.89                                                                                  
Iter = 235  Max. abs. change = 0.00333  Deviance  = 13147.87                                                                                  
Iter = 236  Max. abs. change = 0.00334  Deviance  = 13147.85                                                                                  
Iter = 237  Max. abs. change = 0.00335  Deviance  = 13147.83                                                                                  
Iter = 238  Max. abs. change = 0.00336  Deviance  = 13147.81                                                                                  
Iter = 239  Max. abs. change = 0.00337  Deviance  = 13147.80                                                                                  
Iter = 240  Max. abs. change = 0.00338  Deviance  = 13147.78                                                                                  
Iter = 241  Max. abs. change = 0.00339  Deviance  = 13147.76                                                                                  
Iter = 242  Max. abs. change = 0.00339  Deviance  = 13147.75                                                                                  
Iter = 243  Max. abs. change = 0.00338  Deviance  = 13147.73                                                                                  
Iter = 244  Max. abs. change = 0.00339  Deviance  = 13147.71                                                                                  
Iter = 245  Max. abs. change = 0.00338  Deviance  = 13147.70                                                                                  
Iter = 246  Max. abs. change = 0.00343  Deviance  = 13147.68                                                                                  
Iter = 247  Max. abs. change = 0.00341  Deviance  = 13147.67                                                                                  
Iter = 248  Max. abs. change = 0.00340  Deviance  = 13147.65                                                                                  
Iter = 249  Max. abs. change = 0.00339  Deviance  = 13147.64                                                                                  
Iter = 250  Max. abs. change = 0.00338  Deviance  = 13147.62                                                                                  
Iter = 251  Max. abs. change = 0.00337  Deviance  = 13147.61                                                                                  
Iter = 252  Max. abs. change = 0.00336  Deviance  = 13147.59                                                                                  
Iter = 253  Max. abs. change = 0.00335  Deviance  = 13147.58                                                                                  
Iter = 254  Max. abs. change = 0.00334  Deviance  = 13147.56                                                                                  
Iter = 255  Max. abs. change = 0.00334  Deviance  = 13147.55                                                                                  
Iter = 256  Max. abs. change = 0.00333  Deviance  = 13147.54                                                                                  
Iter = 257  Max. abs. change = 0.00332  Deviance  = 13147.52                                                                                  
Iter = 258  Max. abs. change = 0.00333  Deviance  = 13147.51                                                                                  
Iter = 259  Max. abs. change = 0.00332  Deviance  = 13147.49                                                                                  
Iter = 260  Max. abs. change = 0.00326  Deviance  = 13147.48                                                                                  
Iter = 261  Max. abs. change = 0.00313  Deviance  = 13147.47                                                                                  
Iter = 262  Max. abs. change = 0.00302  Deviance  = 13147.46                                                                                  
Iter = 263  Max. abs. change = 0.00291  Deviance  = 13147.44                                                                                  
Iter = 264  Max. abs. change = 0.00282  Deviance  = 13147.43                                                                                  
Iter = 265  Max. abs. change = 0.00274  Deviance  = 13147.42                                                                                  
Iter = 266  Max. abs. change = 0.00267  Deviance  = 13147.41                                                                                  
Iter = 267  Max. abs. change = 0.00246  Deviance  = 13147.40                                                                                  
Iter = 268  Max. abs. change = 0.00220  Deviance  = 13147.39                                                                                  
Iter = 269  Max. abs. change = 0.00197  Deviance  = 13147.38                                                                                  
Iter = 270  Max. abs. change = 0.00177  Deviance  = 13147.37                                                                                  
Iter = 271  Max. abs. change = 0.00160  Deviance  = 13147.36                                                                                  
Iter = 272  Max. abs. change = 0.00147  Deviance  = 13147.35                                                                                  
Iter = 273  Max. abs. change = 0.00143  Deviance  = 13147.34                                                                                  
Iter = 274  Max. abs. change = 0.00143  Deviance  = 13147.33                                                                                  
Iter = 275  Max. abs. change = 0.00144  Deviance  = 13147.32                                                                                  
Iter = 276  Max. abs. change = 0.00144  Deviance  = 13147.31                                                                                  
Iter = 277  Max. abs. change = 0.00144  Deviance  = 13147.30                                                                                  
Iter = 278  Max. abs. change = 0.00145  Deviance  = 13147.29                                                                                  
Iter = 279  Max. abs. change = 0.00145  Deviance  = 13147.28                                                                                  
Iter = 280  Max. abs. change = 0.00145  Deviance  = 13147.27                                                                                  
Iter = 281  Max. abs. change = 0.00145  Deviance  = 13147.26                                                                                  
Iter = 282  Max. abs. change = 0.00145  Deviance  = 13147.25                                                                                  
Iter = 283  Max. abs. change = 0.00145  Deviance  = 13147.24                                                                                  
Iter = 284  Max. abs. change = 0.00144  Deviance  = 13147.23                                                                                  
Iter = 285  Max. abs. change = 0.00144  Deviance  = 13147.22                                                                                  
Iter = 286  Max. abs. change = 0.00144  Deviance  = 13147.22                                                                                  
Iter = 287  Max. abs. change = 0.00144  Deviance  = 13147.21                                                                                  
Iter = 288  Max. abs. change = 0.00143  Deviance  = 13147.20                                                                                  
Iter = 289  Max. abs. change = 0.00143  Deviance  = 13147.19                                                                                  
Iter = 290  Max. abs. change = 0.00143  Deviance  = 13147.18                                                                                  
Iter = 291  Max. abs. change = 0.00142  Deviance  = 13147.17                                                                                  
Iter = 292  Max. abs. change = 0.00142  Deviance  = 13147.16                                                                                  
Iter = 293  Max. abs. change = 0.00142  Deviance  = 13147.15                                                                                  
Iter = 294  Max. abs. change = 0.00141  Deviance  = 13147.14                                                                                  
Iter = 295  Max. abs. change = 0.00141  Deviance  = 13147.13                                                                                  
Iter = 296  Max. abs. change = 0.00140  Deviance  = 13147.13                                                                                  
Iter = 297  Max. abs. change = 0.00140  Deviance  = 13147.12                                                                                  
Iter = 298  Max. abs. change = 0.00140  Deviance  = 13147.11                                                                                  
Iter = 299  Max. abs. change = 0.00139  Deviance  = 13147.10                                                                                  
Iter = 300  Max. abs. change = 0.00139  Deviance  = 13147.09                                                                                  
Iter = 301  Max. abs. change = 0.00139  Deviance  = 13147.08                                                                                  
Iter = 302  Max. abs. change = 0.00138  Deviance  = 13147.07                                                                                  
Iter = 303  Max. abs. change = 0.00138  Deviance  = 13147.06                                                                                  
Iter = 304  Max. abs. change = 0.00138  Deviance  = 13147.05                                                                                  
Iter = 305  Max. abs. change = 0.00137  Deviance  = 13147.04                                                                                  
Iter = 306  Max. abs. change = 0.00137  Deviance  = 13147.03                                                                                  
Iter = 307  Max. abs. change = 0.00136  Deviance  = 13147.02                                                                                  
Iter = 308  Max. abs. change = 0.00136  Deviance  = 13147.01                                                                                  
Iter = 309  Max. abs. change = 0.00135  Deviance  = 13147.00                                                                                  
Iter = 310  Max. abs. change = 0.00135  Deviance  = 13146.98                                                                                  
Iter = 311  Max. abs. change = 0.00135  Deviance  = 13146.97                                                                                  
Iter = 312  Max. abs. change = 0.00134  Deviance  = 13146.96                                                                                  
Iter = 313  Max. abs. change = 0.00134  Deviance  = 13146.95                                                                                  
Iter = 314  Max. abs. change = 0.00133  Deviance  = 13146.94                                                                                  
Iter = 315  Max. abs. change = 0.00133  Deviance  = 13146.93                                                                                  
Iter = 316  Max. abs. change = 0.00132  Deviance  = 13146.92                                                                                  
Iter = 317  Max. abs. change = 0.00132  Deviance  = 13146.90                                                                                  
Iter = 318  Max. abs. change = 0.00131  Deviance  = 13146.89                                                                                  
Iter = 319  Max. abs. change = 0.00130  Deviance  = 13146.88                                                                                  
Iter = 320  Max. abs. change = 0.00130  Deviance  = 13146.87                                                                                  
Iter = 321  Max. abs. change = 0.00129  Deviance  = 13146.85                                                                                  
Iter = 322  Max. abs. change = 0.00128  Deviance  = 13146.84                                                                                  
Iter = 323  Max. abs. change = 0.00127  Deviance  = 13146.83                                                                                  
Iter = 324  Max. abs. change = 0.00127  Deviance  = 13146.82                                                                                  
Iter = 325  Max. abs. change = 0.00126  Deviance  = 13146.80                                                                                  
Iter = 326  Max. abs. change = 0.00125  Deviance  = 13146.79                                                                                  
Iter = 327  Max. abs. change = 0.00124  Deviance  = 13146.77                                                                                  
Iter = 328  Max. abs. change = 0.00123  Deviance  = 13146.76                                                                                  
Iter = 329  Max. abs. change = 0.00122  Deviance  = 13146.75                                                                                  
Iter = 330  Max. abs. change = 0.00121  Deviance  = 13146.73                                                                                  
Iter = 331  Max. abs. change = 0.00119  Deviance  = 13146.72                                                                                  
Iter = 332  Max. abs. change = 0.00118  Deviance  = 13146.71                                                                                  
Iter = 333  Max. abs. change = 0.00117  Deviance  = 13146.69                                                                                  
Iter = 334  Max. abs. change = 0.00116  Deviance  = 13146.68                                                                                  
Iter = 335  Max. abs. change = 0.00114  Deviance  = 13146.66                                                                                  
Iter = 336  Max. abs. change = 0.00113  Deviance  = 13146.65                                                                                  
Iter = 337  Max. abs. change = 0.00111  Deviance  = 13146.63                                                                                  
Iter = 338  Max. abs. change = 0.00110  Deviance  = 13146.62                                                                                  
Iter = 339  Max. abs. change = 0.00108  Deviance  = 13146.60                                                                                  
Iter = 340  Max. abs. change = 0.00106  Deviance  = 13146.59                                                                                  
Iter = 341  Max. abs. change = 0.00104  Deviance  = 13146.58                                                                                  
Iter = 342  Max. abs. change = 0.00103  Deviance  = 13146.56                                                                                  
Iter = 343  Max. abs. change = 0.00101  Deviance  = 13146.55                                                                                  
Iter = 344  Max. abs. change = 0.00099  Deviance  = 13146.53                                                                                  
Iter = 345  Max. abs. change = 0.00097  Deviance  = 13146.52                                                                                  
Iter = 346  Max. abs. change = 0.00095  Deviance  = 13146.51                                                                                  
Iter = 347  Max. abs. change = 0.00093  Deviance  = 13146.49                                                                                  
Iter = 348  Max. abs. change = 0.00091  Deviance  = 13146.48                                                                                  
Iter = 349  Max. abs. change = 0.00089  Deviance  = 13146.46                                                                                  
Iter = 350  Max. abs. change = 0.00087  Deviance  = 13146.45                                                                                  
Iter = 351  Max. abs. change = 0.00095  Deviance  = 13146.44                                                                                  
Iter = 352  Max. abs. change = 0.00083  Deviance  = 13146.42                                                                                  
Iter = 353  Max. abs. change = 0.00081  Deviance  = 13146.41                                                                                  
Iter = 354  Max. abs. change = 0.00103  Deviance  = 13146.40                                                                                  
Iter = 355  Max. abs. change = 0.00077  Deviance  = 13146.39                                                                                  
Iter = 356  Max. abs. change = 0.00137  Deviance  = 13146.37                                                                                  
Iter = 357  Max. abs. change = 0.00074  Deviance  = 13146.36                                                                                  
Iter = 358  Max. abs. change = 0.00073  Deviance  = 13146.35                                                                                  
Iter = 359  Max. abs. change = 0.00072  Deviance  = 13146.34                                                                                  
Iter = 360  Max. abs. change = 0.00070  Deviance  = 13146.33                                                                                  
Iter = 361  Max. abs. change = 0.00113  Deviance  = 13146.32                                                                                  
Iter = 362  Max. abs. change = 0.00068  Deviance  = 13146.31                                                                                  
Iter = 363  Max. abs. change = 0.00066  Deviance  = 13146.30                                                                                  
Iter = 364  Max. abs. change = 0.00116  Deviance  = 13146.29                                                                                  
Iter = 365  Max. abs. change = 0.00063  Deviance  = 13146.28                                                                                  
Iter = 366  Max. abs. change = 0.00062  Deviance  = 13146.27                                                                                  
Iter = 367  Max. abs. change = 0.00118  Deviance  = 13146.26                                                                                  
Iter = 368  Max. abs. change = 0.00059  Deviance  = 13146.25                                                                                  
Iter = 369  Max. abs. change = 0.00115  Deviance  = 13146.24                                                                                  
Iter = 370  Max. abs. change = 0.00056  Deviance  = 13146.23                                                                                  
Iter = 371  Max. abs. change = 0.00111  Deviance  = 13146.22                                                                                  
Iter = 372  Max. abs. change = 0.00053  Deviance  = 13146.22                                                                                  
Iter = 373  Max. abs. change = 0.00109  Deviance  = 13146.21                                                                                  
Iter = 374  Max. abs. change = 0.00051  Deviance  = 13146.20                                                                                  
Iter = 375  Max. abs. change = 0.00108  Deviance  = 13146.20                                                                                  
Iter = 376  Max. abs. change = 0.00048  Deviance  = 13146.19                                                                                  
Iter = 377  Max. abs. change = 0.00107  Deviance  = 13146.18                                                                                  
Iter = 378  Max. abs. change = 0.00046  Deviance  = 13146.18                                                                                  
Iter = 379  Max. abs. change = 0.00106  Deviance  = 13146.17                                                                                  
Iter = 380  Max. abs. change = 0.00043  Deviance  = 13146.17                                                                                  
Iter = 381  Max. abs. change = 0.00105  Deviance  = 13146.16                                                                                  
Iter = 382  Max. abs. change = 0.00041  Deviance  = 13146.15                                                                                  
Iter = 383  Max. abs. change = 0.00103  Deviance  = 13146.15                                                                                  
Iter = 384  Max. abs. change = 0.00039  Deviance  = 13146.15                                                                                  
Iter = 385  Max. abs. change = 0.00101  Deviance  = 13146.14                                                                                  
Iter = 386  Max. abs. change = 0.00036  Deviance  = 13146.14                                                                                  
Iter = 387  Max. abs. change = 0.00100  Deviance  = 13146.13                                                                                  
Iter = 388  Max. abs. change = 0.00034  Deviance  = 13146.13                                                                                  
Iter = 389  Max. abs. change = 0.00098  Deviance  = 13146.12                                                                                  
Iter = 390  Max. abs. change = 0.00032  Deviance  = 13146.12                                                                                  
Iter = 391  Max. abs. change = 0.00097  Deviance  = 13146.12                                                                                  
Iter = 392  Max. abs. change = 0.00030  Deviance  = 13146.11                                                                                  
Iter = 393  Max. abs. change = 0.00094  Deviance  = 13146.11                                                                                  
Iter = 394  Max. abs. change = 0.00028  Deviance  = 13146.11                                                                                  
Iter = 395  Max. abs. change = 0.00092  Deviance  = 13146.11                                                                                  
Iter = 396  Max. abs. change = 0.00027  Deviance  = 13146.10                                                                                  
Iter = 397  Max. abs. change = 0.00090  Deviance  = 13146.10                                                                                  
Iter = 398  Max. abs. change = 0.00025  Deviance  = 13146.10                                                                                  
Iter = 399  Max. abs. change = 0.00087  Deviance  = 13146.09                                                                                  
Iter = 400  Max. abs. change = 0.00023  Deviance  = 13146.09                                                                                  
Iter = 401  Max. abs. change = 0.00085  Deviance  = 13146.09                                                                                  
Iter = 402  Max. abs. change = 0.00077  Deviance  = 13146.09                                                                                  
Iter = 403  Max. abs. change = 0.00021  Deviance  = 13146.09                                                                                  
Iter = 404  Max. abs. change = 0.00077  Deviance  = 13146.08                                                                                  
Iter = 405  Max. abs. change = 0.00020  Deviance  = 13146.08                                                                                  
Iter = 406  Max. abs. change = 0.00075  Deviance  = 13146.08                                                                                  
Iter = 407  Max. abs. change = 0.00068  Deviance  = 13146.08                                                                                  
Iter = 408  Max. abs. change = 0.00018  Deviance  = 13146.08                                                                                  
Iter = 409  Max. abs. change = 0.00067  Deviance  = 13146.08                                                                                  
Iter = 410  Max. abs. change = 0.00017  Deviance  = 13146.07                                                                                  
Iter = 411  Max. abs. change = 0.00065  Deviance  = 13146.07                                                                                  
Iter = 412  Max. abs. change = 0.00060  Deviance  = 13146.07                                                                                  
Iter = 413  Max. abs. change = 0.00015  Deviance  = 13146.07                                                                                  
Iter = 414  Max. abs. change = 0.00059  Deviance  = 13146.07                                                                                  
Iter = 415  Max. abs. change = 0.00054  Deviance  = 13146.07                                                                                  
Iter = 416  Max. abs. change = 0.00014  Deviance  = 13146.07                                                                                  
Iter = 417  Max. abs. change = 0.00054  Deviance  = 13146.07                                                                                  
Iter = 418  Max. abs. change = 0.00013  Deviance  = 13146.06                                                                                  
Iter = 419  Max. abs. change = 0.00053  Deviance  = 13146.06                                                                                  
Iter = 420  Max. abs. change = 0.00012  Deviance  = 13146.06                                                                                  
Iter = 421  Max. abs. change = 0.00012  Deviance  = 13146.06                                                                                  
Iter = 422  Max. abs. change = 0.00011  Deviance  = 13146.06                                                                                  
Iter = 423  Max. abs. change = 0.00056  Deviance  = 13146.06                                                                                  
Iter = 424  Max. abs. change = 0.00051  Deviance  = 13146.06                                                                                  
Iter = 425  Max. abs. change = 0.00010  Deviance  = 13146.06                                                                                  
Iter = 426  Max. abs. change = 0.00010  Deviance  = 13146.06                                                                                  
Iter = 427  Max. abs. change = 0.00010  Deviance  = 13146.06                                                                                  

############### ESA ###############
Hull.obj <- validation(data$dat, MQ, CDM.obj, method = "Hull", search.method = "ESA") 
#> Hull  method with  ESA  in  test  level iteration ...
#> Iter  =   1/   1, 6 items have changed, ΔPVAF=1.25418 

## plot Hull curve for item 20
plot(Hull.obj, 20)


############### PAA ###############
Hull.obj <- validation(data$dat, MQ, CDM.obj, method = "Hull", search.method = "PAA") 
#> Hull  method with  PAA  in  test  level iteration ...
#> Iter  =   1/   1, 8 items have changed, ΔPVAF=1.17771 

## plot Hull curve for item 20
plot(Hull.obj, 20)

# }