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

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

Arguments

object

A validation in which method = "Hull".

i

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

...

Additional arguments to be passed to the plotting function.

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)
)


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)