このドキュメントでは、袰岩・篠原・篠原(2019)『PISA調査の解剖』の第4章のコードを再現する。
なお、筆者の環境に合わせてコードを一部加筆修正している。

IRTモデルの種類

スクリプト4-1 PISA2012年調査の解答データの準備

#Load library
library(PISA2012lite)

#Load data
data("scoredItem2012")
data("scoredOtem2012dict")
## Warning in data("scoredOtem2012dict"): data set 'scoredOtem2012dict' not found
#Make dataset of Japan
JPN2012x <- scoredItem2012[scoredItem2012$CNT=="Japan",]
rm("scoredItem2012")

#Summary Math item
summary(JPN2012x[,9:116])
##         PM00FQ01           PM00GQ01           PM00KQ02           PM033Q01   
##  Score 0    : 921   Score 0    :1504   Score 0    :1659   Score 0    : 271  
##  Score 1    : 983   Score 1    : 417   Score 1    : 219   Score 1    :1686  
##  N/A        :4428   N/A        :4416   N/A        :4412   N/A        :4386  
##  Not reached:  19   Not reached:  14   Not reached:  61   Not reached:   8  
##                                                                             
##        PM034Q01T           PM155Q01          PM155Q02D          PM155Q03D   
##  Score 0    : 807   Score 0    : 409   Score 0    : 584   Score 0    :1284  
##  Score 1    :1124   Score 1    :1546   Score 1    : 230   Score 1    : 272  
##  N/A        :4386   N/A        :4386   Score 2    :1142   Score 2    : 399  
##  Not reached:  34   Not reached:  10   N/A        :4386   N/A        :4386  
##                                        Not reached:   9   Not reached:  10  
##        PM155Q04T          PM192Q01T          PM273Q01T           PM305Q01   
##  Score 0    : 808   Score 0    : 783   Score 0    : 690   Score 0    : 778  
##  Score 1    :1146   Score 1    :1155   Score 1    :1238   Score 1    :1161  
##  N/A        :4386   N/A        :4409   N/A        :4414   N/A        :4409  
##  Not reached:  11   Not reached:   4   Not reached:   9   Not reached:   3  
##                                                                             
##         PM406Q01           PM406Q02          PM408Q01T           PM411Q01   
##  Score 0    :1180   Score 0    :1223   Score 0    :1179   Score 0    : 854  
##  Score 1    : 755   Score 1    : 709   Score 1    : 747   Score 1    :1099  
##  N/A        :4409   N/A        :4409   N/A        :4414   N/A        :4386  
##  Not reached:   7   Not reached:  10   Not reached:  11   Not reached:  12  
##                                                                             
##         PM411Q02          PM420Q01T           PM423Q01           PM442Q02   
##  Score 0    : 904   Score 0    :1067   Score 0    : 409   Score 0    : 718  
##  Score 1    :1047   Score 1    : 858   Score 1    :1529   Score 1    :1225  
##  N/A        :4386   N/A        :4414   N/A        :4409   N/A        :4386  
##  Not reached:  14   Not reached:  12   Not reached:   4   Not reached:  22  
##                                                                             
##         PM446Q01           PM446Q02           PM447Q01          PM462Q01D   
##  Score 0    : 421   Score 0    :1636   Score 0    : 265   Score 0    :1592  
##  Score 1    :1504   Score 1    : 283   Score 1    :1665   Score 1    : 201  
##  N/A        :4414   N/A        :4414   N/A        :4414   Score 2    : 146  
##  Not reached:  12   Not reached:  18   Not reached:   7   N/A        :4386  
##                                                           Not reached:  26  
##        PM464Q01T           PM474Q01          PM496Q01T           PM496Q02   
##  Score 0    :1217   Score 0    : 203   Score 0    : 768   Score 0    : 532  
##  Score 1    : 697   Score 1    :1753   Score 1    :1170   Score 1    :1406  
##  N/A        :4414   N/A        :4386   N/A        :4409   N/A        :4409  
##  Not reached:  23   Not reached:   9   Not reached:   4   Not reached:   4  
##                                                                             
##         PM559Q01           PM564Q01           PM564Q02           PM571Q01   
##  Score 0    : 650   Score 0    : 947   Score 0    : 817   Score 0    : 923  
##  Score 1    :1268   Score 1    : 977   Score 1    :1105   Score 1    :1005  
##  N/A        :4414   N/A        :4409   N/A        :4409   N/A        :4409  
##  Not reached:  19   Not reached:  18   Not reached:  20   Not reached:  14  
##                                                                             
##        PM603Q01T           PM800Q01          PM803Q01T           PM828Q01   
##  Score 0    : 941   Score 0    :  77   Score 0    : 870   Score 0    :1147  
##  Score 1    : 990   Score 1    :1837   Score 1    :1078   Score 1    : 771  
##  N/A        :4409   N/A        :4414   N/A        :4386   N/A        :4414  
##  Not reached:  11   Not reached:  23   Not reached:  17   Not reached:  19  
##                                                                             
##         PM828Q02           PM828Q03           PM903Q01           PM903Q03   
##  Score 0    : 859   Score 0    :1747   Score 0    :1141   Score 0    :1082  
##  Score 1    :1057   Score 1    : 168   Score 1    : 189   Score 1    : 827  
##  N/A        :4414   N/A        :4414   Score 2    : 579   N/A        :4428  
##  Not reached:  21   Not reached:  22   N/A        :4428   Not reached:  14  
##                                        Not reached:  14                     
##        PM905Q01T           PM905Q02           PM906Q01           PM906Q02   
##  Score 0    : 256   Score 0    : 738   Score 0    : 776   Score 0    : 857  
##  Score 1    :1697   Score 1    :1212   Score 1    :1142   Score 1    : 515  
##  N/A        :4389   N/A        :4389   N/A        :4412   Score 2    : 543  
##  Not reached:   9   Not reached:  12   Not reached:  21   N/A        :4412  
##                                                           Not reached:  24  
##         PM909Q01           PM909Q02           PM909Q03           PM915Q01   
##  Score 0    : 114   Score 0    : 584   Score 0    : 810   Score 0    : 808  
##  Score 1    :1812   Score 1    :1341   Score 1    :1114   Score 1    :1114  
##  N/A        :4416   N/A        :4416   N/A        :4416   N/A        :4412  
##  Not reached:   9   Not reached:  10   Not reached:  11   Not reached:  17  
##                                                                             
##         PM915Q02           PM918Q01           PM918Q02           PM918Q05   
##  Score 0    : 663   Score 0    : 285   Score 0    : 177   Score 0    : 239  
##  Score 1    :1259   Score 1    :1629   Score 1    :1737   Score 1    :1675  
##  N/A        :4412   N/A        :4428   N/A        :4428   N/A        :4428  
##  Not reached:  17   Not reached:   9   Not reached:   9   Not reached:   9  
##                                                                             
##         PM919Q01           PM919Q02           PM923Q01           PM923Q03   
##  Score 0    : 241   Score 0    :1136   Score 0    : 824   Score 0    : 903  
##  Score 1    :1707   Score 1    : 811   Score 1    :1090   Score 1    :1009  
##  N/A        :4389   N/A        :4389   N/A        :4428   N/A        :4428  
##  Not reached:  14   Not reached:  15   Not reached:   9   Not reached:  11  
##                                                                             
##         PM923Q04           PM924Q02           PM934Q01           PM934Q02   
##  Score 0    :1555   Score 0    : 568   Score 0    :   0   Score 0    :   0  
##  Score 1    : 356   Score 1    :1319   Score 1    :   0   Score 1    :   0  
##  N/A        :4428   N/A        :4429   N/A        :6351   N/A        :6351  
##  Not reached:  12   Not reached:  35   Not reached:   0   Not reached:   0  
##                                                                             
##         PM936Q01           PM936Q02           PM939Q01           PM939Q02   
##  Score 0    :   0   Score 0    :   0   Score 0    :   0   Score 0    :   0  
##  Score 1    :   0   Score 1    :   0   Score 1    :   0   Score 1    :   0  
##  N/A        :6351   N/A        :6351   N/A        :6351   N/A        :6351  
##  Not reached:   0   Not reached:   0   Not reached:   0   Not reached:   0  
##                                                                             
##         PM942Q01           PM942Q02           PM942Q03           PM943Q01   
##  Score 0    :   0   Score 0    :   0   Score 0    :   0   Score 0    : 771  
##  Score 1    :   0   Score 1    :   0   Score 1    :   0   Score 1    :1164  
##  N/A        :6351   N/A        :6351   Score 2    :   0   N/A        :4389  
##  Not reached:   0   Not reached:   0   N/A        :6351   Not reached:  27  
##                                        Not reached:   0                     
##         PM943Q02           PM948Q01           PM948Q02           PM948Q03   
##  Score 0    :1608   Score 0    :   0   Score 0    :   0   Score 0    :   0  
##  Score 1    : 326   Score 1    :   0   Score 1    :   0   Score 1    :   0  
##  N/A        :4389   N/A        :6351   N/A        :6351   N/A        :6351  
##  Not reached:  28   Not reached:   0   Not reached:   0   Not reached:   0  
##                                                                             
##        PM949Q01T          PM949Q02T           PM949Q03           PM953Q02   
##  Score 0    : 302   Score 0    : 531   Score 0    : 590   Score 0    : 895  
##  Score 1    :1621   Score 1    :1392   Score 1    : 170   Score 1    :1000  
##  N/A        :4416   N/A        :4416   Score 2    :1163   N/A        :4389  
##  Not reached:  12   Not reached:  12   N/A        :4416   Not reached:  67  
##                                        Not reached:  12                     
##         PM953Q03          PM953Q04D           PM954Q01           PM954Q02   
##  Score 0    : 750   Score 0    :1398   Score 0    : 466   Score 0    : 808  
##  Score 1    :1135   Score 1    : 171   Score 1    :1479   Score 1    :1131  
##  N/A        :4389   Score 2    : 302   N/A        :4389   N/A        :4389  
##  Not reached:  77   N/A        :4389   Not reached:  17   Not reached:  23  
##                     Not reached:  91                                        
##         PM954Q04           PM955Q01           PM955Q02           PM955Q03   
##  Score 0    :1295   Score 0    : 433   Score 0    :1252   Score 0    :1543  
##  Score 1    : 640   Score 1    :1487   Score 1    : 667   Score 1    : 104  
##  N/A        :4389   N/A        :4416   N/A        :4416   Score 2    : 269  
##  Not reached:  27   Not reached:  15   Not reached:  16   N/A        :4416  
##                                                           Not reached:  19  
##         PM957Q01           PM957Q02           PM957Q03           PM961Q02   
##  Score 0    :   0   Score 0    :   0   Score 0    :   0   Score 0    :   0  
##  Score 1    :   0   Score 1    :   0   Score 1    :   0   Score 1    :   0  
##  N/A        :6351   N/A        :6351   N/A        :6351   N/A        :6351  
##  Not reached:   0   Not reached:   0   Not reached:   0   Not reached:   0  
##                                                                             
##         PM961Q03           PM961Q05           PM967Q01          PM967Q03T   
##  Score 0    :   0   Score 0    :   0   Score 0    :   0   Score 0    :   0  
##  Score 1    :   0   Score 1    :   0   Score 1    :   0   Score 1    :   0  
##  N/A        :6351   Score 2    :   0   N/A        :6351   N/A        :6351  
##  Not reached:   0   N/A        :6351   Not reached:   0   Not reached:   0  
##                     Not reached:   0                                        
##         PM982Q01           PM982Q02          PM982Q03T           PM982Q04   
##  Score 0    : 286   Score 0    :1140   Score 0    : 468   Score 0    : 488  
##  Score 1    :1646   Score 1    : 790   Score 1    :1462   Score 1    :1442  
##  N/A        :4412   N/A        :4412   N/A        :4412   N/A        :4412  
##  Not reached:   7   Not reached:   9   Not reached:   9   Not reached:   9  
##                                                                             
##         PM985Q01           PM985Q02           PM985Q03           PM991Q01   
##  Score 0    :   0   Score 0    :   0   Score 0    :   0   Score 0    :   0  
##  Score 1    :   0   Score 1    :   0   Score 1    :   0   Score 1    :   0  
##  N/A        :6351   N/A        :6351   N/A        :6351   N/A        :6351  
##  Not reached:   0   Not reached:   0   Not reached:   0   Not reached:   0  
##                                                                             
##        PM991Q02D           PM992Q01           PM992Q02           PM992Q03   
##  Score 0    :   0   Score 0    : 220   Score 0    :1094   Score 0    :1582  
##  Score 1    :   0   Score 1    :1709   Score 1    : 832   Score 1    : 340  
##  Score 2    :   0   N/A        :4412   N/A        :4412   N/A        :4412  
##  N/A        :6351   Not reached:  10   Not reached:  13   Not reached:  17  
##  Not reached:   0                                                           
##         PM995Q01           PM995Q02           PM995Q03           PM998Q02   
##  Score 0    : 502   Score 0    :1760   Score 0    : 893   Score 0    : 282  
##  Score 1    :1407   Score 1    : 147   Score 1    :1013   Score 1    :1633  
##  N/A        :4428   N/A        :4428   N/A        :4428   N/A        :4416  
##  Not reached:  14   Not reached:  16   Not reached:  17   Not reached:  20  
## 
#Make dataset for JML
JPN2012m <- as.data.frame(lapply(JPN2012x[,9:116], as.character), stringsAsFactors = F)

JPN2012m[JPN2012m=="Score 0"] <- 0
JPN2012m[JPN2012m=="Score 1"] <- 1
JPN2012m[JPN2012m=="Score 2"] <- 2
JPN2012m[JPN2012m=="N/A"|JPN2012m=="Not reached"] <- NA

JPN2012m <- as.data.frame(lapply(JPN2012m, as.numeric), stringsAsFactors = F)

#delete all .na item
all.na <- apply(JPN2012m, 2, function(x){all(is.na(x))})
JPN2012m <- JPN2012m[, !all.na]

#delete all .na student
all.na <- apply(JPN2012m, 1, function(x){all(is.na(x))})
JPN2012j <-JPN2012m[!all.na,]

スクリプト4-2 同時最尤推定法を用いた「問題の難易度」の推定

#Load library
library(TAM)
## Loading required package: CDM
## Loading required package: mvtnorm
## **********************************
## ** CDM 7.5-15 (2020-03-10 14:19:21)      
## ** Cognitive Diagnostic Models  **
## **********************************
## * TAM 3.5-19 (2020-05-05 22:45:39)
#JML
mod0 <- tam.jml(JPN2012j)
summary(mod0) #item difficulty
## ------------------------------------------------------------
## TAM 3.5-19 (2020-05-05 22:45:39) 
## R version 4.0.3 (2020-10-10) x86_64, mingw32 | nodename=DESKTOP-4VK45GQ | login=turid 
## 
## Start of Analysis: 2020-11-10 05:03:42 
## End of Analysis: 2020-11-10 05:03:45 
## Time difference of 3.293189 secs
## Computation time: 3.293189 
## 
## Joint Maximum Likelihood Estimation in TAM 
## 
## IRT Model
## Call:
## tam.jml(resp = JPN2012j)
## 
## ------------------------------------------------------------
## Number of iterations = 21 
## 
## Deviance = 146268.4  | Log Likelihood = -73134.18 
## Number of persons = 6303 
## Number of items = 83 
## constraint = cases 
## bias = TRUE 
## ------------------------------------------------------------
## Person Parameters xsi
## M = 0 
## SD = 1.46 
## ------------------------------------------------------------
## Item Parameters xsi
##         xsi.label xsi.index    xsi se.xsi
## 1   PM00FQ01_Cat1         1 -0.007  0.054
## 2   PM00GQ01_Cat1         2  1.783  0.063
## 3   PM00KQ02_Cat1         3  2.602  0.079
## 4   PM033Q01_Cat1         4 -2.279  0.073
## 5  PM034Q01T_Cat1         5 -0.369  0.053
## 6   PM155Q01_Cat1         6 -1.655  0.063
## 7  PM155Q02D_Cat1         7  0.262  0.064
## 8  PM155Q02D_Cat2         8 -1.339  0.059
## 9  PM155Q03D_Cat1         9  1.606  0.060
## 10 PM155Q03D_Cat2        10  0.619  0.070
## 11 PM155Q04T_Cat1        11 -0.386  0.053
## 12 PM192Q01T_Cat1        12 -0.491  0.054
## 13 PM273Q01T_Cat1        13 -0.778  0.055
## 14  PM305Q01_Cat1        14 -0.506  0.054
## 15  PM406Q01_Cat1        15  0.639  0.054
## 16  PM406Q02_Cat1        16  0.774  0.055
## 17 PM408Q01T_Cat1        17  0.626  0.054
## 18  PM411Q01_Cat1        18 -0.257  0.053
## 19  PM411Q02_Cat1        19 -0.118  0.052
## 20 PM420Q01T_Cat1        20  0.308  0.053
## 21  PM423Q01_Cat1        21 -1.713  0.063
## 22  PM442Q02_Cat1        22 -0.620  0.054
## 23  PM446Q01_Cat1        23 -1.686  0.063
## 24  PM446Q02_Cat1        24  2.282  0.071
## 25  PM447Q01_Cat1        25 -2.413  0.074
## 26 PM462Q01D_Cat1        26  2.442  0.070
## 27 PM462Q01D_Cat2        27  1.755  0.102
## 28 PM464Q01T_Cat1        28  0.767  0.055
## 29  PM474Q01_Cat1        29 -2.679  0.082
## 30 PM496Q01T_Cat1        30 -0.535  0.054
## 31  PM496Q02_Cat1        31 -1.265  0.059
## 32  PM559Q01_Cat1        32 -0.882  0.056
## 33  PM564Q01_Cat1        33  0.000  0.053
## 34  PM564Q02_Cat1        34 -0.366  0.054
## 35  PM571Q01_Cat1        35 -0.075  0.053
## 36 PM603Q01T_Cat1        36 -0.030  0.053
## 37  PM800Q01_Cat1        37 -3.976  0.124
## 38 PM803Q01T_Cat1        38 -0.208  0.053
## 39  PM828Q01_Cat1        39  0.552  0.054
## 40  PM828Q02_Cat1        40 -0.258  0.054
## 41  PM828Q03_Cat1        41  2.974  0.087
## 42  PM903Q01_Cat1        42  1.709  0.062
## 43  PM903Q01_Cat2        43 -0.232  0.066
## 44  PM903Q03_Cat1        44  0.443  0.054
## 45 PM905Q01T_Cat1        45 -2.639  0.078
## 46  PM905Q02_Cat1        46 -0.707  0.056
## 47  PM906Q01_Cat1        47 -0.515  0.054
## 48  PM906Q02_Cat1        48  0.186  0.058
## 49  PM906Q02_Cat2        49  0.642  0.063
## 50  PM909Q01_Cat1        50 -3.501  0.106
## 51  PM909Q02_Cat1        51 -1.044  0.058
## 52  PM909Q03_Cat1        52 -0.349  0.054
## 53  PM915Q01_Cat1        53 -0.431  0.054
## 54  PM915Q02_Cat1        54 -0.860  0.056
## 55  PM918Q01_Cat1        55 -2.218  0.072
## 56  PM918Q02_Cat1        56 -2.885  0.087
## 57  PM918Q05_Cat1        57 -2.473  0.077
## 58  PM919Q01_Cat1        58 -2.718  0.079
## 59  PM919Q02_Cat1        59  0.477  0.055
## 60  PM923Q01_Cat1        60 -0.298  0.054
## 61  PM923Q03_Cat1        61 -0.068  0.054
## 62  PM923Q04_Cat1        62  2.007  0.066
## 63  PM924Q02_Cat1        63 -1.032  0.058
## 64  PM943Q01_Cat1        64 -0.576  0.056
## 65  PM943Q02_Cat1        65  2.169  0.069
## 66 PM949Q01T_Cat1        66 -2.154  0.071
## 67 PM949Q02T_Cat1        67 -1.218  0.059
## 68  PM949Q03_Cat1        68  0.491  0.067
## 69  PM949Q03_Cat2        69 -1.645  0.063
## 70  PM953Q02_Cat1        70 -0.115  0.055
## 71  PM953Q03_Cat1        71 -0.541  0.056
## 72 PM953Q04D_Cat1        72  2.331  0.069
## 73 PM953Q04D_Cat2        73  0.788  0.081
## 74  PM954Q01_Cat1        74 -1.627  0.063
## 75  PM954Q02_Cat1        75 -0.469  0.055
## 76  PM954Q04_Cat1        76  0.991  0.057
## 77  PM955Q01_Cat1        77 -1.571  0.063
## 78  PM955Q02_Cat1        78  0.936  0.056
## 79  PM955Q03_Cat1        79  3.036  0.073
## 80  PM955Q03_Cat2        80  0.436  0.083
## 81  PM982Q01_Cat1        81 -2.298  0.072
## 82  PM982Q02_Cat1        82  0.490  0.054
## 83 PM982Q03T_Cat1        83 -1.518  0.061
## 84  PM982Q04_Cat1        84 -1.446  0.060
## 85  PM992Q01_Cat1        85 -2.668  0.080
## 86  PM992Q02_Cat1        86  0.367  0.053
## 87  PM992Q03_Cat1        87  2.002  0.067
## 88  PM995Q01_Cat1        88 -1.298  0.060
## 89  PM995Q02_Cat1        89  3.216  0.093
## 90  PM995Q03_Cat1        90 -0.089  0.054
## 91  PM998Q02_Cat1        91 -2.245  0.073
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##         item    N     M xsi.item AXsi_.Cat1 AXsi_.Cat2 B.Cat1.Dim1 B.Cat2.Dim1
## 1   PM00FQ01 1904 0.516   -0.007     -0.007         NA           1           0
## 2   PM00GQ01 1921 0.217    1.783      1.783         NA           1           0
## 3   PM00KQ02 1878 0.117    2.602      2.602         NA           1           0
## 4   PM033Q01 1957 0.862   -2.279     -2.279         NA           1           0
## 5  PM034Q01T 1931 0.582   -0.369     -0.369         NA           1           0
## 6   PM155Q01 1955 0.791   -1.655     -1.655         NA           1           0
## 7  PM155Q02D 1956 1.285   -0.538      0.262     -1.077           1           2
## 8  PM155Q03D 1955 0.547    1.112      1.606      2.225           1           2
## 9  PM155Q04T 1954 0.586   -0.386     -0.386         NA           1           0
## 10 PM192Q01T 1938 0.596   -0.491     -0.491         NA           1           0
## 11 PM273Q01T 1928 0.642   -0.778     -0.778         NA           1           0
## 12  PM305Q01 1939 0.599   -0.506     -0.506         NA           1           0
## 13  PM406Q01 1935 0.390    0.639      0.639         NA           1           0
## 14  PM406Q02 1932 0.367    0.774      0.774         NA           1           0
## 15 PM408Q01T 1926 0.388    0.626      0.626         NA           1           0
## 16  PM411Q01 1953 0.563   -0.257     -0.257         NA           1           0
## 17  PM411Q02 1951 0.537   -0.118     -0.118         NA           1           0
## 18 PM420Q01T 1925 0.446    0.308      0.308         NA           1           0
## 19  PM423Q01 1938 0.789   -1.713     -1.713         NA           1           0
## 20  PM442Q02 1943 0.630   -0.620     -0.620         NA           1           0
## 21  PM446Q01 1925 0.781   -1.686     -1.686         NA           1           0
## 22  PM446Q02 1919 0.147    2.282      2.282         NA           1           0
## 23  PM447Q01 1930 0.863   -2.413     -2.413         NA           1           0
## 24 PM462Q01D 1939 0.254    2.099      2.442      4.197           1           2
## 25 PM464Q01T 1914 0.364    0.767      0.767         NA           1           0
## 26  PM474Q01 1956 0.896   -2.679     -2.679         NA           1           0
## 27 PM496Q01T 1938 0.604   -0.535     -0.535         NA           1           0
## 28  PM496Q02 1938 0.725   -1.265     -1.265         NA           1           0
## 29  PM559Q01 1918 0.661   -0.882     -0.882         NA           1           0
## 30  PM564Q01 1924 0.508    0.000      0.000         NA           1           0
## 31  PM564Q02 1922 0.575   -0.366     -0.366         NA           1           0
## 32  PM571Q01 1928 0.521   -0.075     -0.075         NA           1           0
## 33 PM603Q01T 1931 0.513   -0.030     -0.030         NA           1           0
## 34  PM800Q01 1914 0.960   -3.976     -3.976         NA           1           0
## 35 PM803Q01T 1948 0.553   -0.208     -0.208         NA           1           0
## 36  PM828Q01 1918 0.402    0.552      0.552         NA           1           0
## 37  PM828Q02 1916 0.552   -0.258     -0.258         NA           1           0
## 38  PM828Q03 1915 0.088    2.974      2.974         NA           1           0
## 39  PM903Q01 1909 0.706    0.738      1.709      1.476           1           2
## 40  PM903Q03 1909 0.433    0.443      0.443         NA           1           0
## 41 PM905Q01T 1953 0.869   -2.639     -2.639         NA           1           0
## 42  PM905Q02 1950 0.622   -0.707     -0.707         NA           1           0
## 43  PM906Q01 1918 0.595   -0.515     -0.515         NA           1           0
## 44  PM906Q02 1915 0.836    0.414      0.186      0.828           1           2
## 45  PM909Q01 1926 0.941   -3.501     -3.501         NA           1           0
## 46  PM909Q02 1925 0.697   -1.044     -1.044         NA           1           0
## 47  PM909Q03 1924 0.579   -0.349     -0.349         NA           1           0
## 48  PM915Q01 1922 0.580   -0.431     -0.431         NA           1           0
## 49  PM915Q02 1922 0.655   -0.860     -0.860         NA           1           0
## 50  PM918Q01 1914 0.851   -2.218     -2.218         NA           1           0
## 51  PM918Q02 1914 0.908   -2.885     -2.885         NA           1           0
## 52  PM918Q05 1914 0.875   -2.473     -2.473         NA           1           0
## 53  PM919Q01 1948 0.876   -2.718     -2.718         NA           1           0
## 54  PM919Q02 1947 0.417    0.477      0.477         NA           1           0
## 55  PM923Q01 1914 0.569   -0.298     -0.298         NA           1           0
## 56  PM923Q03 1912 0.528   -0.068     -0.068         NA           1           0
## 57  PM923Q04 1911 0.186    2.007      2.007         NA           1           0
## 58  PM924Q02 1887 0.699   -1.032     -1.032         NA           1           0
## 59  PM943Q01 1935 0.602   -0.576     -0.576         NA           1           0
## 60  PM943Q02 1934 0.169    2.169      2.169         NA           1           0
## 61 PM949Q01T 1923 0.843   -2.154     -2.154         NA           1           0
## 62 PM949Q02T 1923 0.724   -1.218     -1.218         NA           1           0
## 63  PM949Q03 1923 1.298   -0.577      0.491     -1.154           1           2
## 64  PM953Q02 1895 0.528   -0.115     -0.115         NA           1           0
## 65  PM953Q03 1885 0.602   -0.541     -0.541         NA           1           0
## 66 PM953Q04D 1871 0.414    1.560      2.331      3.119           1           2
## 67  PM954Q01 1945 0.760   -1.627     -1.627         NA           1           0
## 68  PM954Q02 1939 0.583   -0.469     -0.469         NA           1           0
## 69  PM954Q04 1935 0.331    0.991      0.991         NA           1           0
## 70  PM955Q01 1920 0.774   -1.571     -1.571         NA           1           0
## 71  PM955Q02 1919 0.348    0.936      0.936         NA           1           0
## 72  PM955Q03 1916 0.335    1.736      3.036      3.472           1           2
## 73  PM982Q01 1932 0.852   -2.298     -2.298         NA           1           0
## 74  PM982Q02 1930 0.409    0.490      0.490         NA           1           0
## 75 PM982Q03T 1930 0.758   -1.518     -1.518         NA           1           0
## 76  PM982Q04 1930 0.747   -1.446     -1.446         NA           1           0
## 77  PM992Q01 1929 0.886   -2.668     -2.668         NA           1           0
## 78  PM992Q02 1926 0.432    0.367      0.367         NA           1           0
## 79  PM992Q03 1922 0.177    2.002      2.002         NA           1           0
## 80  PM995Q01 1909 0.737   -1.298     -1.298         NA           1           0
## 81  PM995Q02 1907 0.077    3.216      3.216         NA           1           0
## 82  PM995Q03 1906 0.531   -0.089     -0.089         NA           1           0
## 83  PM998Q02 1915 0.853   -2.245     -2.245         NA           1           0
mod0$theta #student ability

スクリプト4-3 周辺最尤推定法を用いた「問題難易度」の推定

#MML
mod1 <- tam.mml(JPN2012m)
mod1$xsi #item difficulty
##                         xsi     se.xsi
## PM00FQ01_Cat1  -0.024541064 0.05241313
## PM00GQ01_Cat1   1.704168240 0.06136013
## PM00KQ02_Cat1   2.542710722 0.07729738
## PM033Q01_Cat1  -2.241346504 0.07148742
## PM034Q01T_Cat1 -0.366964492 0.05215372
## PM155Q01_Cat1  -1.636749489 0.06170272
## PM155Q02D_Cat1  0.323828043 0.06283967
## PM155Q02D_Cat2 -1.396448601 0.05800349
## PM155Q03D_Cat1  1.597730553 0.05832519
## PM155Q03D_Cat2  0.485205655 0.06855625
## PM155Q04T_Cat1 -0.400063428 0.05197507
## PM192Q01T_Cat1 -0.480650294 0.05272057
## PM273Q01T_Cat1 -0.762497344 0.05414971
## PM305Q01_Cat1  -0.495128806 0.05275789
## PM406Q01_Cat1   0.608049334 0.05302155
## PM406Q02_Cat1   0.737228598 0.05360316
## PM408Q01T_Cat1  0.596506679 0.05314982
## PM411Q01_Cat1  -0.275926040 0.05164433
## PM411Q02_Cat1  -0.140288235 0.05141879
## PM420Q01T_Cat1  0.287673613 0.05233341
## PM423Q01_Cat1  -1.660474044 0.06178736
## PM442Q02_Cat1  -0.633089297 0.05305127
## PM446Q01_Cat1  -1.641029827 0.06172479
## PM446Q02_Cat1   2.210453327 0.06995048
## PM447Q01_Cat1  -2.338304032 0.07248992
## PM462Q01D_Cat1  2.403947455 0.06831647
## PM462Q01D_Cat2  1.548832538 0.09900803
## PM464Q01T_Cat1  0.732606844 0.05384830
## PM474Q01_Cat1  -2.628733730 0.08009653
## PM496Q01T_Cat1 -0.522454898 0.05286509
## PM496Q02_Cat1  -1.227938616 0.05717866
## PM559Q01_Cat1  -0.864870679 0.05489265
## PM564Q01_Cat1  -0.008049265 0.05206606
## PM564Q02_Cat1  -0.360846305 0.05259849
## PM571Q01_Cat1  -0.080006104 0.05204939
## PM603Q01T_Cat1 -0.036833116 0.05198489
## PM800Q01_Cat1  -3.850466811 0.12151218
## PM803Q01T_Cat1 -0.226696722 0.05160261
## PM828Q01_Cat1   0.524127552 0.05298504
## PM828Q02_Cat1  -0.262198933 0.05252380
## PM828Q03_Cat1   2.889536023 0.08581228
## PM903Q01_Cat1   1.720998972 0.06003034
## PM903Q01_Cat2  -0.358820918 0.06398744
## PM903Q03_Cat1   0.410696082 0.05264978
## PM905Q01T_Cat1 -2.480711962 0.07427590
## PM905Q02_Cat1  -0.675133095 0.05409721
## PM906Q01_Cat1  -0.492711489 0.05290812
## PM906Q02_Cat1   0.233151147 0.05606692
## PM906Q02_Cat2   0.555780969 0.06127143
## PM909Q01_Cat1  -3.389068177 0.10293943
## PM909Q02_Cat1  -1.031762837 0.05642493
## PM909Q03_Cat1  -0.360475451 0.05293691
## PM915Q01_Cat1  -0.411537937 0.05259848
## PM915Q02_Cat1  -0.824595879 0.05435881
## PM918Q01_Cat1  -2.161407388 0.07065109
## PM918Q02_Cat1  -2.802643207 0.08506250
## PM918Q05_Cat1  -2.406356207 0.07549871
## PM919Q01_Cat1  -2.556929592 0.07600795
## PM919Q02_Cat1   0.447943304 0.05308875
## PM923Q01_Cat1  -0.306228105 0.05275176
## PM923Q03_Cat1  -0.084020091 0.05236524
## PM923Q04_Cat1   1.930640581 0.06464215
## PM924Q02_Cat1  -1.019747716 0.05680630
## PM943Q01_Cat1  -0.553870808 0.05381820
## PM943Q02_Cat1   2.066457435 0.06708673
## PM949Q01T_Cat1 -2.102360801 0.06947630
## PM949Q02T_Cat1 -1.200227904 0.05784772
## PM949Q03_Cat1   0.580002063 0.06506119
## PM949Q03_Cat2  -1.706485722 0.06098019
## PM953Q02_Cat1  -0.120206928 0.05331294
## PM953Q03_Cat1  -0.524711094 0.05446294
## PM953Q04D_Cat1  2.300505507 0.06623008
## PM953Q04D_Cat2  0.568769476 0.07825511
## PM954Q01_Cat1  -1.541885617 0.06055553
## PM954Q02_Cat1  -0.452336371 0.05342232
## PM954Q04_Cat1   0.938043762 0.05526401
## PM955Q01_Cat1  -1.541590949 0.06143478
## PM955Q02_Cat1   0.882393342 0.05436340
## PM955Q03_Cat1   2.993394692 0.07090290
## PM955Q03_Cat2   0.231674582 0.08112438
## PM982Q01_Cat1  -2.205266575 0.07004012
## PM982Q02_Cat1   0.478135739 0.05257098
## PM982Q03T_Cat1 -1.457583658 0.05936500
## PM982Q04_Cat1  -1.387966915 0.05864146
## PM992Q01_Cat1  -2.559731944 0.07741971
## PM992Q02_Cat1   0.359313787 0.05230291
## PM992Q03_Cat1   1.945089624 0.06555053
## PM995Q01_Cat1  -1.274823515 0.05860434
## PM995Q02_Cat1   3.105749128 0.09096748
## PM995Q03_Cat1  -0.104519566 0.05247531
## PM998Q02_Cat1  -2.190817204 0.07127495

スクリプト4-4 MLEによる「生徒の能力」の推定

mle1 <- tam.wle(mod1, WLE=F) #mle
## Iteration in WLE/MLE estimation  1   | Maximal change  2.6043 
## Iteration in WLE/MLE estimation  2   | Maximal change  1.5935 
## Iteration in WLE/MLE estimation  3   | Maximal change  0.356 
## Iteration in WLE/MLE estimation  4   | Maximal change  0.0707 
## Iteration in WLE/MLE estimation  5   | Maximal change  0.0024 
## Iteration in WLE/MLE estimation  6   | Maximal change  0 
## ----
##  MLE Reliability= 0.829
View(mle1)

スクリプト4-5 WLEによる「生徒の能力」の推定

wle1 <- tam.wle(mod1) #wle
## Iteration in WLE/MLE estimation  1   | Maximal change  2.8261 
## Iteration in WLE/MLE estimation  2   | Maximal change  1.5552 
## Iteration in WLE/MLE estimation  3   | Maximal change  1.7417 
## Iteration in WLE/MLE estimation  4   | Maximal change  1.9061 
## Iteration in WLE/MLE estimation  5   | Maximal change  2.3144 
## Iteration in WLE/MLE estimation  6   | Maximal change  0.7008 
## Iteration in WLE/MLE estimation  7   | Maximal change  1.3652 
## Iteration in WLE/MLE estimation  8   | Maximal change  1.4786 
## Iteration in WLE/MLE estimation  9   | Maximal change  1.5687 
## Iteration in WLE/MLE estimation  10   | Maximal change  1.7615 
## Iteration in WLE/MLE estimation  11   | Maximal change  0.4832 
## Iteration in WLE/MLE estimation  12   | Maximal change  1.0559 
## Iteration in WLE/MLE estimation  13   | Maximal change  1.0992 
## Iteration in WLE/MLE estimation  14   | Maximal change  1.1311 
## Iteration in WLE/MLE estimation  15   | Maximal change  1.187 
## Iteration in WLE/MLE estimation  16   | Maximal change  1.2284 
## Iteration in WLE/MLE estimation  17   | Maximal change  1.3046 
## Iteration in WLE/MLE estimation  18   | Maximal change  0.3406 
## Iteration in WLE/MLE estimation  19   | Maximal change  0.7691 
## Iteration in WLE/MLE estimation  20   | Maximal change  0.783 
## Iteration in WLE/MLE estimation  21   | Maximal change  0.7933 
## ----
##  WLE Reliability= 0.824
View(wle1)

スクリプト4-6 EAPによる「生徒の能力」の推定

wap1 <- mod1$person$EAP
View(mod1$person)

スクリプト4-7 重み付き平均二乗残差の計算

#item-fit statistics
fit1 <- tam.fit(mod1)
## Item fit calculation based on 5 simulations
## |**********|
## |----------|
View(fit1$itemfit)
fit1$itemfit
##         parameter    Outfit    Outfit_t     Outfit_p Outfit_pholm     Infit
## 1   PM00FQ01_Cat1 0.9045490  -4.5873320 4.489465e-06 1.840680e-04 0.9467884
## 2   PM00GQ01_Cat1 0.7494193  -8.4485378 2.949738e-17 1.946827e-15 0.8867759
## 3   PM00KQ02_Cat1 1.1569017   2.9149698 3.557230e-03 9.003090e-02 1.0098272
## 4   PM033Q01_Cat1 1.3800826   7.4283450 1.099648e-13 6.267996e-12 1.1047007
## 5  PM034Q01T_Cat1 1.0290929   1.3503522 1.769030e-01 1.000000e+00 1.0238672
## 6   PM155Q01_Cat1 1.0128764   0.3806412 7.034695e-01 1.000000e+00 0.9582833
## 7  PM155Q02D_Cat1 1.7028036  18.2552035 1.881086e-74 1.711788e-72 1.1908034
## 8  PM155Q02D_Cat2 1.4448537  13.7588458 4.506645e-43 3.920781e-41 1.2204292
## 9  PM155Q03D_Cat1 0.8275804  -6.3096079 2.797433e-10 1.482640e-08 0.9262116
## 10 PM155Q03D_Cat2 1.0737180   1.9295375 5.366418e-02 9.659552e-01 1.0661923
## 11 PM155Q04T_Cat1 1.2569688  11.0771434 1.619575e-28 1.279465e-26 1.1491027
## 12 PM192Q01T_Cat1 1.0164935   0.7453602 4.560540e-01 1.000000e+00 1.0287673
## 13 PM273Q01T_Cat1 1.1367111   5.3979526 6.740567e-08 3.100661e-06 1.0911075
## 14  PM305Q01_Cat1 1.4133085  16.4466822 8.859007e-61 7.884516e-59 1.2703536
## 15  PM406Q01_Cat1 0.8693637  -6.0339360 1.600135e-09 8.160688e-08 0.8979212
## 16  PM406Q02_Cat1 0.6978049 -14.4932653 1.336360e-47 1.175996e-45 0.7930062
## 17 PM408Q01T_Cat1 1.0737278   3.2000537 1.374020e-03 3.984658e-02 1.0640062
## 18  PM411Q01_Cat1 1.0866769   4.0290497 5.600279e-05 2.128106e-03 1.0480568
## 19  PM411Q02_Cat1 1.0217312   1.0484156 2.944472e-01 1.000000e+00 1.0195590
## 20 PM420Q01T_Cat1 1.4365469  17.8392092 3.506228e-71 3.155605e-69 1.2617072
## 21  PM423Q01_Cat1 1.2914538   8.0042684 1.201790e-15 7.330919e-14 1.1065238
## 22  PM442Q02_Cat1 0.9698497  -1.3437404 1.790324e-01 1.000000e+00 0.9523852
## 23  PM446Q01_Cat1 0.8751275  -3.9116952 9.165055e-05 3.299420e-03 0.8839972
## 24  PM446Q02_Cat1 0.6482848  -9.4723117 2.737178e-21 1.970768e-19 0.8926494
## 25  PM447Q01_Cat1 1.0055080   0.1298055 8.967203e-01 1.000000e+00 0.9885425
## 26 PM462Q01D_Cat1 0.7803146  -5.9291065 3.045875e-09 1.522937e-07 0.9321831
## 27 PM462Q01D_Cat2 1.3869360   5.1606822 2.460515e-07 1.058022e-05 1.1054936
## 28 PM464Q01T_Cat1 0.8250879  -8.0153602 1.098147e-15 6.808512e-14 0.9014299
## 29  PM474Q01_Cat1 1.5486168   8.4973682 1.939375e-17 1.299381e-15 1.0827635
## 30 PM496Q01T_Cat1 0.9350603  -2.9584632 3.091772e-03 8.347783e-02 0.9381285
## 31  PM496Q02_Cat1 1.0026803   0.1006972 9.197908e-01 1.000000e+00 0.9664322
## 32  PM559Q01_Cat1 1.0135608   0.5456960 5.852749e-01 1.000000e+00 0.9981074
## 33  PM564Q01_Cat1 1.1801950   8.0036811 1.207539e-15 7.330919e-14 1.1194487
## 34  PM564Q02_Cat1 1.0996841   4.3896794 1.135179e-05 4.540717e-04 1.0598054
## 35  PM571Q01_Cat1 0.9465053  -2.5561609 1.058342e-02 2.116683e-01 0.9538155
## 36 PM603Q01T_Cat1 1.0663212   3.0608222 2.207302e-03 6.180444e-02 1.0266174
## 37  PM800Q01_Cat1 1.0505100   0.5195290 6.033919e-01 1.000000e+00 1.0055217
## 38 PM803Q01T_Cat1 0.8871194  -5.6497946 1.606397e-08 7.710705e-07 0.9188193
## 39  PM828Q01_Cat1 0.9191732  -3.7261338 1.944392e-04 6.610932e-03 0.9607078
## 40  PM828Q02_Cat1 1.1334259   5.8416450 5.168787e-09 2.532706e-07 1.0853204
## 41  PM828Q03_Cat1 0.7932461  -3.6580653 2.541263e-04 8.132043e-03 0.9873423
## 42  PM903Q01_Cat1 1.3370179   9.6718030 3.973157e-22 2.940136e-20 1.1097079
## 43  PM903Q01_Cat2 1.2281167   6.5259492 6.757223e-11 3.648900e-09 1.0452180
## 44  PM903Q03_Cat1 0.8881630  -5.3731794 7.736030e-08 3.481213e-06 0.9143944
## 45 PM905Q01T_Cat1 1.1993004   3.9838828 6.779832e-05 2.508538e-03 1.0367176
## 46  PM905Q02_Cat1 0.7186954 -12.7483866 3.182638e-37 2.705242e-35 0.8028677
## 47  PM906Q01_Cat1 0.9366704  -2.8664128 4.151526e-03 9.548509e-02 0.9569910
## 48  PM906Q02_Cat1 0.7536955 -10.4809985 1.056227e-25 8.238569e-24 0.8340351
## 49  PM906Q02_Cat2 1.0745561   2.4649584 1.370292e-02 2.603554e-01 1.0968968
## 50  PM909Q01_Cat1 0.9093645  -1.1823003 2.370866e-01 1.000000e+00 0.9180268
## 51  PM909Q02_Cat1 0.9067411  -3.5623986 3.674818e-04 1.102446e-02 0.9295843
## 52  PM909Q03_Cat1 0.7395584 -12.7473372 3.225766e-37 2.709643e-35 0.8099073
## 53  PM915Q01_Cat1 1.0267106   1.1971414 2.312514e-01 1.000000e+00 1.0201102
## 54  PM915Q02_Cat1 0.9798361  -0.8221055 4.110169e-01 1.000000e+00 0.9732967
## 55  PM918Q01_Cat1 1.7054547  13.4814804 2.010324e-41 1.728878e-39 1.1572518
## 56  PM918Q02_Cat1 1.6463630   9.1653530 4.938506e-20 3.506339e-18 1.0246035
## 57  PM918Q05_Cat1 1.0435183   0.8875277 3.747948e-01 1.000000e+00 1.0318006
## 58  PM919Q01_Cat1 1.1846990   3.5829155 3.397806e-04 1.053320e-02 0.9827130
## 59  PM919Q02_Cat1 1.2372885   9.7500269 1.844195e-22 1.401588e-20 1.1724305
## 60  PM923Q01_Cat1 1.0304426   1.3578678 1.745056e-01 1.000000e+00 1.0373010
## 61  PM923Q03_Cat1 1.1834473   8.0307384 9.688775e-16 6.103928e-14 1.1119426
## 62  PM923Q04_Cat1 0.7301270  -8.1889292 2.635606e-16 1.713144e-14 0.9170495
## 63  PM924Q02_Cat1 0.7578178  -9.7141785 2.623561e-22 1.967670e-20 0.8611843
## 64  PM943Q01_Cat1 1.1013559   4.0832353 4.441301e-05 1.732107e-03 1.0451408
## 65  PM943Q02_Cat1 0.6167227 -11.5313091 9.173808e-31 7.430784e-29 0.8440379
## 66 PM949Q01T_Cat1 0.8512245  -3.7176395 2.010929e-04 6.636066e-03 0.9180366
## 67 PM949Q02T_Cat1 0.9203201  -2.8580902 4.261993e-03 9.548509e-02 0.9385131
## 68  PM949Q03_Cat1 1.0900631   2.5911680 9.565079e-03 2.008667e-01 1.0496809
## 69  PM949Q03_Cat2 1.3273139   9.4789301 2.569036e-21 1.875396e-19 1.1532578
## 70  PM953Q02_Cat1 0.8315433  -7.8850125 3.145042e-15 1.855575e-13 0.8870735
## 71  PM953Q03_Cat1 0.8175635  -8.0332709 9.490782e-16 6.074101e-14 0.8501448
## 72 PM953Q04D_Cat1 0.7544201  -7.5377742 4.780607e-14 2.772752e-12 0.9361371
## 73 PM953Q04D_Cat2 0.7648155  -6.0453273 1.491070e-09 7.753564e-08 0.9996884
## 74  PM954Q01_Cat1 0.7904150  -7.0701554 1.547603e-12 8.511818e-11 0.8681969
## 75  PM954Q02_Cat1 0.8891070  -4.8969388 9.734111e-07 4.088327e-05 0.9185050
## 76  PM954Q04_Cat1 0.7928335  -8.9566974 3.345482e-19 2.341837e-17 0.9078457
## 77  PM955Q01_Cat1 1.4807843  12.7364804 3.707464e-37 3.077195e-35 1.1544534
## 78  PM955Q02_Cat1 0.9773333  -0.9492097 3.425140e-01 1.000000e+00 1.0109534
## 79  PM955Q03_Cat1 0.9928089  -0.1830373 8.547688e-01 1.000000e+00 1.0615546
## 80  PM955Q03_Cat2 0.7660791  -5.4982614 3.835540e-08 1.802704e-06 1.0746601
## 81  PM982Q01_Cat1 1.5108311  10.2450506 1.245596e-24 9.591092e-23 1.0989354
## 82  PM982Q02_Cat1 1.2740165  11.5050119 1.244722e-30 9.957778e-29 1.2163832
## 83 PM982Q03T_Cat1 1.4111832  11.8806197 1.492567e-32 1.223905e-30 1.1278759
## 84  PM982Q04_Cat1 0.9151559  -2.9233629 3.462727e-03 9.003090e-02 0.9360951
## 85  PM992Q01_Cat1 0.8128833  -3.8794318 1.047007e-04 3.664526e-03 0.9395036
## 86  PM992Q02_Cat1 0.8907740  -5.2655698 1.397552e-07 6.149230e-06 0.9235102
## 87  PM992Q03_Cat1 0.7024784  -8.8605796 7.959953e-19 5.492368e-17 0.9068513
## 88  PM995Q01_Cat1 0.8032350  -7.1240524 1.047992e-12 5.868755e-11 0.8753030
## 89  PM995Q02_Cat1 0.8169602  -2.9117271 3.594365e-03 9.003090e-02 0.9329113
## 90  PM995Q03_Cat1 1.0377081   1.7133525 8.664771e-02 1.000000e+00 1.0110757
## 91  PM998Q02_Cat1 1.4304420   8.6372279 5.759344e-18 3.916354e-16 1.0855525
##         Infit_t      Infit_p  Infit_pholm
## 1  -2.514236576 1.192904e-02 5.606648e-01
## 2  -3.612660732 3.030711e-04 1.818427e-02
## 3   0.207433487 8.356713e-01 1.000000e+00
## 4   2.229413189 2.578643e-02 1.000000e+00
## 5   1.114102993 2.652350e-01 1.000000e+00
## 6  -1.228543700 2.192429e-01 1.000000e+00
## 7   5.642433223 1.676636e-08 1.341309e-06
## 8   7.248283749 4.220857e-13 3.587728e-11
## 9  -2.598466172 9.364127e-03 4.588422e-01
## 10  1.785990095 7.410086e-02 1.000000e+00
## 11  6.634329006 3.259820e-11 2.673052e-09
## 12  1.287993197 1.977483e-01 1.000000e+00
## 13  3.654120524 2.580650e-04 1.625810e-02
## 14 11.176494482 5.314813e-29 4.783331e-27
## 15 -4.658363386 3.187332e-06 2.358626e-04
## 16 -9.536228219 1.481217e-21 1.318283e-19
## 17  2.788970003 5.287596e-03 2.802426e-01
## 18  2.265674822 2.347130e-02 1.000000e+00
## 19  0.947395793 3.434371e-01 1.000000e+00
## 20 11.205267078 3.841933e-29 3.496159e-27
## 21  3.092807160 1.982729e-03 1.090501e-01
## 22 -2.116435341 3.430780e-02 1.000000e+00
## 23 -3.617185171 2.978242e-04 1.816728e-02
## 24 -2.606031562 9.159802e-03 4.579901e-01
## 25 -0.240976819 8.095731e-01 1.000000e+00
## 26 -1.720946737 8.526049e-02 1.000000e+00
## 27  1.584918555 1.129848e-01 1.000000e+00
## 28 -4.386128908 1.153858e-05 8.307774e-04
## 29  1.472157060 1.409785e-01 1.000000e+00
## 30 -2.812196847 4.920438e-03 2.657037e-01
## 31 -1.212465195 2.253344e-01 1.000000e+00
## 32 -0.069816257 9.443399e-01 1.000000e+00
## 33  5.406122283 6.440383e-08 5.087903e-06
## 34  2.681009313 7.340047e-03 3.816825e-01
## 35 -2.199790224 2.782178e-02 1.000000e+00
## 36  1.243817198 2.135668e-01 1.000000e+00
## 37  0.088198217 9.297191e-01 1.000000e+00
## 38 -4.012523488 6.007310e-05 4.024898e-03
## 39 -1.782488558 7.466960e-02 1.000000e+00
## 40  3.792867770 1.489175e-04 9.530718e-03
## 41 -0.191519421 8.481187e-01 1.000000e+00
## 42  3.544887196 3.927811e-04 2.278131e-02
## 43  1.391100991 1.641948e-01 1.000000e+00
## 44 -4.068245537 4.736845e-05 3.221055e-03
## 45  0.786911359 4.313338e-01 1.000000e+00
## 46 -8.624891620 6.415338e-18 5.517191e-16
## 47 -1.930773090 5.351112e-02 1.000000e+00
## 48 -6.820620456 9.064814e-12 7.523796e-10
## 49  3.192130388 1.412276e-03 7.908744e-02
## 50 -1.056964443 2.905278e-01 1.000000e+00
## 51 -2.665374258 7.690268e-03 3.922037e-01
## 52 -9.038861348 1.583122e-19 1.377316e-17
## 53  0.904480088 3.657409e-01 1.000000e+00
## 54 -1.091660209 2.749825e-01 1.000000e+00
## 55  3.465284366 5.296711e-04 3.019125e-02
## 56  0.430568716 6.667820e-01 1.000000e+00
## 57  0.660937626 5.086523e-01 1.000000e+00
## 58 -0.341801196 7.325005e-01 1.000000e+00
## 59  7.220122838 5.194063e-13 4.363013e-11
## 60  1.663042688 9.630389e-02 1.000000e+00
## 61  5.007826281 5.504818e-07 4.183662e-05
## 62 -2.332576058 1.967041e-02 9.048387e-01
## 63 -5.343774681 9.103071e-08 7.100396e-06
## 64  1.856428827 6.339246e-02 1.000000e+00
## 65 -4.254874619 2.091662e-05 1.443247e-03
## 66 -1.987717073 4.684299e-02 1.000000e+00
## 67 -2.180763490 2.920091e-02 1.000000e+00
## 68  1.461236465 1.439506e-01 1.000000e+00
## 69  4.694283445 2.675429e-06 2.006571e-04
## 70 -5.173218778 2.300953e-07 1.771734e-05
## 71 -6.514904205 7.273606e-11 5.891621e-09
## 72 -1.818945204 6.891979e-02 1.000000e+00
## 73  0.007472419 9.940379e-01 1.000000e+00
## 74 -4.306178214 1.660993e-05 1.162695e-03
## 75 -3.562186330 3.677792e-04 2.169897e-02
## 76 -3.810081336 1.389211e-04 9.029870e-03
## 77  4.476899939 7.573472e-06 5.528635e-04
## 78  0.457404535 6.473803e-01 1.000000e+00
## 79  1.498759710 1.339360e-01 1.000000e+00
## 80  1.585675004 1.128131e-01 1.000000e+00
## 81  2.233209553 2.553513e-02 1.000000e+00
## 82  9.235387821 2.573520e-20 2.264698e-18
## 83  4.003423238 6.243246e-05 4.120543e-03
## 84 -2.182625855 2.906337e-02 1.000000e+00
## 85 -1.184543520 2.361980e-01 1.000000e+00
## 86 -3.639563743 2.731003e-04 1.693222e-02
## 87 -2.549460869 1.078896e-02 5.178702e-01
## 88 -4.385094432 1.159355e-05 8.307774e-04
## 89 -1.006192532 3.143230e-01 1.000000e+00
## 90  0.512864884 6.080458e-01 1.000000e+00
## 91  1.901258904 5.726811e-02 1.000000e+00

スクリプト4-8 点双列相関係数の計算

ctt1 <- tam.ctt(JPN2012m, wlescore = wle1$theta)
## |**********| Group 1 
## |----------|
View(ctt1)
ctt1$rpb.WLE
##   [1] -0.55264330  0.55264330 -0.51722857  0.51722857 -0.33905856  0.33905856
##   [7] -0.29143290  0.29143290 -0.47657465  0.47657465 -0.46045620  0.46045620
##  [13] -0.53643024 -0.03334447  0.51981567 -0.61821286  0.23870994  0.52328958
##  [19] -0.37251323  0.37251323 -0.48538058  0.48538058 -0.42602005  0.42602005
##  [25] -0.29352832  0.29352832 -0.58874573  0.58874573 -0.65879030  0.65879030
##  [31] -0.44922914  0.44922914 -0.45254533  0.45254533 -0.48211312  0.48211312
##  [37] -0.30553407  0.30553407 -0.34176590  0.34176590 -0.52277965  0.52277965
##  [43] -0.53966185  0.53966185 -0.47413200  0.47413200 -0.40563093  0.40563093
##  [49] -0.51189305  0.31829704  0.37592032 -0.56883386  0.56883386 -0.26519552
##  [55]  0.26519552 -0.54999599  0.54999599 -0.48895134  0.48895134 -0.49080288
##  [61]  0.49080288 -0.41205030  0.41205030 -0.46509466  0.46509466 -0.54144292
##  [67]  0.54144292 -0.49188681  0.49188681 -0.25996396  0.25996396 -0.56270847
##  [73]  0.56270847 -0.52887876  0.52887876 -0.44485019  0.44485019 -0.34196100
##  [79]  0.34196100 -0.58872460  0.04550045  0.59845291 -0.55901641  0.55901641
##  [85] -0.39157359  0.39157359 -0.65843193  0.65843193 -0.53808494  0.53808494
##  [91] -0.68657492  0.24898072  0.51249486 -0.36351250  0.36351250 -0.53986096
##  [97]  0.53986096 -0.64455357  0.64455357 -0.49834127  0.49834127 -0.51666275
## [103]  0.51666275 -0.25799033  0.25799033 -0.28711192  0.28711192 -0.35939847
## [109]  0.35939847 -0.41129461  0.41129461 -0.39786326  0.39786326 -0.48120471
## [115]  0.48120471 -0.42096507  0.42096507 -0.48675637  0.48675637 -0.58530492
## [121]  0.58530492 -0.49522775  0.49522775 -0.52272193  0.52272193 -0.49051703
## [127]  0.49051703 -0.52675569  0.52675569 -0.62477769  0.01116665  0.58286148
## [133] -0.60640648  0.60640648 -0.62959382  0.62959382 -0.59884550  0.22449742
## [139]  0.53159036 -0.58619531  0.58619531 -0.58521612  0.58521612 -0.56285767
## [145]  0.56285767 -0.33111134  0.33111134 -0.48370537  0.48370537 -0.50922346
## [151]  0.14047584  0.48877723 -0.29483163  0.29483163 -0.34072161  0.34072161
## [157] -0.34541986  0.34541986 -0.51460899  0.51460899 -0.42751419  0.42751419
## [163] -0.56296414  0.56296414 -0.49548659  0.49548659 -0.56168072  0.56168072
## [169] -0.36294270  0.36294270 -0.49586259  0.49586259 -0.33330149  0.33330149