この章では，潜在クラス分析（LCA）と潜在ランク分析（LRA）を紹介します。サンプルデータJ15S500（15項目・500人の二値データ）を使用します。
dat <- J15S500
TestStatistics(dat)
Test Statistics
value
TestLength 15.0000000
SampleSize 500.0000000
Mean 9.6640000
SEofMean 0.1190738
Variance 7.0892826
SD 2.6625707
Skewness -0.4116220
Kurtosis -0.4471624
Min 2.0000000
Max 15.0000000
Range 13.0000000
Q1.25% 8.0000000
Median.50% 10.0000000
Q3.75% 12.0000000
IQR 4.0000000
Stanine.4% 5.0000000
Stanine.11% 6.0000000
Stanine.23% 7.0000000
Stanine.40% 9.0000000
Stanine.60% 11.0000000
Stanine.77% 12.0000000
Stanine.89% 13.0000000
Stanine.96% 14.0000000
潜在クラス分析（LCA）
潜在クラス分析は，受検者を潜在的なグループに分類するモデルです。ncls引数でクラス数を指定します。
result.LCA <- LCA(dat, ncls = 6, verbose = FALSE)
result.LCA
Item Reference Profile
IRP1 IRP2 IRP3 IRP4 IRP5 IRP6
Item01 0.4370 0.7608 0.73618 0.789 0.8459 0.883
Item02 0.5916 0.4784 0.75372 0.990 0.8738 0.805
Item03 0.7695 0.4027 0.89807 0.673 0.7384 0.855
Item04 0.5757 0.3974 0.87205 0.883 0.8866 1.000
Item05 0.6023 0.7820 0.94283 0.797 0.7931 0.883
Item06 0.6508 0.7042 0.92835 0.988 1.0000 0.881
Item07 0.5395 0.3102 0.82178 0.757 0.9169 0.910
Item08 0.3767 0.3255 0.60377 0.670 0.8828 0.635
Item09 0.2945 0.3467 0.16135 0.636 0.0107 0.739
Item10 0.5200 0.5570 0.79602 0.552 0.7070 0.819
Item11 0.1053 0.0472 0.00488 0.208 0.6864 0.656
Item12 0.0729 0.0776 0.16864 0.244 0.3015 0.764
Item13 0.2142 0.4370 0.95899 0.649 0.6426 0.842
Item14 0.2379 0.7530 0.76640 0.874 0.9085 1.000
Item15 0.3935 0.5389 0.86050 0.717 0.8220 0.863
Test Profile
Class 1 Class 2 Class 3 Class 4 Class 5 Class 6
Test Reference Profile 6.381 6.919 10.274 10.428 11.016 12.535
Latent Class Ditribution 76.000 74.000 105.000 82.000 91.000 72.000
Class Membership Distribution 77.345 80.034 88.778 85.807 84.592 83.444
Item Fit Indices
model_log_like bench_log_like null_log_like model_Chi_sq null_Chi_sq
Item01 -258.896 -240.190 -283.343 37.414 86.307
Item02 -235.421 -235.436 -278.949 -0.032 87.025
Item03 -262.373 -260.906 -293.598 2.934 65.383
Item04 -201.256 -192.072 -265.962 18.369 147.780
Item05 -230.005 -206.537 -247.403 46.935 81.732
Item06 -157.551 -153.940 -198.817 7.223 89.755
Item07 -241.548 -228.379 -298.345 26.338 139.933
Item08 -301.042 -293.225 -338.789 15.634 91.127
Item09 -246.942 -300.492 -327.842 -107.100 54.700
Item10 -303.019 -288.198 -319.850 29.641 63.303
Item11 -194.120 -224.085 -299.265 -59.931 150.360
Item12 -227.324 -214.797 -293.598 25.054 157.603
Item13 -257.389 -262.031 -328.396 -9.282 132.730
Item14 -193.802 -204.953 -273.212 -22.302 136.519
Item15 -267.063 -254.764 -302.847 24.598 96.166
model_df null_df NFI RFI IFI TLI CFI RMSEA AIC CAIC
Item01 8 13 0.567 0.296 0.624 0.348 0.599 0.086 21.414 -20.303
Item02 8 13 1.000 1.000 1.000 1.000 1.000 0.000 -16.032 -57.749
Item03 8 13 0.955 0.927 1.000 1.000 1.000 0.000 -13.066 -54.783
Item04 8 13 0.876 0.798 0.926 0.875 0.923 0.051 2.369 -39.348
Item05 8 13 0.426 0.067 0.472 0.079 0.434 0.099 30.935 -10.782
Item06 8 13 0.920 0.869 1.000 1.000 1.000 0.000 -8.777 -50.494
Item07 8 13 0.812 0.694 0.861 0.765 0.856 0.068 10.338 -31.379
Item08 8 13 0.828 0.721 0.908 0.841 0.902 0.044 -0.366 -42.083
Item09 8 13 1.000 1.000 1.000 1.000 1.000 0.000 -123.100 -164.817
Item10 8 13 0.532 0.239 0.609 0.301 0.570 0.074 13.641 -28.076
Item11 8 13 1.000 1.000 1.000 1.000 1.000 0.000 -75.931 -117.648
Item12 8 13 0.841 0.742 0.886 0.808 0.882 0.065 9.054 -32.663
Item13 8 13 1.000 1.000 1.000 1.000 1.000 0.000 -25.282 -66.999
Item14 8 13 1.000 1.000 1.000 1.000 1.000 0.000 -38.302 -80.019
Item15 8 13 0.744 0.584 0.812 0.676 0.800 0.064 8.598 -33.119
BIC
Item01 -12.303
Item02 -49.749
Item03 -46.783
Item04 -31.348
Item05 -2.782
Item06 -42.494
Item07 -23.379
Item08 -34.083
Item09 -156.817
Item10 -20.076
Item11 -109.648
Item12 -24.663
Item13 -58.999
Item14 -72.019
Item15 -25.119
Model Fit Indices
Number of Latent class: 6
Number of EM cycle: 75
value
model_log_like -3577.752
bench_log_like -3560.005
null_log_like -4350.217
model_Chi_sq 35.494
null_Chi_sq 1580.424
model_df 120.000
null_df 195.000
NFI 0.978
RFI 0.964
IFI 1.000
TLI 1.000
CFI 1.000
RMSEA 0.000
AIC -204.506
CAIC -830.259
BIC -710.259
受検者情報
result.LCA$Students |> head()
Membership 1 Membership 2 Membership 3 Membership 4 Membership 5
Student001 0.7260153212 0.1695828123 0.0191959227 0.048856576 3.634937e-02
Student002 0.0289874633 0.0254959545 0.8260430686 0.079770428 3.970303e-02
Student003 0.0064609145 0.0694589721 0.7665502806 0.118988645 2.246314e-02
Student004 0.0022440776 0.0037648933 0.1986288018 0.338531342 3.159317e-01
Student005 0.1089417615 0.8873608716 0.0008618367 0.002630128 3.770563e-08
Student006 0.0002507583 0.0002997263 0.0034460370 0.080211142 8.556562e-01
Membership 6 Estimate
Student001 1.643797e-12 1
Student002 5.150005e-08 3
Student003 1.607805e-02 3
Student004 1.408992e-01 4
Student005 2.053643e-04 2
Student006 6.013617e-02 5
項目参照プロファイル（IRP）
項目ごと・クラスごとの正答率を示します。
IRP1 IRP2 IRP3 IRP4 IRP5 IRP6
Item01 0.43697714 0.76082606 0.736182286 0.7888704 0.84587512 0.8833284
Item02 0.59162865 0.47842615 0.753719163 0.9895872 0.87381506 0.8053917
Item03 0.76947911 0.40266981 0.898069972 0.6729179 0.73839500 0.8547668
Item04 0.57568548 0.39740342 0.872051963 0.8834114 0.88663263 0.9999987
Item05 0.60228148 0.78201881 0.942825081 0.7970466 0.79313086 0.8825286
Item06 0.65081695 0.70419410 0.928346145 0.9880396 0.99999819 0.8809962
Item07 0.53954860 0.31021765 0.821782975 0.7573892 0.91694500 0.9099388
Item08 0.37665418 0.32548664 0.603770254 0.6703679 0.88279332 0.6353566
Item09 0.29449208 0.34671215 0.161352112 0.6363038 0.01069097 0.7387628
Item10 0.51999141 0.55701126 0.796021391 0.5519760 0.70703883 0.8192215
Item11 0.10527790 0.04723862 0.004876396 0.2075675 0.68644801 0.6563071
Item12 0.07286478 0.07761944 0.168639693 0.2437380 0.30148250 0.7641428
Item13 0.21415120 0.43700977 0.958994723 0.6494997 0.64262783 0.8416495
Item14 0.23788534 0.75296124 0.766397233 0.8740889 0.90850482 0.9999995
Item15 0.39351809 0.53891044 0.860504438 0.7168047 0.82195096 0.8628674
可視化（baseグラフィックス）
plot(result.LCA, type = "IRP", items = 1:4, nr = 2, nc = 2)
クラスメンバーシッププロファイル（CMP）は，受検者がどのクラスに所属しやすいかの確率を表します。
plot(result.LCA, type = "CMP", students = 1:6, nr = 2, nc = 3)
テスト参照プロファイル（TRP）は，テスト得点とクラスの分類を可視化します。
plot(result.LCA, type = "TRP")
潜在クラス分布（LCD）は，クラスの分布を表示します。棒グラフがLatent Class Distribution，折れ線グラフがClass Membership Distributionです。
plot(result.LCA, type = "LCD")
可視化（ggExametrika）
plotIRP_gg(result.LCA)[[1]]
plotCMP_gg(result.LCA)[[1]]
潜在ランク分析（LRA）
LCAの潜在クラスに序列性を持たせたものが潜在ランク分析（LRA）です。nrank引数でランク数を指定し，mic = TRUEで単調増加制約を課します。
result.LRA <- LRA(dat, nrank = 6, mic = TRUE)
result.LRA
estimating method is GTM
Monotonic increasing IRP option is TRUE.
Item Reference Profile
IRP1 IRP2 IRP3 IRP4 IRP5 IRP6
Item01 0.5813 0.6370 0.711 0.780 0.849 0.901
Item02 0.5257 0.6280 0.754 0.837 0.879 0.883
Item03 0.6112 0.6127 0.702 0.768 0.807 0.839
Item04 0.4415 0.5963 0.790 0.889 0.943 0.972
Item05 0.6481 0.7458 0.816 0.829 0.864 0.911
Item06 0.6476 0.7794 0.913 0.937 0.948 0.951
Item07 0.4078 0.5103 0.717 0.841 0.891 0.902
Item08 0.3332 0.4315 0.605 0.702 0.717 0.721
Item09 0.3154 0.3179 0.322 0.334 0.380 0.503
Item10 0.5043 0.5783 0.681 0.724 0.728 0.745
Item11 0.0882 0.0922 0.138 0.274 0.466 0.621
Item12 0.0622 0.0959 0.159 0.253 0.422 0.616
Item13 0.2875 0.4833 0.710 0.766 0.769 0.771
Item14 0.4780 0.6005 0.732 0.844 0.930 0.975
Item15 0.4044 0.5671 0.751 0.824 0.835 0.838
Item Reference Profile Indices
Alpha A Beta B Gamma C
Item01 2 0.0735 1 0.581 0 0
Item02 2 0.1264 1 0.526 0 0
Item03 2 0.0893 1 0.611 0 0
Item04 2 0.1935 1 0.442 0 0
Item05 1 0.0977 1 0.648 0 0
Item06 2 0.1331 1 0.648 0 0
Item07 2 0.2069 2 0.510 0 0
Item08 2 0.1734 2 0.431 0 0
Item09 5 0.1231 6 0.503 0 0
Item10 2 0.1027 1 0.504 0 0
Item11 4 0.1911 5 0.466 0 0
Item12 5 0.1939 5 0.422 0 0
Item13 2 0.2264 2 0.483 0 0
Item14 2 0.1316 1 0.478 0 0
Item15 2 0.1837 2 0.567 0 0
Test Profile
Rank 1 Rank 2 Rank 3 Rank 4 Rank 5 Rank 6
Test Reference Profile 6.336 7.676 9.499 10.603 11.426 12.149
Latent Rank Ditribution 97.000 56.000 90.000 89.000 65.000 103.000
Rank Membership Distribution 83.037 77.984 81.981 84.777 84.710 87.511
Item Fit Indices
model_log_like bench_log_like null_log_like model_Chi_sq null_Chi_sq
Item01 -264.521 -240.190 -283.343 48.662 86.307
Item02 -253.391 -235.436 -278.949 35.909 87.025
Item03 -282.696 -260.906 -293.598 43.580 65.383
Item04 -206.656 -192.072 -265.962 29.169 147.780
Item05 -234.649 -206.537 -247.403 56.224 81.732
Item06 -172.010 -153.940 -198.817 36.141 89.755
Item07 -249.856 -228.379 -298.345 42.954 139.933
Item08 -312.980 -293.225 -338.789 39.510 91.127
Item09 -322.072 -300.492 -327.842 43.159 54.700
Item10 -310.319 -288.198 -319.850 44.240 63.303
Item11 -243.621 -224.085 -299.265 39.071 150.360
Item12 -239.220 -214.797 -293.598 48.847 157.603
Item13 -287.805 -262.031 -328.396 51.549 132.730
Item14 -222.496 -204.953 -273.212 35.086 136.519
Item15 -268.522 -254.764 -302.847 27.518 96.166
model_df null_df NFI RFI IFI TLI CFI RMSEA AIC CAIC
Item01 9.233 13 0.436 0.206 0.488 0.243 0.462 0.093 30.197 -17.948
Item02 9.233 13 0.587 0.419 0.657 0.493 0.640 0.076 17.443 -30.702
Item03 9.233 13 0.333 0.062 0.388 0.077 0.344 0.086 25.114 -23.031
Item04 9.233 13 0.803 0.722 0.856 0.792 0.852 0.066 10.704 -37.441
Item05 9.233 13 0.312 0.031 0.352 0.037 0.316 0.101 37.758 -10.387
Item06 9.233 13 0.597 0.433 0.666 0.506 0.649 0.076 17.676 -30.469
Item07 9.233 13 0.693 0.568 0.742 0.626 0.734 0.086 24.489 -23.656
Item08 9.233 13 0.566 0.390 0.630 0.454 0.612 0.081 21.044 -27.101
Item09 9.233 13 0.211 0.000 0.254 0.000 0.186 0.086 24.694 -23.451
Item10 9.233 13 0.301 0.016 0.353 0.020 0.304 0.087 25.775 -22.370
Item11 9.233 13 0.740 0.634 0.789 0.694 0.783 0.080 20.606 -27.539
Item12 9.233 13 0.690 0.564 0.733 0.614 0.726 0.093 30.382 -17.763
Item13 9.233 13 0.612 0.453 0.657 0.502 0.647 0.096 33.084 -15.062
Item14 9.233 13 0.743 0.638 0.797 0.705 0.791 0.075 16.621 -31.524
Item15 9.233 13 0.714 0.597 0.790 0.690 0.780 0.063 9.052 -39.093
BIC
Item01 -8.716
Item02 -21.469
Item03 -13.798
Item04 -28.209
Item05 -1.154
Item06 -21.236
Item07 -14.424
Item08 -17.868
Item09 -14.219
Item10 -13.137
Item11 -18.307
Item12 -8.531
Item13 -5.829
Item14 -22.292
Item15 -29.860
Model Fit Indices
Number of Latent rank: 6
Number of EM cycle: 13
value
model_log_like -3870.815
bench_log_like -3560.005
null_log_like -4350.217
model_Chi_sq 621.620
null_Chi_sq 1580.424
model_df 138.491
null_df 195.000
NFI 0.607
RFI 0.446
IFI 0.665
TLI 0.509
CFI 0.651
RMSEA 0.084
AIC 344.638
CAIC -377.538
BIC -239.047
受検者情報
Rank-Up OddsやRank-Down Oddsが表示され，上のランクへの上がりやすさ・下のランクへの落ちやすさを示します。
result.LRA$Students |> head()
Membership 1 Membership 2 Membership 3 Membership 4 Membership 5
Student001 0.2649442154 0.401777727 0.25199194 0.069833913 0.010587063
Student002 0.0320802124 0.165197013 0.47017520 0.262193334 0.061017540
Student003 0.0256087173 0.143643145 0.36931821 0.263791224 0.137653365
Student004 0.0019080554 0.015030869 0.09499327 0.201622664 0.343207280
Student005 0.5745639230 0.379140089 0.03754276 0.006239969 0.001910557
Student006 0.0003651887 0.003620252 0.04607054 0.202440568 0.398545000
Membership 6 Estimate Rank-Up Odds Rank-Down Odds
Student001 0.0008651363 2 0.6271924 0.6594298
Student002 0.0093367003 3 0.5576503 0.3513520
Student003 0.0599853347 3 0.7142654 0.3889414
Student004 0.3432378584 6 NA 0.9999109
Student005 0.0006027066 1 0.6598745 NA
Student006 0.3489584503 5 0.8755811 0.5079491
項目参照プロファイル（IRP）
IRP1 IRP2 IRP3 IRP4 IRP5 IRP6
Item01 0.58134579 0.63703070 0.7105624 0.7799727 0.8488455 0.9005402
Item02 0.52566747 0.62802753 0.7544298 0.8369062 0.8793933 0.8828570
Item03 0.61116426 0.61266166 0.7019998 0.7679128 0.8071646 0.8391724
Item04 0.44152626 0.59634830 0.7898921 0.8885698 0.9427475 0.9724996
Item05 0.64810054 0.74581736 0.8158043 0.8292063 0.8635791 0.9113865
Item06 0.64762411 0.77943717 0.9125559 0.9366776 0.9476421 0.9507004
Item07 0.40777315 0.51032060 0.7172665 0.8414449 0.8909572 0.9019490
Item08 0.33320297 0.43146180 0.6048313 0.7022176 0.7165168 0.7207851
Item09 0.31536164 0.31793335 0.3215534 0.3337615 0.3799428 0.5030880
Item10 0.50433135 0.57829599 0.6809487 0.7244593 0.7284557 0.7447081
Item11 0.08816694 0.09217932 0.1376948 0.2744389 0.4655814 0.6209129
Item12 0.06219226 0.09589473 0.1590574 0.2528391 0.4223461 0.6162779
Item13 0.28748283 0.48325773 0.7096872 0.7658707 0.7689499 0.7711838
Item14 0.47797956 0.60051446 0.7321160 0.8442909 0.9295404 0.9747505
Item15 0.40437730 0.56707341 0.7507473 0.8243016 0.8346267 0.8378010
IRPIndex
IRPの要約指標として，以下の3つのインデックスが算出されます。
- A（Item Slope Index）：識別力に相当する指標
- B（Item Location Index）：困難度に相当する指標
- C（Item Monotonicity Index）：単調増加性の指標
Alpha A Beta B Gamma C
Item01 2 0.07353170 1 0.5813458 0 0
Item02 2 0.12640232 1 0.5256675 0 0
Item03 2 0.08933814 1 0.6111643 0 0
Item04 2 0.19354385 1 0.4415263 0 0
Item05 1 0.09771682 1 0.6481005 0 0
Item06 2 0.13311875 1 0.6476241 0 0
Item07 2 0.20694595 2 0.5103206 0 0
Item08 2 0.17336955 2 0.4314618 0 0
Item09 5 0.12314521 6 0.5030880 0 0
Item10 2 0.10265274 1 0.5043314 0 0
Item11 4 0.19114249 5 0.4655814 0 0
Item12 5 0.19393177 5 0.4223461 0 0
Item13 2 0.22642950 2 0.4832577 0 0
Item14 2 0.13160157 1 0.4779796 0 0
Item15 2 0.18367392 2 0.5670734 0 0
可視化（baseグラフィックス）
plot(result.LRA, type = "IRP", items = 1:4, nr = 2, nc = 2)
plot(result.LRA, type = "RMP", students = 1:6, nr = 2, nc = 3)
plot(result.LRA, type = "TRP")
plot(result.LRA, type = "LRD")
可視化（ggExametrika）
plotIRP_gg(result.LRA)[[1]]
plotRMP_gg(result.LRA)[[1]]
推定法の選択：GTM vs SOM
GTM（Generative Topographic Mapping）
デフォルトの推定法です。項目とランクとの関係を表す行列\(\Pi_R\)（サイズ \(J \times R\)）に，緩やかな順序制約をつけたフィルタ行列\(S\)（サイズ \(R \times R\)）を乗算しながらEMアルゴリズムで推定します。データサイズが大きくなっても安定的に推定が進みます。
SOM（Self-Organizing Map）
自己組織化マップの方法も選択可能です。最初にランダムに生成した行列\(\Pi_R\)に対し，データ行列に近い勝者ベクトルが周囲の重みをアップデートしていきます。乱数による近似なので，再現性のためにはシード値の設定が必要です。
result.SOM <- LRA(dat, nrank = 6, method = "SOM", seed = 12345)
Reached the maximum number of iterations.
Warning: Algorithm may not have converged. Interpret results with caution.
estimating method is SOM
Item Reference Profile
IRP1 IRP2 IRP3 IRP4 IRP5 IRP6
Item01 0.5960 0.6358 0.710 0.781 0.844 0.892
Item02 0.5435 0.6388 0.758 0.849 0.884 0.891
Item03 0.6035 0.6239 0.682 0.760 0.816 0.847
Item04 0.5025 0.6308 0.774 0.880 0.944 0.971
Item05 0.6823 0.7469 0.791 0.827 0.869 0.910
Item06 0.6893 0.7904 0.897 0.956 0.963 0.943
Item07 0.4398 0.5431 0.695 0.832 0.900 0.922
Item08 0.3663 0.4677 0.596 0.674 0.712 0.744
Item09 0.3333 0.3177 0.308 0.328 0.395 0.462
Item10 0.5351 0.5855 0.662 0.717 0.733 0.754
Item11 0.0716 0.0753 0.123 0.262 0.473 0.635
Item12 0.0694 0.1027 0.161 0.252 0.413 0.585
Item13 0.3763 0.5105 0.665 0.735 0.765 0.795
Item14 0.5207 0.6021 0.724 0.852 0.937 0.971
Item15 0.4808 0.5876 0.713 0.807 0.849 0.859
Item Reference Profile Indices
Alpha A Beta B Gamma C
Item01 2 0.0741 1 0.596 0.0 0.0000
Item02 2 0.1196 1 0.544 0.0 0.0000
Item03 3 0.0782 1 0.603 0.0 0.0000
Item04 2 0.1430 1 0.503 0.0 0.0000
Item05 1 0.0646 1 0.682 0.0 0.0000
Item06 2 0.1061 1 0.689 0.2 -0.0195
Item07 2 0.1515 2 0.543 0.0 0.0000
Item08 2 0.1280 2 0.468 0.0 0.0000
Item09 5 0.0671 6 0.462 0.4 -0.0254
Item10 2 0.0764 1 0.535 0.0 0.0000
Item11 4 0.2113 5 0.473 0.0 0.0000
Item12 5 0.1730 6 0.585 0.0 0.0000
Item13 2 0.1542 2 0.510 0.0 0.0000
Item14 3 0.1282 1 0.521 0.0 0.0000
Item15 2 0.1257 1 0.481 0.0 0.0000
Test Profile
Rank 1 Rank 2 Rank 3 Rank 4 Rank 5 Rank 6
Test Reference Profile 6.810 7.859 9.257 10.511 11.497 12.181
Latent Rank Ditribution 110.000 47.000 88.000 91.000 57.000 107.000
Rank Membership Distribution 88.291 77.753 78.235 83.372 84.584 87.765
Item Fit Indices
model_log_like bench_log_like null_log_like model_Chi_sq null_Chi_sq
Item01 -265.054 -240.190 -283.343 49.729 86.307
Item02 -252.528 -235.436 -278.949 34.183 87.025
Item03 -282.154 -260.906 -293.598 42.495 65.383
Item04 -211.074 -192.072 -265.962 38.005 147.780
Item05 -235.901 -206.537 -247.403 58.727 81.732
Item06 -171.930 -153.940 -198.817 35.980 89.755
Item07 -251.168 -228.379 -298.345 45.579 139.933
Item08 -315.097 -293.225 -338.789 43.745 91.127
Item09 -323.478 -300.492 -327.842 45.972 54.700
Item10 -310.781 -288.198 -319.850 45.164 63.303
Item11 -239.989 -224.085 -299.265 31.806 150.360
Item12 -242.908 -214.797 -293.598 56.222 157.603
Item13 -295.624 -262.031 -328.396 67.186 132.730
Item14 -223.067 -204.953 -273.212 36.228 136.519
Item15 -273.041 -254.764 -302.847 36.555 96.166
model_df null_df NFI RFI IFI TLI CFI RMSEA AIC CAIC
Item01 8 13 0.424 0.064 0.467 0.075 0.431 0.102 33.729 -7.988
Item02 8 13 0.607 0.362 0.669 0.425 0.646 0.081 18.183 -23.534
Item03 8 13 0.350 0.000 0.399 0.000 0.341 0.093 26.495 -15.221
Item04 8 13 0.743 0.582 0.785 0.638 0.777 0.087 22.005 -19.712
Item05 8 13 0.281 0.000 0.312 0.000 0.262 0.113 42.727 1.011
Item06 8 13 0.599 0.349 0.658 0.408 0.635 0.084 19.980 -21.737
Item07 8 13 0.674 0.471 0.715 0.519 0.704 0.097 29.579 -12.138
Item08 8 13 0.520 0.220 0.570 0.257 0.542 0.095 27.745 -13.972
Item09 8 13 0.160 0.000 0.187 0.000 0.089 0.098 29.972 -11.745
Item10 8 13 0.287 0.000 0.328 0.000 0.261 0.096 29.164 -12.552
Item11 8 13 0.788 0.656 0.833 0.718 0.827 0.077 15.806 -25.911
Item12 8 13 0.643 0.420 0.678 0.458 0.667 0.110 40.222 -1.495
Item13 8 13 0.494 0.177 0.525 0.197 0.506 0.122 51.186 9.469
Item14 8 13 0.735 0.569 0.780 0.629 0.771 0.084 20.228 -21.489
Item15 8 13 0.620 0.382 0.676 0.442 0.657 0.085 20.555 -21.162
BIC
Item01 0.012
Item02 -15.534
Item03 -7.221
Item04 -11.712
Item05 9.011
Item06 -13.737
Item07 -4.138
Item08 -5.972
Item09 -3.745
Item10 -4.552
Item11 -17.911
Item12 6.505
Item13 17.469
Item14 -13.489
Item15 -13.162
Model Fit Indices
Number of Latent rank: 6
Number of EM cycle: 100
value
model_log_like -3893.793
bench_log_like -3560.005
null_log_like -4350.217
model_Chi_sq 667.575
null_Chi_sq 1580.424
model_df 120.000
null_df 195.000
NFI 0.578
RFI 0.314
IFI 0.625
TLI 0.358
CFI 0.605
RMSEA 0.096
AIC 427.575
CAIC -198.178
BIC -78.178
結果の比較
result.LRA$TestFitIndices
model_log_like bench_log_like null_log_like model_Chi_sq null_Chi_sq model_df
1 -3870.815 -3560.005 -4350.217 621.6196 1580.424 138.4909
null_df NFI RFI IFI TLI CFI RMSEA AIC
1 195 0.6066754 0.4461853 0.6649437 0.5089864 0.6512774 0.08361236 344.6378
CAIC BIC
1 -377.5381 -239.0471
result.SOM$TestFitIndices
model_log_like bench_log_like null_log_like model_Chi_sq null_Chi_sq model_df
1 -3893.793 -3560.005 -4350.217 667.5754 1580.424 120
null_df NFI RFI IFI TLI CFI RMSEA AIC
1 195 0.5775972 0.3135955 0.6250572 0.3577344 0.6047596 0.09562712 427.5754
CAIC BIC
1 -198.1775 -78.17753
多値データへの展開
多肢選択（rated）データ
サンプルデータJ35S5000で多肢選択データの分析例を示します。
result.LRArated <- LRA(J35S5000, nrank = 10, mic = TRUE)
result.LRArated
Monotonic increasing IRP option is TRUE.
Test Statistics
value
SampleSize 5000.00000000
TestLength 35.00000000
Median 17.00000000
Max 35.00000000
Min 2.00000000
Range 33.00000000
Mean 16.91100000
SD 4.97699036
Skewness 0.31342138
Kurtosis -0.07429596
Alpha 0.70437957
Item Statistics
ItemLabel Obs ObsRatio ItemMean ItemSD ItemCORR ItemCORR_R
1 V1 4983 0.997 0.347 0.476 0.268 0.1762
2 V2 4993 0.999 0.284 0.451 0.133 0.0425
3 V3 4933 0.987 0.770 0.421 0.280 0.1992
4 V4 4997 0.999 0.338 0.473 0.341 0.2530
5 V5 4997 0.999 0.283 0.450 0.251 0.1636
6 V6 4995 0.999 0.867 0.340 0.221 0.1550
7 V7 4982 0.996 0.372 0.483 0.177 0.0808
8 V8 4999 1.000 0.372 0.483 0.359 0.2698
9 V9 4999 1.000 0.653 0.476 0.311 0.2211
10 V10 4991 0.998 0.396 0.489 0.377 0.2885
11 V11 4998 1.000 0.629 0.483 0.210 0.1147
12 V12 4996 0.999 0.571 0.495 0.372 0.2821
13 V13 4997 0.999 0.356 0.479 0.319 0.2291
14 V14 4977 0.995 0.330 0.470 0.312 0.2234
15 V15 4999 1.000 0.552 0.497 0.290 0.1952
16 V16 4996 0.999 0.354 0.478 0.286 0.1941
17 V17 4911 0.982 0.348 0.476 0.267 0.1747
18 V18 4999 1.000 0.753 0.431 0.352 0.2732
19 V19 4992 0.998 0.521 0.500 0.383 0.2927
20 V20 4996 0.999 0.271 0.444 0.230 0.1426
21 V21 4995 0.999 0.479 0.500 0.277 0.1806
22 V22 4984 0.997 0.524 0.499 0.302 0.2068
23 V23 4993 0.999 0.484 0.500 0.306 0.2105
24 V24 4998 1.000 0.508 0.500 0.381 0.2906
25 V25 4996 0.999 0.635 0.482 0.338 0.2478
26 V26 4991 0.998 0.382 0.486 0.391 0.3036
27 V27 4969 0.994 0.669 0.471 0.340 0.2520
28 V28 4997 0.999 0.466 0.499 0.402 0.3127
29 V29 4998 1.000 0.542 0.498 0.356 0.2643
30 V30 4994 0.999 0.784 0.412 0.330 0.2529
31 V31 4998 1.000 0.461 0.498 0.306 0.2115
32 V32 4974 0.995 0.247 0.432 0.227 0.1420
33 V33 4996 0.999 0.282 0.450 0.254 0.1666
34 V34 4996 0.999 0.492 0.500 0.229 0.1309
35 V35 4995 0.999 0.630 0.483 0.286 0.1937
Item Quantile Reference Matrix
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
V1 0.178 0.261 0.210 0.314 0.322 0.354 0.399 0.409 0.486 0.669
V2 0.197 0.217 0.251 0.278 0.278 0.295 0.294 0.346 0.355 0.382
V3 0.517 0.673 0.722 0.765 0.745 0.809 0.853 0.845 0.896 0.957
V4 0.159 0.194 0.229 0.257 0.271 0.348 0.390 0.445 0.520 0.763
V5 0.159 0.202 0.199 0.223 0.257 0.281 0.285 0.328 0.380 0.637
V6 0.701 0.798 0.849 0.878 0.879 0.916 0.933 0.928 0.932 0.965
V7 0.259 0.305 0.275 0.326 0.365 0.402 0.423 0.423 0.454 0.570
V8 0.184 0.217 0.245 0.278 0.307 0.388 0.408 0.476 0.611 0.801
V9 0.370 0.534 0.596 0.631 0.664 0.697 0.712 0.802 0.801 0.898
V10 0.187 0.249 0.264 0.261 0.337 0.419 0.420 0.508 0.636 0.871
V11 0.474 0.541 0.596 0.602 0.618 0.652 0.644 0.699 0.732 0.849
V12 0.300 0.397 0.434 0.506 0.573 0.576 0.635 0.712 0.824 0.927
V13 0.163 0.233 0.272 0.283 0.312 0.334 0.383 0.456 0.558 0.726
V14 0.124 0.207 0.226 0.271 0.304 0.357 0.331 0.443 0.518 0.648
V15 0.314 0.428 0.504 0.542 0.539 0.531 0.571 0.672 0.742 0.828
V16 0.159 0.272 0.264 0.288 0.344 0.334 0.408 0.407 0.514 0.691
V17 0.144 0.218 0.310 0.271 0.344 0.368 0.411 0.449 0.461 0.599
V18 0.487 0.607 0.671 0.688 0.762 0.809 0.865 0.890 0.949 0.978
V19 0.252 0.339 0.399 0.441 0.470 0.598 0.620 0.659 0.748 0.938
V20 0.153 0.191 0.218 0.204 0.227 0.287 0.291 0.333 0.398 0.524
V21 0.246 0.345 0.380 0.475 0.485 0.517 0.543 0.584 0.664 0.704
V22 0.295 0.386 0.445 0.448 0.504 0.556 0.601 0.622 0.732 0.809
V23 0.262 0.339 0.356 0.393 0.478 0.520 0.601 0.614 0.674 0.758
V24 0.193 0.321 0.399 0.436 0.533 0.579 0.641 0.645 0.717 0.844
V25 0.312 0.502 0.544 0.576 0.667 0.750 0.742 0.777 0.814 0.855
V26 0.130 0.194 0.275 0.297 0.328 0.449 0.436 0.526 0.609 0.806
V27 0.386 0.500 0.569 0.612 0.696 0.733 0.733 0.814 0.856 0.911
V28 0.187 0.274 0.340 0.355 0.457 0.514 0.540 0.611 0.704 0.892
V29 0.290 0.373 0.445 0.463 0.521 0.570 0.635 0.658 0.784 0.890
V30 0.486 0.678 0.701 0.815 0.811 0.857 0.887 0.881 0.937 0.954
V31 0.236 0.336 0.380 0.396 0.473 0.441 0.494 0.550 0.626 0.831
V32 0.125 0.169 0.175 0.194 0.227 0.272 0.258 0.292 0.372 0.481
V33 0.137 0.189 0.181 0.211 0.278 0.303 0.359 0.341 0.387 0.559
V34 0.308 0.373 0.474 0.453 0.484 0.503 0.580 0.575 0.632 0.683
V35 0.404 0.498 0.601 0.568 0.630 0.683 0.675 0.726 0.791 0.890
Item Category Reference Profile
ItemLabel CategoryLabel rank1 rank2 rank3 rank4 rank5
1 V1 V1-Cat1 0.160702 0.151981 1.39e-01 1.29e-01 1.26e-01
2 V1 V1-Cat2 0.171401 0.165577 1.61e-01 1.47e-01 1.39e-01
3 V1 V1-Cat3 0.250322 0.258561 2.74e-01 3.01e-01 3.25e-01
4 V1 V1-Cat4 0.240354 0.234908 2.31e-01 2.31e-01 2.23e-01
5 V1 V1-Cat5 0.177221 0.188973 1.95e-01 1.92e-01 1.87e-01
6 V2 V2-Cat1 0.167136 0.198017 2.34e-01 2.52e-01 2.67e-01
7 V2 V2-Cat2 0.256135 0.207010 1.51e-01 1.11e-01 7.35e-02
8 V2 V2-Cat3 0.255201 0.256119 2.64e-01 2.72e-01 2.75e-01
9 V2 V2-Cat4 0.321529 0.338855 3.52e-01 3.66e-01 3.84e-01
10 V3 V3-Cat1 0.101926 0.064995 3.88e-02 3.16e-02 2.95e-02
11 V3 V3-Cat2 0.207859 0.166968 1.23e-01 1.01e-01 9.19e-02
12 V3 V3-Cat3 0.568325 0.643477 7.11e-01 7.49e-01 7.75e-01
13 V3 V3-Cat4 0.121890 0.124560 1.27e-01 1.18e-01 1.03e-01
14 V4 V4-Cat1 0.085362 0.082838 8.75e-02 8.88e-02 9.01e-02
15 V4 V4-Cat2 0.295254 0.296079 2.86e-01 2.85e-01 2.55e-01
16 V4 V4-Cat3 0.209903 0.215406 2.23e-01 2.25e-01 2.61e-01
17 V4 V4-Cat4 0.246144 0.242142 2.25e-01 2.77e-01 2.95e-01
18 V4 V4-Cat5 0.115594 0.113855 1.26e-01 8.93e-02 7.11e-02
19 V4 V4-Cat6 0.047743 0.049681 5.23e-02 3.47e-02 2.74e-02
20 V5 V5-Cat1 0.155779 0.127442 9.09e-02 6.43e-02 5.37e-02
21 V5 V5-Cat2 0.218851 0.220231 2.27e-01 2.40e-01 2.46e-01
22 V5 V5-Cat3 0.380675 0.425797 4.71e-01 4.96e-01 5.16e-01
23 V5 V5-Cat4 0.244695 0.226530 2.11e-01 2.00e-01 1.84e-01
24 V6 V6-Cat1 0.010337 0.004712 1.47e-03 1.10e-03 1.15e-03
25 V6 V6-Cat2 0.084484 0.076870 5.93e-02 4.32e-02 3.78e-02
26 V6 V6-Cat3 0.141265 0.120281 1.01e-01 8.91e-02 7.21e-02
27 V6 V6-Cat4 0.020483 0.011283 5.28e-03 4.94e-03 4.65e-03
28 V6 V6-Cat5 0.738872 0.783464 8.30e-01 8.58e-01 8.81e-01
29 V6 V6-Cat6 0.004558 0.003389 3.11e-03 3.24e-03 3.33e-03
30 V7 V7-Cat1 0.071050 0.067340 7.44e-02 1.13e-01 3.36e-02
31 V7 V7-Cat2 0.376140 0.378440 3.78e-01 3.49e-01 3.95e-01
32 V7 V7-Cat3 0.334140 0.336463 3.38e-01 3.42e-01 3.47e-01
33 V7 V7-Cat4 0.218670 0.217756 2.10e-01 1.96e-01 2.24e-01
34 V8 V8-Cat1 0.194270 0.193325 1.92e-01 1.97e-01 1.88e-01
35 V8 V8-Cat2 0.187308 0.204674 2.32e-01 2.53e-01 2.71e-01
36 V8 V8-Cat3 0.119084 0.114607 1.09e-01 9.90e-02 8.20e-02
37 V8 V8-Cat4 0.207077 0.224882 2.51e-01 2.74e-01 3.03e-01
38 V8 V8-Cat5 0.128616 0.097776 6.24e-02 4.13e-02 3.06e-02
39 V8 V8-Cat6 0.163645 0.164736 1.54e-01 1.36e-01 1.25e-01
40 V9 V9-Cat1 0.066599 0.044366 2.47e-02 1.63e-02 1.34e-02
41 V9 V9-Cat2 0.118450 0.098472 7.94e-02 6.94e-02 6.52e-02
42 V9 V9-Cat3 0.110387 0.090098 6.25e-02 4.07e-02 2.89e-02
43 V9 V9-Cat4 0.436433 0.507443 5.82e-01 6.19e-01 6.42e-01
44 V9 V9-Cat5 0.114586 0.096521 8.04e-02 7.48e-02 6.82e-02
45 V9 V9-Cat6 0.153546 0.163100 1.71e-01 1.80e-01 1.82e-01
46 V10 V10-Cat1 0.278156 0.292461 3.26e-01 3.62e-01 3.71e-01
47 V10 V10-Cat2 0.129973 0.115018 9.73e-02 8.71e-02 7.53e-02
48 V10 V10-Cat3 0.346028 0.336355 3.19e-01 2.87e-01 2.52e-01
49 V10 V10-Cat4 0.244458 0.255767 2.57e-01 2.64e-01 3.02e-01
50 V10 V10-Cat5 0.001386 0.000399 5.54e-06 1.20e-10 5.65e-12
51 V11 V11-Cat1 0.098465 0.091053 8.65e-02 7.81e-02 8.52e-02
52 V11 V11-Cat2 0.274928 0.271579 2.59e-01 2.69e-01 2.60e-01
53 V11 V11-Cat3 0.514996 0.559695 6.06e-01 6.19e-01 6.20e-01
54 V11 V11-Cat4 0.110236 0.077271 4.85e-02 3.37e-02 3.55e-02
55 V11 V11-Cat5 0.001375 0.000402 7.41e-06 3.14e-10 3.33e-09
56 V12 V12-Cat1 0.253810 0.253306 2.40e-01 2.26e-01 2.28e-01
57 V12 V12-Cat2 0.054170 0.040727 2.70e-02 2.14e-02 2.00e-02
58 V12 V12-Cat3 0.166075 0.126333 8.69e-02 7.01e-02 6.50e-02
59 V12 V12-Cat4 0.103467 0.087702 7.61e-02 6.83e-02 5.98e-02
60 V12 V12-Cat5 0.080713 0.095045 1.03e-01 1.02e-01 9.36e-02
61 V12 V12-Cat6 0.341765 0.396888 4.66e-01 5.12e-01 5.33e-01
62 V13 V13-Cat1 0.262536 0.306057 3.65e-01 4.09e-01 4.25e-01
63 V13 V13-Cat2 0.219088 0.239018 2.61e-01 2.76e-01 2.91e-01
64 V13 V13-Cat3 0.124337 0.092505 6.13e-02 4.93e-02 4.90e-02
65 V13 V13-Cat4 0.209241 0.211712 1.97e-01 1.74e-01 1.66e-01
66 V13 V13-Cat5 0.181466 0.148642 1.15e-01 9.04e-02 6.84e-02
67 V13 V13-Cat6 0.003331 0.002065 1.14e-03 6.73e-04 2.36e-04
68 V14 V14-Cat1 0.127174 0.110982 8.94e-02 7.58e-02 7.35e-02
69 V14 V14-Cat2 0.053256 0.043999 4.01e-02 3.95e-02 4.27e-02
70 V14 V14-Cat3 0.401542 0.404420 4.03e-01 4.14e-01 4.18e-01
71 V14 V14-Cat4 0.169232 0.199198 2.40e-01 2.73e-01 3.00e-01
72 V14 V14-Cat5 0.124973 0.113546 9.80e-02 8.09e-02 6.75e-02
73 V14 V14-Cat6 0.123825 0.127855 1.30e-01 1.17e-01 9.89e-02
74 V15 V15-Cat1 0.113251 0.111643 9.55e-02 6.93e-02 5.58e-02
75 V15 V15-Cat2 0.221394 0.205947 1.82e-01 1.57e-01 1.46e-01
76 V15 V15-Cat3 0.308392 0.253994 2.17e-01 2.26e-01 2.51e-01
77 V15 V15-Cat4 0.355762 0.426277 5.04e-01 5.47e-01 5.47e-01
78 V15 V15-Cat5 0.001041 0.001623 9.94e-04 2.26e-04 3.06e-07
79 V15 V15-Cat6 0.000161 0.000516 6.35e-04 3.69e-04 7.82e-05
80 V16 V16-Cat1 0.147395 0.135862 1.40e-01 1.50e-01 1.50e-01
81 V16 V16-Cat2 0.171606 0.171205 1.64e-01 1.59e-01 1.64e-01
82 V16 V16-Cat3 0.135333 0.107247 6.84e-02 4.49e-02 3.52e-02
83 V16 V16-Cat4 0.242538 0.260492 2.79e-01 2.80e-01 2.77e-01
84 V16 V16-Cat5 0.224554 0.248058 2.79e-01 3.06e-01 3.25e-01
85 V16 V16-Cat6 0.078574 0.077136 6.97e-02 5.96e-02 4.83e-02
86 V17 V17-Cat1 0.181961 0.224921 2.75e-01 3.14e-01 3.54e-01
87 V17 V17-Cat2 0.172907 0.172655 1.75e-01 1.72e-01 1.69e-01
88 V17 V17-Cat3 0.243380 0.254842 2.65e-01 2.71e-01 2.65e-01
89 V17 V17-Cat4 0.122512 0.098008 7.50e-02 5.99e-02 5.10e-02
90 V17 V17-Cat5 0.197089 0.173737 1.45e-01 1.27e-01 1.08e-01
91 V17 V17-Cat6 0.082150 0.075837 6.53e-02 5.59e-02 5.22e-02
92 V18 V18-Cat1 0.113421 0.105425 9.13e-02 7.57e-02 6.58e-02
93 V18 V18-Cat2 0.541136 0.585410 6.39e-01 6.81e-01 7.29e-01
94 V18 V18-Cat3 0.212346 0.180239 1.54e-01 1.45e-01 1.25e-01
95 V18 V18-Cat4 0.133097 0.128926 1.16e-01 9.78e-02 8.04e-02
96 V19 V19-Cat1 0.161588 0.140610 1.17e-01 1.09e-01 1.03e-01
97 V19 V19-Cat2 0.301880 0.313536 3.16e-01 3.00e-01 2.84e-01
98 V19 V19-Cat3 0.304595 0.339441 3.85e-01 4.26e-01 4.72e-01
99 V19 V19-Cat4 0.231937 0.206414 1.82e-01 1.65e-01 1.41e-01
100 V20 V20-Cat1 0.188485 0.201553 2.12e-01 2.19e-01 2.35e-01
101 V20 V20-Cat2 0.231254 0.213300 1.98e-01 1.90e-01 1.83e-01
102 V20 V20-Cat3 0.402854 0.431543 4.60e-01 4.73e-01 4.72e-01
103 V20 V20-Cat4 0.177407 0.153604 1.30e-01 1.17e-01 1.11e-01
104 V21 V21-Cat1 0.291439 0.339249 3.99e-01 4.47e-01 4.80e-01
105 V21 V21-Cat2 0.195266 0.206700 2.13e-01 2.00e-01 1.82e-01
106 V21 V21-Cat3 0.134619 0.115961 9.77e-02 8.44e-02 7.28e-02
107 V21 V21-Cat4 0.163155 0.164282 1.61e-01 1.54e-01 1.51e-01
108 V21 V21-Cat5 0.087605 0.067845 4.13e-02 2.84e-02 2.43e-02
109 V21 V21-Cat6 0.127915 0.105964 8.88e-02 8.70e-02 8.97e-02
110 V22 V22-Cat1 0.353845 0.393110 4.30e-01 4.58e-01 4.95e-01
111 V22 V22-Cat2 0.258570 0.248252 2.38e-01 2.31e-01 2.19e-01
112 V22 V22-Cat3 0.304569 0.288038 2.68e-01 2.52e-01 2.34e-01
113 V22 V22-Cat4 0.083016 0.070601 6.41e-02 5.92e-02 5.17e-02
114 V23 V23-Cat1 0.075094 0.071572 7.79e-02 8.38e-02 7.72e-02
115 V23 V23-Cat2 0.098889 0.080867 6.51e-02 5.40e-02 4.60e-02
116 V23 V23-Cat3 0.327978 0.341034 3.61e-01 4.03e-01 4.58e-01
117 V23 V23-Cat4 0.205509 0.219643 2.11e-01 1.87e-01 1.67e-01
118 V23 V23-Cat5 0.168429 0.162206 1.66e-01 1.77e-01 1.79e-01
119 V23 V23-Cat6 0.124102 0.124678 1.18e-01 9.60e-02 7.27e-02
120 V24 V24-Cat1 0.151197 0.130124 1.13e-01 1.01e-01 7.72e-02
121 V24 V24-Cat2 0.385733 0.345418 2.89e-01 2.36e-01 1.95e-01
122 V24 V24-Cat3 0.249757 0.229586 2.13e-01 2.12e-01 2.13e-01
123 V24 V24-Cat4 0.213313 0.294873 3.85e-01 4.50e-01 5.15e-01
124 V25 V25-Cat1 0.213057 0.201623 1.83e-01 1.64e-01 1.49e-01
125 V25 V25-Cat2 0.147003 0.110309 7.89e-02 6.51e-02 5.84e-02
126 V25 V25-Cat3 0.376683 0.446406 5.23e-01 5.89e-01 6.54e-01
127 V25 V25-Cat4 0.263257 0.241662 2.15e-01 1.83e-01 1.39e-01
128 V26 V26-Cat1 0.407068 0.408253 4.00e-01 3.71e-01 3.15e-01
129 V26 V26-Cat2 0.205853 0.195390 1.93e-01 2.02e-01 2.05e-01
130 V26 V26-Cat3 0.203517 0.191830 1.69e-01 1.53e-01 1.53e-01
131 V26 V26-Cat4 0.181319 0.203483 2.37e-01 2.74e-01 3.26e-01
132 V26 V26-Cat5 0.002242 0.001045 3.10e-04 7.23e-05 5.92e-06
133 V27 V27-Cat1 0.098952 0.064574 3.70e-02 2.70e-02 2.24e-02
134 V27 V27-Cat2 0.147000 0.129052 1.06e-01 9.16e-02 8.83e-02
135 V27 V27-Cat3 0.413926 0.477579 5.60e-01 6.36e-01 6.95e-01
136 V27 V27-Cat4 0.257137 0.262822 2.48e-01 2.06e-01 1.62e-01
137 V27 V27-Cat5 0.082986 0.065973 4.95e-02 3.98e-02 3.23e-02
138 V28 V28-Cat1 0.162789 0.152142 1.45e-01 1.48e-01 1.53e-01
139 V28 V28-Cat2 0.216774 0.258750 3.12e-01 3.71e-01 4.39e-01
140 V28 V28-Cat3 0.198249 0.161397 1.33e-01 1.27e-01 1.21e-01
141 V28 V28-Cat4 0.147478 0.147008 1.37e-01 1.07e-01 7.74e-02
142 V28 V28-Cat5 0.177291 0.193067 2.00e-01 1.85e-01 1.61e-01
143 V28 V28-Cat6 0.097419 0.087636 7.39e-02 6.16e-02 4.79e-02
144 V29 V29-Cat1 0.161205 0.148828 1.23e-01 9.84e-02 7.97e-02
145 V29 V29-Cat2 0.351848 0.389699 4.28e-01 4.54e-01 4.86e-01
146 V29 V29-Cat3 0.394410 0.404743 4.21e-01 4.29e-01 4.18e-01
147 V29 V29-Cat4 0.088743 0.053975 2.62e-02 1.71e-02 1.69e-02
148 V29 V29-Cat5 0.003003 0.001272 3.80e-04 4.21e-04 3.29e-04
149 V29 V29-Cat6 0.000791 0.001482 1.16e-03 4.06e-04 6.45e-05
150 V30 V30-Cat1 0.125107 0.110867 9.44e-02 7.94e-02 6.57e-02
151 V30 V30-Cat2 0.226068 0.182668 1.30e-01 8.99e-02 6.53e-02
152 V30 V30-Cat3 0.136420 0.100250 6.57e-02 4.96e-02 4.22e-02
153 V30 V30-Cat4 0.511024 0.605816 7.10e-01 7.81e-01 8.27e-01
154 V30 V30-Cat5 0.001382 0.000399 5.54e-06 1.20e-10 5.65e-12
155 V31 V31-Cat1 0.189911 0.213328 2.40e-01 2.51e-01 2.47e-01
156 V31 V31-Cat2 0.128855 0.109379 8.88e-02 7.71e-02 7.19e-02
157 V31 V31-Cat3 0.300060 0.343712 3.91e-01 4.19e-01 4.37e-01
158 V31 V31-Cat4 0.138347 0.098160 6.59e-02 6.20e-02 7.00e-02
159 V31 V31-Cat5 0.102230 0.101983 9.81e-02 9.24e-02 8.79e-02
160 V31 V31-Cat6 0.140596 0.133438 1.16e-01 9.84e-02 8.60e-02
161 V32 V32-Cat1 0.236462 0.249584 2.59e-01 2.65e-01 2.68e-01
162 V32 V32-Cat2 0.221174 0.206664 1.84e-01 1.65e-01 1.51e-01
163 V32 V32-Cat3 0.359929 0.359792 3.64e-01 3.63e-01 3.53e-01
164 V32 V32-Cat4 0.182435 0.183960 1.92e-01 2.07e-01 2.28e-01
165 V33 V33-Cat1 0.165271 0.144629 1.20e-01 9.71e-02 8.23e-02
166 V33 V33-Cat2 0.181101 0.177636 1.75e-01 1.74e-01 1.67e-01
167 V33 V33-Cat3 0.239750 0.233243 2.28e-01 2.27e-01 2.29e-01
168 V33 V33-Cat4 0.144066 0.144048 1.41e-01 1.33e-01 1.29e-01
169 V33 V33-Cat5 0.171627 0.191742 2.11e-01 2.34e-01 2.63e-01
170 V33 V33-Cat6 0.098184 0.108703 1.26e-01 1.34e-01 1.29e-01
171 V34 V34-Cat1 0.142739 0.128452 1.19e-01 1.17e-01 1.12e-01
172 V34 V34-Cat2 0.371022 0.411988 4.49e-01 4.59e-01 4.76e-01
173 V34 V34-Cat3 0.299943 0.261322 2.08e-01 1.73e-01 1.57e-01
174 V34 V34-Cat4 0.186296 0.198238 2.24e-01 2.51e-01 2.55e-01
175 V35 V35-Cat1 0.452647 0.522290 5.87e-01 6.04e-01 6.14e-01
176 V35 V35-Cat2 0.093240 0.069967 5.28e-02 4.59e-02 4.02e-02
177 V35 V35-Cat3 0.175810 0.161466 1.46e-01 1.43e-01 1.45e-01
178 V35 V35-Cat4 0.278303 0.246277 2.14e-01 2.07e-01 2.01e-01
rank6 rank7 rank8 rank9 rank10
1 1.24e-01 1.25e-01 1.26e-01 1.09e-01 8.29e-02
2 1.39e-01 1.38e-01 1.36e-01 1.21e-01 9.46e-02
3 3.40e-01 3.55e-01 3.83e-01 4.61e-01 5.63e-01
4 2.11e-01 2.00e-01 1.89e-01 1.64e-01 1.34e-01
5 1.87e-01 1.82e-01 1.66e-01 1.44e-01 1.26e-01
6 2.95e-01 3.25e-01 3.43e-01 3.64e-01 3.88e-01
7 4.18e-02 2.27e-02 1.07e-02 3.54e-03 1.33e-03
8 2.80e-01 2.93e-01 3.06e-01 3.17e-01 3.29e-01
9 3.83e-01 3.60e-01 3.40e-01 3.15e-01 2.82e-01
10 2.85e-02 2.86e-02 2.86e-02 2.07e-02 8.74e-03
11 7.89e-02 6.67e-02 6.11e-02 5.18e-02 4.04e-02
12 8.07e-01 8.39e-01 8.59e-01 8.83e-01 9.12e-01
13 8.54e-02 6.56e-02 5.12e-02 4.45e-02 3.91e-02
14 9.06e-02 8.92e-02 8.13e-02 6.91e-02 6.11e-02
15 2.15e-01 1.81e-01 1.54e-01 1.15e-01 7.55e-02
16 3.13e-01 3.68e-01 4.34e-01 5.43e-01 6.52e-01
17 2.91e-01 2.71e-01 2.46e-01 2.12e-01 1.76e-01
18 6.46e-02 6.19e-02 5.76e-02 4.13e-02 2.30e-02
19 2.66e-02 2.82e-02 2.69e-02 1.91e-02 1.20e-02
20 5.05e-02 4.61e-02 4.03e-02 3.80e-02 3.78e-02
21 2.50e-01 2.61e-01 2.87e-01 3.84e-01 5.24e-01
22 5.25e-01 5.16e-01 4.94e-01 4.32e-01 3.40e-01
23 1.75e-01 1.77e-01 1.78e-01 1.45e-01 9.80e-02
24 9.22e-04 1.24e-03 1.99e-03 1.88e-03 2.03e-03
25 3.58e-02 2.95e-02 2.63e-02 2.40e-02 2.18e-02
26 5.37e-02 4.48e-02 4.40e-02 4.34e-02 3.63e-02
27 3.46e-03 3.41e-03 3.95e-03 3.60e-03 2.50e-03
28 9.04e-01 9.19e-01 9.22e-01 9.26e-01 9.37e-01
29 2.53e-03 1.61e-03 1.52e-03 1.49e-03 6.29e-04
30 1.68e-02 1.32e-02 1.66e-02 2.06e-02 1.46e-02
31 3.79e-01 3.58e-01 3.40e-01 3.02e-01 2.60e-01
32 3.68e-01 3.87e-01 3.91e-01 4.16e-01 4.77e-01
33 2.36e-01 2.42e-01 2.52e-01 2.61e-01 2.48e-01
34 1.72e-01 1.60e-01 1.35e-01 8.87e-02 5.37e-02
35 2.82e-01 2.71e-01 2.42e-01 2.02e-01 1.67e-01
36 6.15e-02 4.95e-02 4.11e-02 2.86e-02 2.03e-02
37 3.43e-01 3.95e-01 4.78e-01 6.09e-01 7.17e-01
38 2.32e-02 1.86e-02 1.40e-02 7.42e-03 3.10e-03
39 1.18e-01 1.06e-01 9.01e-02 6.44e-02 3.94e-02
40 1.15e-02 9.30e-03 5.38e-03 1.88e-03 4.18e-04
41 6.31e-02 5.63e-02 4.84e-02 3.98e-02 3.04e-02
42 2.28e-02 1.74e-02 1.13e-02 7.18e-03 6.43e-03
43 6.76e-01 7.23e-01 7.69e-01 8.05e-01 8.36e-01
44 5.26e-02 3.61e-02 2.33e-02 1.18e-02 4.54e-03
45 1.74e-01 1.58e-01 1.43e-01 1.35e-01 1.22e-01
46 3.55e-01 3.30e-01 2.96e-01 2.35e-01 1.63e-01
47 6.20e-02 5.10e-02 4.16e-02 2.98e-02 2.06e-02
48 2.21e-01 1.94e-01 1.51e-01 8.76e-02 3.88e-02
49 3.62e-01 4.25e-01 5.11e-01 6.47e-01 7.78e-01
50 1.46e-12 2.71e-13 4.89e-14 4.54e-15 3.49e-17
51 6.36e-02 4.64e-02 2.84e-02 1.63e-02 1.11e-02
52 2.84e-01 3.03e-01 3.05e-01 2.61e-01 2.01e-01
53 6.20e-01 6.28e-01 6.53e-01 7.15e-01 7.86e-01
54 3.26e-02 2.28e-02 1.36e-02 6.85e-03 2.22e-03
55 8.10e-11 1.29e-11 1.78e-12 1.11e-13 2.59e-16
56 2.41e-01 2.33e-01 1.92e-01 1.28e-01 7.40e-02
57 1.81e-02 1.54e-02 1.21e-02 7.31e-03 4.43e-03
58 5.79e-02 4.14e-02 2.30e-02 1.03e-02 4.99e-03
59 5.02e-02 4.09e-02 3.35e-02 2.54e-02 1.66e-02
60 7.89e-02 6.17e-02 4.25e-02 2.43e-02 1.25e-02
61 5.54e-01 6.08e-01 6.97e-01 8.05e-01 8.87e-01
62 4.08e-01 3.73e-01 3.30e-01 2.80e-01 2.34e-01
63 3.16e-01 3.63e-01 4.44e-01 5.60e-01 6.58e-01
64 5.80e-02 7.04e-02 7.37e-02 5.71e-02 3.45e-02
65 1.67e-01 1.56e-01 1.28e-01 9.15e-02 6.77e-02
66 5.08e-02 3.75e-02 2.38e-02 1.18e-02 5.56e-03
67 3.48e-05 1.15e-06 1.04e-08 1.72e-09 8.18e-11
68 7.53e-02 7.51e-02 6.97e-02 5.85e-02 4.80e-02
69 5.00e-02 5.39e-02 5.00e-02 5.04e-02 5.45e-02
70 4.01e-01 3.71e-01 3.25e-01 2.75e-01 2.45e-01
71 3.23e-01 3.58e-01 4.24e-01 5.08e-01 5.67e-01
72 6.08e-02 5.45e-02 4.43e-02 3.36e-02 2.76e-02
73 8.96e-02 8.83e-02 8.74e-02 7.43e-02 5.83e-02
74 5.86e-02 4.68e-02 3.48e-02 2.69e-02 2.48e-02
75 1.50e-01 1.38e-01 1.21e-01 9.15e-02 6.05e-02
76 2.39e-01 2.54e-01 2.29e-01 1.81e-01 1.46e-01
77 5.51e-01 5.61e-01 6.15e-01 7.01e-01 7.69e-01
78 1.59e-05 1.32e-07 4.12e-08 8.17e-09 4.41e-10
79 1.84e-04 1.66e-05 1.00e-06 7.82e-09 7.03e-10
80 1.42e-01 1.35e-01 1.28e-01 1.06e-01 7.90e-02
81 1.76e-01 1.87e-01 2.00e-01 2.07e-01 1.95e-01
82 3.04e-02 2.96e-02 2.72e-02 1.90e-02 1.02e-02
83 2.70e-01 2.45e-01 1.98e-01 1.39e-01 1.02e-01
84 3.44e-01 3.72e-01 4.11e-01 4.92e-01 5.88e-01
85 3.77e-02 3.19e-02 3.50e-02 3.76e-02 2.63e-02
86 3.88e-01 4.11e-01 4.20e-01 4.46e-01 5.03e-01
87 1.76e-01 1.76e-01 1.58e-01 1.43e-01 1.43e-01
88 2.45e-01 2.31e-01 2.45e-01 2.61e-01 2.46e-01
89 5.02e-02 5.47e-02 5.96e-02 5.13e-02 2.95e-02
90 8.79e-02 7.72e-02 7.59e-02 6.83e-02 5.51e-02
91 5.19e-02 5.00e-02 4.20e-02 3.07e-02 2.38e-02
92 5.40e-02 3.99e-02 2.69e-02 1.69e-02 1.10e-02
93 7.86e-01 8.43e-01 8.95e-01 9.41e-01 9.66e-01
94 9.56e-02 6.80e-02 4.71e-02 2.84e-02 1.78e-02
95 6.49e-02 4.90e-02 3.05e-02 1.40e-02 5.61e-03
96 9.12e-02 7.73e-02 6.08e-02 4.27e-02 2.85e-02
97 2.70e-01 2.56e-01 2.26e-01 1.52e-01 7.83e-02
98 5.26e-01 5.78e-01 6.44e-01 7.60e-01 8.65e-01
99 1.13e-01 8.93e-02 6.90e-02 4.48e-02 2.81e-02
100 2.57e-01 2.82e-01 3.27e-01 3.91e-01 4.34e-01
101 1.84e-01 1.93e-01 1.93e-01 1.95e-01 2.05e-01
102 4.51e-01 4.17e-01 3.62e-01 2.81e-01 2.18e-01
103 1.07e-01 1.08e-01 1.18e-01 1.32e-01 1.43e-01
104 5.12e-01 5.46e-01 5.79e-01 6.14e-01 6.43e-01
105 1.69e-01 1.69e-01 1.78e-01 1.68e-01 1.38e-01
106 6.54e-02 5.63e-02 4.39e-02 3.16e-02 2.40e-02
107 1.46e-01 1.37e-01 1.31e-01 1.40e-01 1.54e-01
108 1.82e-02 1.25e-02 9.24e-03 6.62e-03 5.79e-03
109 8.86e-02 7.92e-02 5.90e-02 3.98e-02 3.45e-02
110 5.39e-01 5.79e-01 6.23e-01 6.85e-01 7.41e-01
111 2.02e-01 1.85e-01 1.71e-01 1.46e-01 1.15e-01
112 2.11e-01 1.92e-01 1.69e-01 1.43e-01 1.26e-01
113 4.78e-02 4.41e-02 3.67e-02 2.63e-02 1.80e-02
114 7.02e-02 6.55e-02 6.12e-02 5.81e-02 5.39e-02
115 4.28e-02 3.94e-02 3.33e-02 2.45e-02 1.55e-02
116 5.13e-01 5.57e-01 5.95e-01 6.46e-01 6.95e-01
117 1.49e-01 1.39e-01 1.40e-01 1.40e-01 1.36e-01
118 1.69e-01 1.57e-01 1.40e-01 1.12e-01 8.67e-02
119 5.53e-02 4.21e-02 3.06e-02 1.91e-02 1.23e-02
120 5.66e-02 5.05e-02 4.76e-02 3.43e-02 1.78e-02
121 1.69e-01 1.53e-01 1.44e-01 1.29e-01 1.05e-01
122 1.98e-01 1.74e-01 1.61e-01 1.41e-01 1.11e-01
123 5.76e-01 6.22e-01 6.47e-01 6.95e-01 7.66e-01
124 1.39e-01 1.31e-01 1.18e-01 9.62e-02 7.66e-02
125 5.46e-02 5.27e-02 5.30e-02 5.82e-02 6.74e-02
126 7.05e-01 7.39e-01 7.70e-01 8.00e-01 8.18e-01
127 1.01e-01 7.75e-02 5.93e-02 4.52e-02 3.82e-02
128 2.51e-01 2.08e-01 1.69e-01 1.20e-01 8.16e-02
129 1.99e-01 1.91e-01 1.85e-01 1.55e-01 1.07e-01
130 1.60e-01 1.52e-01 1.32e-01 1.12e-01 9.74e-02
131 3.90e-01 4.49e-01 5.14e-01 6.13e-01 7.14e-01
132 5.09e-08 4.06e-09 2.04e-09 4.98e-10 2.05e-11
133 2.10e-02 2.06e-02 1.77e-02 1.14e-02 6.53e-03
134 9.07e-02 8.82e-02 7.60e-02 6.12e-02 5.27e-02
135 7.35e-01 7.63e-01 7.88e-01 8.23e-01 8.61e-01
136 1.29e-01 1.12e-01 1.06e-01 9.35e-02 6.99e-02
137 2.44e-02 1.69e-02 1.21e-02 1.06e-02 9.75e-03
138 1.51e-01 1.43e-01 1.21e-01 8.90e-02 6.25e-02
139 4.96e-01 5.36e-01 5.94e-01 7.09e-01 8.17e-01
140 1.12e-01 9.75e-02 7.74e-02 5.05e-02 2.92e-02
141 6.00e-02 5.22e-02 4.06e-02 1.95e-02 5.42e-03
142 1.45e-01 1.42e-01 1.43e-01 1.20e-01 8.12e-02
143 3.65e-02 2.99e-02 2.35e-02 1.27e-02 4.29e-03
144 6.98e-02 7.30e-02 7.21e-02 4.74e-02 2.47e-02
145 5.34e-01 5.89e-01 6.55e-01 7.62e-01 8.56e-01
146 3.79e-01 3.22e-01 2.60e-01 1.83e-01 1.15e-01
147 1.78e-02 1.64e-02 1.30e-02 7.60e-03 4.09e-03
148 1.00e-04 9.23e-06 2.13e-07 4.66e-08 5.11e-09
149 8.06e-06 3.40e-06 8.69e-07 1.47e-07 1.51e-08
150 5.51e-02 4.96e-02 4.85e-02 4.38e-02 4.09e-02
151 5.33e-02 4.94e-02 4.91e-02 3.72e-02 2.17e-02
152 3.43e-02 2.50e-02 1.61e-02 8.22e-03 4.09e-03
153 8.57e-01 8.76e-01 8.86e-01 9.11e-01 9.33e-01
154 1.46e-12 2.71e-13 4.89e-14 4.53e-15 3.49e-17
155 2.38e-01 2.19e-01 1.83e-01 1.32e-01 9.49e-02
156 6.89e-02 6.53e-02 5.57e-02 3.57e-02 1.88e-02
157 4.48e-01 4.64e-01 5.15e-01 6.23e-01 7.28e-01
158 7.77e-02 8.12e-02 8.21e-02 7.83e-02 6.92e-02
159 8.78e-02 9.21e-02 8.86e-02 6.94e-02 4.83e-02
160 7.94e-02 7.79e-02 7.55e-02 6.17e-02 4.08e-02
161 2.60e-01 2.41e-01 2.26e-01 2.04e-01 1.70e-01
162 1.43e-01 1.35e-01 1.30e-01 1.29e-01 1.21e-01
163 3.54e-01 3.72e-01 3.70e-01 3.33e-01 3.02e-01
164 2.43e-01 2.53e-01 2.74e-01 3.34e-01 4.07e-01
165 7.99e-02 8.09e-02 7.54e-02 5.67e-02 3.97e-02
166 1.55e-01 1.48e-01 1.49e-01 1.42e-01 1.17e-01
167 2.27e-01 2.23e-01 2.18e-01 2.02e-01 1.89e-01
168 1.23e-01 1.15e-01 1.09e-01 9.78e-02 8.18e-02
169 2.92e-01 3.15e-01 3.30e-01 3.86e-01 4.64e-01
170 1.23e-01 1.18e-01 1.19e-01 1.15e-01 1.09e-01
171 1.06e-01 1.10e-01 1.30e-01 1.28e-01 9.54e-02
172 5.09e-01 5.37e-01 5.50e-01 5.75e-01 6.15e-01
173 1.45e-01 1.29e-01 1.14e-01 9.63e-02 7.54e-02
174 2.40e-01 2.24e-01 2.06e-01 2.00e-01 2.14e-01
175 6.29e-01 6.50e-01 6.95e-01 7.68e-01 8.35e-01
176 3.43e-02 2.88e-02 2.33e-02 1.61e-02 1.06e-02
177 1.51e-01 1.51e-01 1.30e-01 1.03e-01 8.64e-02
178 1.86e-01 1.70e-01 1.51e-01 1.12e-01 6.83e-02
Test Profile
Rank 1 Rank 2 Rank 3 Rank 4 Rank 5 Rank 6
Test Reference Profile 11.221 12.526 13.999 15.103 16.155 17.284
Latent Rank Ditribution 605.000 453.000 513.000 462.000 504.000 449.000
Rank Membership Distribution 537.070 500.858 510.664 511.630 517.705 511.854
Rank 7 Rank 8 Rank 9 Rank 10
Test Reference Profile 18.443 19.889 22.255 24.641
Latent Rank Ditribution 494.000 533.000 460.000 527.000
Rank Membership Distribution 502.493 483.411 442.111 482.205
Item Fit Indices
model_log_like bench_log_like null_log_like model_Chi_sq null_Chi_sq
V1 -7567.150 -7543.816 -7669.959 46.668 252.286
V2 -6199.571 -6147.573 -6493.515 103.997 691.883
V3 -3648.104 -3626.982 -3832.371 42.242 410.777
V4 -7511.898 -7502.414 -7814.675 18.967 624.521
V5 -5899.644 -5868.361 -6080.987 62.565 425.253
V6 -2519.741 -2506.394 -2619.774 26.693 226.759
V7 -5955.665 -6002.712 -6049.723 0.000 94.022
V8 -7502.169 -7493.878 -7915.418 16.581 843.079
V9 -5363.749 -5344.718 -5651.512 38.062 613.589
V10 -5863.850 -5832.549 -6278.749 62.603 892.400
V11 -4584.566 -4559.094 -4739.475 50.942 360.761
V12 -5957.646 -5945.691 -6334.969 23.911 778.557
V13 -6692.829 -6676.599 -7052.877 32.460 752.556
V14 -7272.464 -7264.750 -7484.136 15.430 438.773
V15 -5494.622 -5482.526 -5671.696 24.191 378.339
V16 -7695.819 -7677.771 -7932.825 36.096 510.108
V17 -7668.913 -7648.705 -7840.940 40.415 384.469
V18 -3796.026 -3783.318 -4111.067 25.415 655.498
V19 -5510.826 -5480.577 -5875.229 60.497 789.305
V20 -6408.038 -6398.886 -6530.508 18.303 263.243
V21 -7059.259 -7044.781 -7265.923 28.956 442.284
V22 -5566.685 -5555.075 -5725.569 23.221 340.988
V23 -7106.103 -7077.207 -7325.641 57.792 496.868
V24 -5624.034 -5595.718 -5977.572 56.632 763.708
V25 -4929.768 -4919.555 -5213.298 20.426 587.487
V26 -6249.252 -6231.147 -6623.748 36.208 785.201
V27 -4811.700 -4793.779 -5093.165 35.843 598.773
V28 -7120.441 -7076.521 -7566.925 87.841 980.807
V29 -4785.925 -4746.734 -5115.821 78.381 738.173
V30 -3467.230 -3457.352 -3770.525 19.755 626.346
V31 -7343.773 -7310.918 -7557.430 65.710 493.023
V32 -6628.563 -6610.731 -6707.124 35.664 192.786
V33 -8455.109 -8439.761 -8583.957 30.696 288.392
V34 -6061.489 -6028.028 -6176.327 66.922 296.598
V35 -4914.306 -4897.214 -5070.488 34.183 346.546
model_df null_df NFI RFI IFI TLI CFI RMSEA AIC CAIC
V1 114.8 136 0.815 0.781 1.00 1.000 1.00 0.000 -182.932 -1045.515
V2 86.1 102 0.850 0.822 0.97 0.964 0.97 0.006 -68.203 -715.313
V3 86.1 102 0.897 0.878 1.00 1.000 1.00 0.000 -129.958 -776.026
V4 143.5 170 0.970 0.964 1.00 1.000 1.00 0.000 -268.033 -1346.664
V5 86.1 102 0.853 0.826 1.00 1.000 1.00 0.000 -109.635 -756.814
V6 143.5 170 0.882 0.861 1.00 1.000 1.00 0.000 -260.307 -1338.880
V7 86.1 102 1.000 1.000 1.00 0.000 0.00 0.000 -172.200 -819.120
V8 143.5 170 0.980 0.977 1.00 1.000 1.00 0.000 -270.419 -1349.108
V9 143.5 170 0.938 0.927 1.00 1.000 1.00 0.000 -248.938 -1327.627
V10 114.8 136 0.930 0.917 1.00 1.000 1.00 0.000 -166.997 -1029.764
V11 114.8 136 0.859 0.833 1.00 1.000 1.00 0.000 -178.658 -1041.586
V12 143.5 170 0.969 0.964 1.00 1.000 1.00 0.000 -263.089 -1341.691
V13 143.5 170 0.957 0.949 1.00 1.000 1.00 0.000 -254.540 -1333.171
V14 143.5 170 0.965 0.958 1.00 1.000 1.00 0.000 -271.570 -1349.626
V15 143.5 170 0.936 0.924 1.00 1.000 1.00 0.000 -262.809 -1341.497
V16 143.5 170 0.929 0.916 1.00 1.000 1.00 0.000 -250.904 -1329.506
V17 143.5 170 0.895 0.875 1.00 1.000 1.00 0.000 -246.585 -1322.725
V18 86.1 102 0.961 0.954 1.00 1.000 1.00 0.000 -146.785 -793.998
V19 86.1 102 0.923 0.909 1.00 1.000 1.00 0.000 -111.703 -758.795
V20 86.1 102 0.930 0.918 1.00 1.000 1.00 0.000 -153.897 -801.058
V21 143.5 170 0.935 0.922 1.00 1.000 1.00 0.000 -258.044 -1336.618
V22 86.1 102 0.932 0.919 1.00 1.000 1.00 0.000 -148.979 -795.933
V23 143.5 170 0.884 0.862 1.00 1.000 1.00 0.000 -229.208 -1307.724
V24 86.1 102 0.926 0.912 1.00 1.000 1.00 0.000 -115.568 -762.764
V25 86.1 102 0.965 0.959 1.00 1.000 1.00 0.000 -151.774 -798.935
V26 114.8 136 0.954 0.945 1.00 1.000 1.00 0.000 -193.392 -1056.158
V27 114.8 136 0.940 0.929 1.00 1.000 1.00 0.000 -193.757 -1056.017
V28 143.5 170 0.910 0.894 1.00 1.000 1.00 0.000 -199.159 -1277.790
V29 143.5 170 0.894 0.874 1.00 1.000 1.00 0.000 -208.619 -1287.279
V30 114.8 136 0.968 0.963 1.00 1.000 1.00 0.000 -209.845 -1072.680
V31 143.5 170 0.867 0.842 1.00 1.000 1.00 0.000 -221.290 -1299.950
V32 86.1 102 0.815 0.781 1.00 1.000 1.00 0.000 -136.536 -783.318
V33 143.5 170 0.894 0.874 1.00 1.000 1.00 0.000 -256.304 -1334.906
V34 86.1 102 0.774 0.733 1.00 1.000 1.00 0.000 -105.278 -752.439
V35 86.1 102 0.901 0.883 1.00 1.000 1.00 0.000 -138.017 -785.161
BIC
V1 -930.715
V2 -629.213
V3 -689.926
V4 -1203.164
V5 -670.714
V6 -1195.380
V7 -733.020
V8 -1205.608
V9 -1184.127
V10 -914.964
V11 -926.786
V12 -1198.191
V13 -1189.671
V14 -1206.126
V15 -1197.997
V16 -1186.006
V17 -1179.225
V18 -707.898
V19 -672.695
V20 -714.958
V21 -1193.118
V22 -709.833
V23 -1164.224
V24 -676.664
V25 -712.835
V26 -941.358
V27 -941.217
V28 -1134.290
V29 -1143.779
V30 -957.880
V31 -1156.450
V32 -697.218
V33 -1191.406
V34 -666.339
V35 -699.061
Model Fit Indices
Number of Latent rank: 10
Number of EM cycle: 3
value
model_log_like -209248.370
bench_log_like -208571.836
null_log_like -217753.915
model_Chi_sq 1424.270
null_Chi_sq 18364.158
model_df 4104.100
null_df 4862.000
NFI 0.922
RFI 0.908
IFI 1.000
TLI 1.000
CFI 1.000
RMSEA 0.000
AIC -6783.930
CAIC -52217.449
BIC -48113.349
可視化（baseグラフィックス）
plot(result.LRArated, type = "ScoreFreq")
plot(result.LRArated, type = "ScoreRank")
plot(result.LRArated, type = "ICRP", items = 1:6, nc = 3, nr = 2)
plot(result.LRArated, type = "RMP", students = 1:6, nc = 3, nr = 2)
可視化（ggExametrika）
plotScoreFreq_gg(result.LRArated)
plotScoreRank_gg(result.LRArated)
plotICRP_gg(result.LRArated, items = 1)
順序データ
サンプルデータJ15S3810（4件法）で順序データの分析例を示します。
result.LRAord <- LRA(J15S3810, nrank = 3, mic = TRUE)
result.LRAord
Monotonic increasing IRP option is TRUE.
Test Statistics
value
SampleSize 3810.0000000
TestLength 15.0000000
Median 15.0000000
Max 27.0000000
Min 0.0000000
Range 27.0000000
Mean 14.9939633
SD 4.5139980
Skewness 0.3003000
Kurtosis -0.4333525
Alpha 0.4496500
Item Statistics
ItemLabel Obs ObsRatio ItemMean ItemSD ItemCORR ItemCORR_R
1 V1 3810 1.000 1.82 0.933 0.630 0.479
2 V2 3810 1.000 1.81 0.821 0.534 0.384
3 V3 3810 1.000 2.06 0.855 0.493 0.329
4 V4 2046 0.537 1.59 0.929 0.634 0.498
5 V5 2046 0.537 1.65 0.918 0.595 0.453
6 V6 2046 0.537 1.47 1.105 0.709 0.566
7 V7 985 0.259 1.39 0.819 0.554 0.381
8 V8 985 0.259 0.71 0.793 0.454 0.269
9 V9 985 0.259 1.35 0.910 0.522 0.319
10 V10 1513 0.397 2.04 0.827 0.486 0.311
11 V11 1513 0.397 1.42 0.966 0.593 0.408
12 V12 1513 0.397 1.85 0.822 0.360 0.172
13 V13 3076 0.807 1.48 0.928 0.616 0.457
14 V14 3076 0.807 1.73 0.876 0.353 0.163
15 V15 3076 0.807 1.45 0.757 0.526 0.384
Item Category Reference Profile
ItemLabel CategoryLabel rank1 rank2 rank3
1 V1 V1-Cat1 0.17393 0.06951 0.00704
2 V1 V1-Cat2 0.42330 0.27640 0.07185
3 V1 V1-Cat3 0.33817 0.44564 0.31088
4 V1 V1-Cat4 0.06460 0.20845 0.61023
5 V2 V2-Cat1 0.09199 0.04891 0.01161
6 V2 V2-Cat2 0.41088 0.28949 0.12343
7 V2 V2-Cat3 0.43340 0.51812 0.39887
8 V2 V2-Cat4 0.06373 0.14348 0.46609
9 V3 V3-Cat1 0.09074 0.02676 0.00868
10 V3 V3-Cat2 0.29715 0.19562 0.09573
11 V3 V3-Cat3 0.42516 0.41144 0.35395
12 V3 V3-Cat4 0.18695 0.36617 0.54165
13 V4 V4-Cat1 0.27087 0.10688 0.02022
14 V4 V4-Cat2 0.47221 0.35211 0.16032
15 V4 V4-Cat3 0.23312 0.43312 0.42526
16 V4 V4-Cat4 0.02380 0.10789 0.39420
17 V5 V5-Cat1 0.22340 0.09038 0.02552
18 V5 V5-Cat2 0.45741 0.36696 0.14520
19 V5 V5-Cat3 0.27537 0.41469 0.42625
20 V5 V5-Cat4 0.04382 0.12797 0.40303
21 V6 V6-Cat1 0.43038 0.25635 0.04169
22 V6 V6-Cat2 0.41436 0.37635 0.11136
23 V6 V6-Cat3 0.13945 0.24502 0.26558
24 V6 V6-Cat4 0.01581 0.12228 0.58137
25 V7 V7-Cat1 0.19342 0.08500 0.02569
26 V7 V7-Cat2 0.52560 0.48260 0.23858
27 V7 V7-Cat3 0.25818 0.38193 0.38562
28 V7 V7-Cat4 0.02281 0.05046 0.35011
29 V8 V8-Cat1 0.56243 0.46781 0.27695
30 V8 V8-Cat2 0.33366 0.42709 0.32737
31 V8 V8-Cat3 0.09674 0.09705 0.28664
32 V8 V8-Cat4 0.00718 0.00805 0.10904
33 V9 V9-Cat1 0.26564 0.15281 0.06193
34 V9 V9-Cat2 0.44314 0.40111 0.25979
35 V9 V9-Cat3 0.25546 0.33277 0.37397
36 V9 V9-Cat4 0.03576 0.11331 0.30432
37 V10 V10-Cat1 0.08296 0.02333 0.01380
38 V10 V10-Cat2 0.32586 0.18196 0.06768
39 V10 V10-Cat3 0.41930 0.47685 0.41845
40 V10 V10-Cat4 0.17188 0.31785 0.50008
41 V11 V11-Cat1 0.29385 0.19159 0.05163
42 V11 V11-Cat2 0.43936 0.44759 0.17525
43 V11 V11-Cat3 0.23040 0.28055 0.37228
44 V11 V11-Cat4 0.03638 0.08028 0.40084
45 V12 V12-Cat1 0.08050 0.03378 0.02447
46 V12 V12-Cat2 0.35319 0.27987 0.20563
47 V12 V12-Cat3 0.39439 0.45647 0.48503
48 V12 V12-Cat4 0.17192 0.22988 0.28487
49 V13 V13-Cat1 0.23012 0.14655 0.02526
50 V13 V13-Cat2 0.52102 0.44594 0.18083
51 V13 V13-Cat3 0.22398 0.33397 0.34235
52 V13 V13-Cat4 0.02488 0.07354 0.45155
53 V14 V14-Cat1 0.11483 0.07507 0.05915
54 V14 V14-Cat2 0.37410 0.28213 0.22853
55 V14 V14-Cat3 0.36439 0.44259 0.44626
56 V14 V14-Cat4 0.14668 0.20021 0.26606
57 V15 V15-Cat1 0.15989 0.06605 0.01194
58 V15 V15-Cat2 0.57231 0.45914 0.28880
59 V15 V15-Cat3 0.25821 0.43886 0.48419
60 V15 V15-Cat4 0.00959 0.03596 0.21506
Test Profile
Rank 1 Rank 2 Rank 3
Test Reference Profile 18.132 23.240 31.867
Latent Rank Ditribution 1400.000 1360.000 1050.000
Rank Membership Distribution 1390.233 1326.565 1093.202
Item Fit Indices
model_log_like bench_log_like null_log_like model_Chi_sq null_Chi_sq
V1 -4194.252 -4138.683 -4922.273 111.139 1567.180
V2 -4130.419 -4096.318 -4574.412 68.203 956.188
V3 -4294.276 -4212.421 -4562.273 163.711 699.705
V4 -2308.585 -2216.974 -2675.639 183.221 917.331
V5 -2351.710 -2295.513 -2652.801 112.395 714.576
V6 -2266.300 -2168.314 -2823.022 195.972 1309.416
V7 -1070.247 -1014.803 -1184.386 110.888 339.167
V8 -1006.878 -983.347 -1068.390 47.061 170.085
V9 -1198.215 -1143.101 -1270.518 110.228 254.833
V10 -1668.660 -1594.943 -1785.080 147.434 380.274
V11 -1791.440 -1762.699 -2015.011 57.482 504.624
V12 -1782.452 -1746.861 -1814.057 71.183 134.393
V13 -3450.743 -3336.976 -4001.750 227.532 1329.547
V14 -3810.641 -3807.989 -3868.310 5.304 120.643
V15 -3144.090 -3069.644 -3488.638 148.893 837.988
model_df null_df NFI RFI IFI TLI CFI RMSEA AIC CAIC
V1 36.616 42 0.929 0.919 0.951 0.944 0.951 0.023 37.907 -227.388
V2 36.616 42 0.929 0.918 0.966 0.960 0.965 0.015 -5.029 -270.324
V3 36.616 42 0.766 0.732 0.808 0.778 0.807 0.030 90.479 -174.816
V4 36.616 42 0.800 0.771 0.834 0.808 0.833 0.044 109.990 -132.540
V5 36.616 42 0.843 0.820 0.888 0.871 0.887 0.032 39.163 -203.367
V6 36.616 42 0.850 0.828 0.875 0.856 0.874 0.046 122.741 -119.789
V7 36.616 42 0.673 0.625 0.755 0.713 0.750 0.045 37.656 -178.107
V8 36.616 42 0.723 0.683 0.922 0.906 0.918 0.017 -26.170 -241.934
V9 36.616 42 0.567 0.504 0.663 0.603 0.654 0.045 36.996 -178.768
V10 36.616 42 0.612 0.555 0.678 0.624 0.672 0.045 74.202 -157.277
V11 36.616 42 0.886 0.869 0.955 0.948 0.955 0.019 -15.750 -247.229
V12 36.616 42 0.470 0.392 0.646 0.571 0.626 0.025 -2.049 -233.528
V13 36.616 42 0.829 0.804 0.852 0.830 0.852 0.041 154.301 -103.159
V14 36.616 42 0.956 0.950 1.000 1.000 1.000 0.000 -67.927 -325.387
V15 36.616 42 0.822 0.796 0.860 0.838 0.859 0.032 75.661 -181.798
BIC
V1 -190.773
V2 -233.708
V3 -138.200
V4 -95.925
V5 -166.751
V6 -83.173
V7 -141.492
V8 -205.318
V9 -142.152
V10 -120.662
V11 -210.614
V12 -196.912
V13 -66.543
V14 -288.771
V15 -145.183
Model Fit Indices
Number of Latent rank: 3
Number of EM cycle: 9
value
model_log_like -38467.180
bench_log_like -37588.585
null_log_like -42706.560
model_Chi_sq 1760.646
null_Chi_sq 10235.950
model_df 549.237
null_df 630.000
NFI 0.828
RFI 0.803
IFI 0.875
TLI 0.855
CFI 0.874
RMSEA 0.008
AIC 662.172
CAIC -4524.057
BIC -3974.820
可視化（baseグラフィックス）
plot(result.LRAord, type = "ScoreFreq")
plot(result.LRAord, type = "ScoreRank")
plot(result.LRAord, type = "ICBR", items = 1:6, nc = 3, nr = 2)
plot(result.LRAord, type = "ICRP", items = 1:6, nc = 3, nr = 2)
plot(result.LRAord, type = "RMP", students = 1:6, nc = 3, nr = 2)
可視化（ggExametrika）
plotICBR_gg(result.LRAord, items = 1)
plotICRP_gg(result.LRAord, items = 1)
plotRMP_gg(result.LRAord)[[1]]
