Se compararon los paquetes IRTpp y MIRT, usando los valores por defecto de cada paquete, algunos de los parametros son :
- epsilon de convergencia : 0.00002
- Iteraciones maximas BFGS : 15
- Valores Iniciales : Metodo de Andrade
- epsilon de convergencia : 0.00001
- Iteraciones BFGS : Algoritmo adaptativo
- Valores Iniciales : MIRT
Los siguientes escenarios de pruebas fueron considerados :
## dataset.models dataset.items dataset.individuals
## [1,] "1PL" 100 10000
## [2,] "1PL" 10 1000
## [3,] "1PL" 20 2000
## [4,] "1PL" 50 5000
## [5,] "2PL" 100 10000
## [6,] "2PL" 10 1000
## [7,] "2PL" 20 2000
## [8,] "2PL" 50 5000
## [9,] "3PL" 100 10000
## [10,] "3PL" 10 1000
## [11,] "3PL" 20 2000
## [12,] "3PL" 50 5000
## dataset.models dataset.items dataset.individuals Estimacion
## [1,] "1PL" 100 10000 0.8043309
## [2,] "1PL" 10 1000 19.1358
## [3,] "1PL" 20 2000 5.457581
## [4,] "1PL" 50 5000 2.116401
## [5,] "2PL" 100 10000 1.387647
## [6,] "2PL" 10 1000 11.67753
## [7,] "2PL" 20 2000 4.156149
## [8,] "2PL" 50 5000 2.443699
## [9,] "3PL" 100 10000 5.805688
## [10,] "3PL" 10 1000 13.49596
## [11,] "3PL" 20 2000 20.16917
## [12,] "3PL" 50 5000 14.09623
## EAP MAP
## [1,] 0.6286856 24.46091
## [2,] 7.552989 122.0999
## [3,] 2.324178 80.27191
## [4,] 1.01496 43.23527
## [5,] 0.6116914 25.80069
## [6,] 3.575829 138.4676
## [7,] 2.23532 83.96392
## [8,] 0.9698576 44.62752
## [9,] 0.465441 21.38497
## [10,] 2.760523 101.3315
## [11,] 1.452084 67.59496
## [12,] 1.091339 30.84445
Bajo la linea MIRT es mas rapido que IRTpp
Bajo la linea MIRT es mas rapido que IRTpp
Bajo la linea MIRT es mas rapido que IRTpp , en este caso la linea no alcanza a ser vista
## dataset.models dataset.items dataset.individuals mirt irtpp
## [1,] "1PL" 100 10000 2.8532 3.54774
## [2,] "1PL" 10 1000 0.42768 0.033335
## [3,] "1PL" 20 2000 0.412825 0.0758
## [4,] "1PL" 50 5000 1.29586 0.61471
## [5,] "2PL" 100 10000 5.84846 4.21822
## [6,] "2PL" 10 1000 0.371065 0.04434
## [7,] "2PL" 20 2000 0.561675 0.135605
## [8,] "2PL" 50 5000 2.23561 0.91653
## [9,] "3PL" 100 10000 47.65388 8.4123
## [10,] "3PL" 10 1000 1.190255 0.12141
## [11,] "3PL" 20 2000 3.66057 0.22583
## [12,] "3PL" 50 5000 18.51232 1.46911
## m-eap m-map i-eap i-map
## [1,] 2.5068 26.84008 3.988 1.09754
## [2,] 0.14547 0.81734 0.019725 0.007135
## [3,] 0.36674 3.47409 0.158655 0.045055
## [4,] 1.0167 11.06349 1.00231 0.25597
## [5,] 2.5327 27.13292 4.14066 1.05296
## [6,] 0.074625 0.97658 0.02085 0.007105
## [7,] 0.3936 3.861165 0.176315 0.046085
## [8,] 1.08572 12.62563 1.12 0.28327
## [9,] 2.42328 30.42788 5.20834 1.42456
## [10,] 0.06756 0.8427 0.02449 0.00834
## [11,] 0.301315 3.872315 0.209005 0.06582
## [12,] 1.52596 11.70899 1.4225 0.57898
Bajo la linea IRTpp tuvo un tiempo mas bajo que MIRT
Bajo la linea IRTpp tuvo un tiempo mas bajo que MIRT
Bajo la linea IRTpp tuvo un tiempo mas bajo que MIRT
##Log verosimilitudes
Mas negativos se considera mejor (minimizando)
La ultimas columnas indican la proporcion de los que fueron minimos en el conjunto de experimentos
## dataset.models dataset.items dataset.individuals ll.irtpp.eap
## [1,] "1PL" 100 10000 -918400
## [2,] "1PL" 10 1000 -3596
## [3,] "1PL" 20 2000 -34100
## [4,] "1PL" 50 5000 -227900
## [5,] "2PL" 100 10000 -878100
## [6,] "2PL" 10 1000 -3479
## [7,] "2PL" 20 2000 -33940
## [8,] "2PL" 50 5000 -223200
## [9,] "3PL" 100 10000 -949700
## [10,] "3PL" 10 1000 -3447
## [11,] "3PL" 20 2000 -33160
## [12,] "3PL" 50 5000 -228300
## ll.mirt.eap ll.irtpp.map ll.mirt.map w.irtpp w.mirt
## [1,] -864700 -917200 -864700 1 0
## [2,] -3409 -3591 -3409 1 0
## [3,] -32900 -33990 -32900 1 0
## [4,] -215100 -227300 -215100 1 0
## [5,] -872600 -876000 -872600 1 0
## [6,] -3460 -3462 -3460 1 0
## [7,] -33520 -33740 -33520 1 0
## [8,] -222900 -222300 -222900 0.97 0.03
## [9,] -809900 -940000 -809900 1 0
## [10,] -3502 -3434 -3502 0.045 0.955
## [11,] -31420 -32830 -31420 0.99 0.01
## [12,] -201600 -225300 -201600 1 0
Sobre la linea indica que IRTpp tuvo una menor logverosimilitud que MIRT
Sobre la linea indica que IRTpp tuvo una menor logverosimilitud que MIRT
A continuacion se detalla como se acercaron los parametros estimados a los parametros poblacionales
## dataset.models dataset.items dataset.individuals a b
## [1,] "1PL" 100 10000 "irtpp" "mirt"
## [2,] "1PL" 10 1000 "irtpp" "mirt"
## [3,] "1PL" 20 2000 "irtpp" "mirt"
## [4,] "1PL" 50 5000 "irtpp" "mirt"
## [5,] "2PL" 100 10000 "irtpp" "mirt"
## [6,] "2PL" 10 1000 "mirt" "mirt"
## [7,] "2PL" 20 2000 "irtpp" "irtpp"
## [8,] "2PL" 50 5000 "irtpp" "irtpp"
## [9,] "3PL" 100 10000 "mirt" "mirt"
## [10,] "3PL" 10 1000 "irtpp" "irtpp"
## [11,] "3PL" 20 2000 "mirt" "mirt"
## [12,] "3PL" 50 5000 "mirt" "mirt"
## c
## [1,] "irtpp"
## [2,] "irtpp"
## [3,] "irtpp"
## [4,] "irtpp"
## [5,] "irtpp"
## [6,] "irtpp"
## [7,] "irtpp"
## [8,] "irtpp"
## [9,] "irtpp"
## [10,] "mirt"
## [11,] "mirt"
## [12,] "irtpp"
## $a
##
## irtpp mirt
## 4 4
##
## $b
##
## irtpp mirt
## 3 5
##
## $c
##
## irtpp mirt
## 2 2
## irtpp-a irtpp-b irtpp-c
## [1,] 0.000000000 0.0097954701 0.000000000
## [2,] 0.000000000 0.0009041383 0.000000000
## [3,] 0.000000000 0.0003851609 0.000000000
## [4,] 0.000000000 0.0015585453 0.000000000
## [5,] 0.008009260 0.0092439561 0.000000000
## [6,] 0.006987940 0.0091618297 0.000000000
## [7,] 0.001427794 0.0019494485 0.000000000
## [8,] 0.004881142 0.0044550297 0.000000000
## [9,] 0.063597366 0.1802555132 0.016494821
## [10,] 0.009143821 0.0096135408 0.003935445
## [11,] 0.004651412 0.0113272641 0.002662803
## [12,] 0.010672767 0.0225873910 0.006935525
## mirt-a mirt-b mirt-c
## [1,] 0.000000000 0.0053051474 0.000000000
## [2,] 0.000000000 0.0006756141 0.000000000
## [3,] 0.000000000 0.0003470963 0.000000000
## [4,] 0.000000000 0.0013058941 0.000000000
## [5,] 0.009001292 0.0089465538 0.000000000
## [6,] 0.006979964 0.0091442628 0.000000000
## [7,] 0.001441320 0.0019848097 0.000000000
## [8,] 0.004922750 0.0045400535 0.000000000
## [9,] 0.028216508 0.0578874556 0.019167559
## [10,] 0.010252351 0.0097018076 0.003833067
## [11,] 0.004150950 0.0092282066 0.002628287
## [12,] 0.008918215 0.0197040444 0.007253595
