Ex3. Calibrando modelo de Rasch
Araê Cainã e Gustavo Martins
06/07/2021
library(tidyverse)
library(readxl)
library(TAM)
library(CTT)
library(WrightMap)
library(RColorBrewer)
library(psych)
library(mirt)Exercicio 1. Análise de rasch com gf_matrix
gf_matrix <- read_excel("gf_matrix.xlsx", range = "A2:R1184")- Calibrando o modelo de Rasch com TAM
mod1 <- tam.jml(gf_matrix[ , 2:17])## ....................................................
## Iteration 1 2021-07-06 16:58:24
## MLE/WLE estimation |----
## Item parameter estimation |----
## Deviance= 18109.2789
## Maximum MLE/WLE change: 0.694528
## Maximum item parameter change: 0.392883
## ....................................................
## Iteration 2 2021-07-06 16:58:24
## MLE/WLE estimation |---
## Item parameter estimation |---
## Deviance= 18084.0385 | Deviance change: 25.2404
## Maximum MLE/WLE change: 0.161007
## Maximum item parameter change: 0.081043
## ....................................................
## Iteration 3 2021-07-06 16:58:24
## MLE/WLE estimation |---
## Item parameter estimation |---
## Deviance= 18081.574 | Deviance change: 2.4644
## Maximum MLE/WLE change: 0.047064
## Maximum item parameter change: 0.020993
## ....................................................
## Iteration 4 2021-07-06 16:58:24
## MLE/WLE estimation |--
## Item parameter estimation |--
## Deviance= 18081.2789 | Deviance change: 0.2951
## Maximum MLE/WLE change: 0.012848
## Maximum item parameter change: 0.005696
## ....................................................
## Iteration 5 2021-07-06 16:58:24
## MLE/WLE estimation |--
## Item parameter estimation |--
## Deviance= 18081.2269 | Deviance change: 0.052
## Maximum MLE/WLE change: 0.003505
## Maximum item parameter change: 0.00156
## ....................................................
## Iteration 6 2021-07-06 16:58:24
## MLE/WLE estimation |--
## Item parameter estimation |--
## Deviance= 18081.2149 | Deviance change: 0.0121
## Maximum MLE/WLE change: 0.000959
## Maximum item parameter change: 0.000428
## ....................................................
## Iteration 7 2021-07-06 16:58:24
## MLE/WLE estimation |--
## Item parameter estimation |--
## Deviance= 18081.2117 | Deviance change: 0.0031
## Maximum MLE/WLE change: 0.000262
## Maximum item parameter change: 0.000119
## ....................................................
## Iteration 8 2021-07-06 16:58:24
## MLE/WLE estimation |--
## Item parameter estimation |-
## Deviance= 18081.2108 | Deviance change: 9e-04
## Maximum MLE/WLE change: 7.5e-05
## Maximum item parameter change: 6.1e-05
##
## MLE/WLE estimation |------
## ....................................................
##
## Start: 2021-07-06 16:58:24
## End: 2021-07-06 16:58:24
## Time difference of 0.1644681 secs- Examinando os parâmetros
summary(mod1)## ------------------------------------------------------------
## TAM 3.7-16 (2021-06-24 14:31:37)
## R version 4.0.2 (2020-06-22) x86_64, mingw32 | nodename=DESKTOP-U0L65SJ | login=araec
##
## Start of Analysis: 2021-07-06 16:58:24
## End of Analysis: 2021-07-06 16:58:24
## Time difference of 0.1644681 secs
## Computation time: 0.1644681
##
## Joint Maximum Likelihood Estimation in TAM
##
## IRT Model
## Call:
## tam.jml(resp = gf_matrix[, 2:17])
##
## ------------------------------------------------------------
## Number of iterations = 8
##
## Deviance = 18081.21 | Log Likelihood = -9040.61
## Number of persons = 1182
## Number of items = 16
## constraint = cases
## bias = TRUE
## ------------------------------------------------------------
## Person Parameters xsi
## M = 0
## SD = 1.45
## ------------------------------------------------------------
## Item Parameters xsi
## item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
## i03 i03 1182 0.816 -1.870 -1.870 1
## i02 i02 1182 0.794 -1.689 -1.689 1
## i04 i04 1182 0.740 -1.312 -1.312 1
## i10 i10 1182 0.718 -1.170 -1.170 1
## i09 i09 1182 0.692 -1.009 -1.009 1
## i06 i06 1182 0.691 -1.004 -1.004 1
## i08 i08 1182 0.685 -0.969 -0.969 1
## i01 i01 1182 0.684 -0.964 -0.964 1
## i07 i07 1182 0.669 -0.875 -0.875 1
## i05 i05 1182 0.650 -0.764 -0.764 1
## i12 i12 1182 0.525 -0.102 -0.102 1
## i15 i15 1182 0.420 0.442 0.442 1
## i13 i13 1182 0.387 0.616 0.616 1
## i14 i14 1182 0.365 0.734 0.734 1
## i11 i11 1182 0.351 0.808 0.808 1
## i16 i16 1182 0.287 1.177 1.177 1
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## xsi.label xsi.index xsi se.xsi
## 1 i03 1 -1.870 0.087
## 2 i02 2 -1.689 0.083
## 3 i04 3 -1.312 0.077
## 4 i10 4 -1.170 0.075
## 5 i09 5 -1.009 0.074
## 6 i06 6 -1.004 0.073
## 7 i08 7 -0.969 0.073
## 8 i01 8 -0.964 0.073
## 9 i07 9 -0.875 0.072
## 10 i05 10 -0.764 0.071
## 11 i12 11 -0.102 0.068
## 12 i15 12 0.442 0.069
## 13 i13 13 0.616 0.069
## 14 i14 14 0.734 0.070
## 15 i11 15 0.808 0.070
## 16 i16 16 1.177 0.074 hist(mod1$WLE)
hist(mod1$theta)
hist(mod1$xsi)
plot(mod1$theta, mod1$WLE)
hist(mod1$WLE)
hist(mod1$xsi)
- Índices de ajuste
fit <- tam.jml.fit(mod1)
fit$fit.item## item outfitItem outfitItem_t infitItem infitItem_t
## i03 i03 0.7217011 -2.6565123 0.8441380 -3.3885367
## i02 i02 0.7159880 -2.9996979 0.8392531 -3.7678806
## i04 i04 0.7339456 -3.4002861 0.8600785 -3.7537701
## i10 i10 0.8748909 -1.6091533 0.9574437 -1.1504169
## i09 i09 0.9288570 -0.9592000 0.9757072 -0.6842518
## i06 i06 0.8965486 -1.4260337 0.9451401 -1.5792164
## i08 i08 0.8655852 -1.9124917 0.9280742 -2.1105171
## i01 i01 1.0987792 1.3421909 1.0200374 0.5854330
## i07 i07 1.1692270 2.3196468 1.1191164 3.4095461
## i05 i05 0.8475233 -2.3840088 0.9392019 -1.8890413
## i12 i12 0.9791754 -0.3350563 0.9852370 -0.5078990
## i15 i15 1.0183110 0.2953270 1.0051125 0.1862480
## i13 i13 1.2421142 3.1701024 1.1387465 4.4822041
## i14 i14 0.9559142 -0.5688571 1.0128857 0.4318407
## i11 i11 1.0831534 1.0637972 1.0667803 2.1205122
## i16 i16 0.9583265 -0.4190579 0.9540679 -1.3381996- Psicometria classica
CTT::reliability(as.data.frame(gf_matrix[ , 2:17]))##
## Number of Items
## 16
##
## Number of Examinees
## 1182
##
## Coefficient Alpha
## 0.796- Visualizando as CCI’s
plot(mod1, items = 1:16, ngroups=10)
## ....................................................
## Plots exported in png format into folder:
## C:/Users/araec/Documents/Doutorado/Disciplinas/1 semestre/TRI/Exercicios/Ex3/Plots- Precisão Rasch
WLErel(mod1$WLE, mod1$errorWLE)## [1] 0.747385- Mapa de itens e pessoas
WrightMap::wrightMap(
thetas = mod1$theta,
thresholds = mod1$xsi,
new.quartz = TRUE
)## [,1]
## [1,] -1.8702977
## [2,] -1.6885580
## [3,] -1.3116613
## [4,] -1.1701927
## [5,] -1.0094246
## [6,] -1.0043628
## [7,] -0.9691278
## [8,] -0.9641219
## [9,] -0.8751272
## [10,] -0.7641857
## [11,] -0.1016410
## [12,] 0.4420985
## [13,] 0.6157308
## [14,] 0.7338873
## [15,] 0.8078235
## [16,] 1.1767551WrightMap::wrightMap(thetas = mod1$theta, thresholds = mod1$xsi, new.quartz = TRUE)## [,1]
## [1,] -1.8702977
## [2,] -1.6885580
## [3,] -1.3116613
## [4,] -1.1701927
## [5,] -1.0094246
## [6,] -1.0043628
## [7,] -0.9691278
## [8,] -0.9641219
## [9,] -0.8751272
## [10,] -0.7641857
## [11,] -0.1016410
## [12,] 0.4420985
## [13,] 0.6157308
## [14,] 0.7338873
## [15,] 0.8078235
## [16,] 1.1767551- Criando curvas empíricas
dev.new()
gf_matrix %>%
ggplot(aes(y = i03, x = Score)) +
geom_smooth() +
geom_point(
data = {
gf_matrix %>% select(i03, Score) %>%
group_by(Score) %>%
dplyr::summarise(i03 = mean(i03, na.rm=TRUE))
},
mapping = aes(y = i03, x = Score),
stat = "identity"
) +
theme_light() Exercício 2. Tente você com os dados do ENEM
- Faça o download do arquivo de http://www.labape.com.br/rprimi/TRI/2019_slides_exerc/enem_2015.RData
load("enem_2015.RData")
gabMT## D B B B A D C A D A E A E D C A D C B E C A A E D A C C C E B D E C A B D B E E
## 4 2 2 2 1 4 3 1 4 1 5 1 5 4 3 1 4 3 2 5 3 1 1 5 4 1 3 3 3 5 2 4 5 3 1 2 4 2 5 5
## D E B C C
## 4 5 2 3 3score_mt2 <- score_mt %>% sample_n(size = 10000) mod2 <- tam.jml(score_mt2)## ....................................................
## Iteration 1 2021-07-06 16:58:34
## MLE/WLE estimation |-----
## Item parameter estimation |---
## Deviance= 462481.3586
## Maximum MLE/WLE change: 1.263815
## Maximum item parameter change: 0.117363
## ....................................................
## Iteration 2 2021-07-06 16:58:34
## MLE/WLE estimation |---
## Item parameter estimation |--
## Deviance= 462472.5095 | Deviance change: 8.8491
## Maximum MLE/WLE change: 0.031345
## Maximum item parameter change: 0.014284
## ....................................................
## Iteration 3 2021-07-06 16:58:34
## MLE/WLE estimation |--
## Item parameter estimation |--
## Deviance= 462472.2992 | Deviance change: 0.2104
## Maximum MLE/WLE change: 0.005264
## Maximum item parameter change: 0.001865
## ....................................................
## Iteration 4 2021-07-06 16:58:34
## MLE/WLE estimation |--
## Item parameter estimation |--
## Deviance= 462472.2915 | Deviance change: 0.0077
## Maximum MLE/WLE change: 0.000808
## Maximum item parameter change: 0.000254
## ....................................................
## Iteration 5 2021-07-06 16:58:34
## MLE/WLE estimation |--
## Item parameter estimation |-
## Deviance= 462472.2909 | Deviance change: 6e-04
## Maximum MLE/WLE change: 0.000114
## Maximum item parameter change: 3.5e-05
## ....................................................
## Iteration 6 2021-07-06 16:58:34
## MLE/WLE estimation |-
## Item parameter estimation |-
## Deviance= 462472.2908 | Deviance change: 1e-04
## Maximum MLE/WLE change: 2.2e-05
## Maximum item parameter change: 5e-06
##
## MLE/WLE estimation |------
## ....................................................
##
## Start: 2021-07-06 16:58:34
## End: 2021-07-06 16:58:35
## Time difference of 0.7519429 secs- Examinando os parâmetros
summary(mod2)## ------------------------------------------------------------
## TAM 3.7-16 (2021-06-24 14:31:37)
## R version 4.0.2 (2020-06-22) x86_64, mingw32 | nodename=DESKTOP-U0L65SJ | login=araec
##
## Start of Analysis: 2021-07-06 16:58:34
## End of Analysis: 2021-07-06 16:58:35
## Time difference of 0.7519429 secs
## Computation time: 0.7519429
##
## Joint Maximum Likelihood Estimation in TAM
##
## IRT Model
## Call:
## tam.jml(resp = score_mt2)
##
## ------------------------------------------------------------
## Number of iterations = 6
##
## Deviance = 462472.3 | Log Likelihood = -231236.1
## Number of persons = 10000
## Number of items = 45
## constraint = cases
## bias = TRUE
## ------------------------------------------------------------
## Person Parameters xsi
## M = 0
## SD = 0.6
## ------------------------------------------------------------
## Item Parameters xsi
## item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
## mt_1 mt_1 10000 0.224 1.301 1.301 1
## mt_2 mt_2 10000 0.195 1.480 1.480 1
## mt_3 mt_3 10000 0.565 -0.280 -0.280 1
## mt_4 mt_4 10000 0.285 0.962 0.962 1
## mt_5 mt_5 10000 0.263 1.074 1.074 1
## mt_6 mt_6 10000 0.342 0.680 0.680 1
## mt_7 mt_7 10000 0.208 1.396 1.396 1
## mt_8 mt_8 10000 0.364 0.583 0.583 1
## mt_9 mt_9 10000 0.332 0.730 0.730 1
## mt_10 mt_10 10000 0.114 2.132 2.132 1
## mt_11 mt_11 10000 0.189 1.523 1.523 1
## mt_12 mt_12 10000 0.227 1.280 1.280 1
## mt_13 mt_13 10000 0.262 1.083 1.083 1
## mt_14 mt_14 10000 0.116 2.120 2.120 1
## mt_15 mt_15 10000 0.328 0.746 0.746 1
## mt_16 mt_16 10000 0.369 0.560 0.560 1
## mt_17 mt_17 10000 0.290 0.937 0.937 1
## mt_18 mt_18 10000 0.204 1.421 1.421 1
## mt_19 mt_19 10000 0.386 0.484 0.484 1
## mt_20 mt_20 10000 0.145 1.848 1.848 1
## mt_21 mt_21 10000 0.239 1.208 1.208 1
## mt_22 mt_22 10000 0.241 1.197 1.197 1
## mt_23 mt_23 10000 0.113 2.143 2.143 1
## mt_24 mt_24 10000 0.162 1.718 1.718 1
## mt_25 mt_25 10000 0.174 1.628 1.628 1
## mt_26 mt_26 10000 0.316 0.803 0.803 1
## mt_27 mt_27 10000 0.272 1.031 1.031 1
## mt_28 mt_28 10000 0.262 1.080 1.080 1
## mt_29 mt_29 10000 0.205 1.417 1.417 1
## mt_30 mt_30 10000 0.135 1.935 1.935 1
## mt_31 mt_31 10000 0.126 2.018 2.018 1
## mt_32 mt_32 10000 0.210 1.382 1.382 1
## mt_33 mt_33 10000 0.201 1.442 1.442 1
## mt_34 mt_34 10000 0.261 1.090 1.090 1
## mt_35 mt_35 10000 0.202 1.437 1.437 1
## mt_36 mt_36 10000 0.238 1.216 1.216 1
## mt_37 mt_37 10000 0.386 0.483 0.483 1
## mt_38 mt_38 10000 0.330 0.739 0.739 1
## mt_39 mt_39 10000 0.192 1.504 1.504 1
## mt_40 mt_40 10000 0.214 1.358 1.358 1
## mt_41 mt_41 10000 0.174 1.624 1.624 1
## mt_42 mt_42 10000 0.325 0.761 0.761 1
## mt_43 mt_43 10000 0.524 -0.107 -0.107 1
## mt_44 mt_44 10000 0.198 1.462 1.462 1
## mt_45 mt_45 10000 0.520 -0.088 -0.088 1
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## xsi.label xsi.index xsi se.xsi
## 1 mt_1 1 1.301 0.025
## 2 mt_2 2 1.480 0.026
## 3 mt_3 3 -0.280 0.021
## 4 mt_4 4 0.962 0.023
## 5 mt_5 5 1.074 0.023
## 6 mt_6 6 0.680 0.022
## 7 mt_7 7 1.396 0.025
## 8 mt_8 8 0.583 0.022
## 9 mt_9 9 0.730 0.022
## 10 mt_10 10 2.132 0.032
## 11 mt_11 11 1.523 0.026
## 12 mt_12 12 1.280 0.025
## 13 mt_13 13 1.083 0.024
## 14 mt_14 14 2.120 0.032
## 15 mt_15 15 0.746 0.022
## 16 mt_16 16 0.560 0.021
## 17 mt_17 17 0.937 0.023
## 18 mt_18 18 1.421 0.026
## 19 mt_19 19 0.484 0.021
## 20 mt_20 20 1.848 0.029
## 21 mt_21 21 1.208 0.024
## 22 mt_22 22 1.197 0.024
## 23 mt_23 23 2.143 0.032
## 24 mt_24 24 1.718 0.028
## 25 mt_25 25 1.628 0.027
## 26 mt_26 26 0.803 0.022
## 27 mt_27 27 1.031 0.023
## 28 mt_28 28 1.080 0.024
## 29 mt_29 29 1.417 0.026
## 30 mt_30 30 1.935 0.030
## 31 mt_31 31 2.018 0.031
## 32 mt_32 32 1.382 0.025
## 33 mt_33 33 1.442 0.026
## 34 mt_34 34 1.090 0.024
## 35 mt_35 35 1.437 0.026
## 36 mt_36 36 1.216 0.024
## 37 mt_37 37 0.483 0.021
## 38 mt_38 38 0.739 0.022
## 39 mt_39 39 1.504 0.026
## 40 mt_40 40 1.358 0.025
## 41 mt_41 41 1.624 0.027
## 42 mt_42 42 0.761 0.022
## 43 mt_43 43 -0.107 0.021
## 44 mt_44 44 1.462 0.026
## 45 mt_45 45 -0.088 0.021 hist(mod2$WLE)
hist(mod2$theta)
hist(mod2$xsi)
plot(mod2$theta, mod2$WLE)
- Índices de ajuste
fit <- tam.jml.fit(mod2)
fit$fit.item## item outfitItem outfitItem_t infitItem infitItem_t
## mt_1 mt_1 1.0854641 4.95559898 1.0534831 3.9464056
## mt_2 mt_2 1.0452558 2.34059869 0.9997534 -0.0112197
## mt_3 mt_3 0.8983118 -14.20716745 0.9206937 -15.3943248
## mt_4 mt_4 1.0226212 1.74380186 1.0201029 1.9525986
## mt_5 mt_5 1.0185398 1.30850057 1.0090768 0.8101249
## mt_6 mt_6 0.8831011 -11.97343852 0.8991955 -12.9976465
## mt_7 mt_7 1.0186136 1.03369436 1.0042458 0.3015706
## mt_8 mt_8 0.9133727 -9.53951226 0.9218500 -10.9097244
## mt_9 mt_9 0.8834591 -11.42288709 0.8996507 -12.3625785
## mt_10 mt_10 1.0842787 2.83091778 1.0439884 1.8909830
## mt_11 mt_11 1.0278091 1.40674659 1.0151051 0.9680749
## mt_12 mt_12 1.0367723 2.20228608 1.0179649 1.3645894
## mt_13 mt_13 0.9359799 -4.59580590 0.9581253 -3.7567652
## mt_14 mt_14 1.1444839 4.79258473 1.0507947 2.1934515
## mt_15 mt_15 1.0115973 1.07651103 1.0118749 1.3910335
## mt_16 mt_16 0.9998739 -0.01069136 1.0039292 0.5471450
## mt_17 mt_17 1.0060102 0.47839293 1.0093592 0.9327680
## mt_18 mt_18 1.0072729 0.40209701 0.9889418 -0.7586142
## mt_19 mt_19 0.9351867 -7.70197974 0.9423552 -8.7437839
## mt_20 mt_20 0.9955206 -0.17576241 0.9844340 -0.8031431
## mt_21 mt_21 0.9877055 -0.78253079 0.9864921 -1.0863450
## mt_22 mt_22 1.0621930 3.92645178 1.0484040 3.8646712
## mt_23 mt_23 1.1226488 4.04232430 1.0464305 1.9819135
## mt_24 mt_24 0.9462817 -2.43126761 0.9403142 -3.4199602
## mt_25 mt_25 0.9588170 -1.96976548 0.9583485 -2.5165068
## mt_26 mt_26 0.9990812 -0.07750838 0.9980531 -0.2144615
## mt_27 mt_27 0.9861651 -1.01339197 0.9848817 -1.3980152
## mt_28 mt_28 1.0036467 0.26124400 0.9959340 -0.3573492
## mt_29 mt_29 0.9290445 -3.97464930 0.9426285 -4.0321853
## mt_30 mt_30 1.0528403 2.02464811 1.0357746 1.7394414
## mt_31 mt_31 1.0337929 1.24165733 0.9925535 -0.3404838
## mt_32 mt_32 1.0225563 1.26268140 1.0098936 0.7022090
## mt_33 mt_33 0.9447949 -3.01958078 0.9701145 -2.0416521
## mt_34 mt_34 0.9020043 -7.08349291 0.9182246 -7.4020588
## mt_35 mt_35 1.0686103 3.62686389 1.0467402 3.1354039
## mt_36 mt_36 1.0475035 2.97158010 1.0318807 2.5241666
## mt_37 mt_37 0.9682399 -3.73246361 0.9733157 -4.0066062
## mt_38 mt_38 0.9387284 -5.84531885 0.9426179 -6.9112113
## mt_39 mt_39 0.9387237 -3.21639068 0.9448901 -3.6411362
## mt_40 mt_40 1.0500239 2.81581046 1.0404005 2.8729069
## mt_41 mt_41 1.0798085 3.69744887 1.0581578 3.4207905
## mt_42 mt_42 0.9646553 -3.27501456 0.9663252 -3.9409596
## mt_43 mt_43 0.9425000 -8.59026235 0.9471726 -10.9427479
## mt_44 mt_44 1.0220909 1.16922934 1.0017116 0.1193271
## mt_45 mt_45 0.9243063 -11.43791424 0.9380199 -12.9181891- Psicometria classica (como no último exercicio)
CTT::reliability(score_mt2)##
## Number of Items
## 45
##
## Number of Examinees
## 10000
##
## Coefficient Alpha
## 0.655- Visualizando as CCI’s
plot(mod2, items = 23, ngroups=10)
## ....................................................
## Plots exported in png format into folder:
## C:/Users/araec/Documents/Doutorado/Disciplinas/1 semestre/TRI/Exercicios/Ex3/Plots- Precisão Rasch
WLErel(mod2$WLE, mod2$errorWLE)## [1] 0.5783161- Mapa de itens e pessoas
WrightMap::wrightMap(
thetas = mod2$theta,
thresholds = mod2$xsi,
new.quartz = TRUE
)## [,1]
## [1,] 1.30071832
## [2,] 1.48042294
## [3,] -0.27980455
## [4,] 0.96167482
## [5,] 1.07441632
## [6,] 0.67970438
## [7,] 1.39627469
## [8,] 0.58303743
## [9,] 0.73048722
## [10,] 2.13239259
## [11,] 1.52336555
## [12,] 1.27978513
## [13,] 1.08252638
## [14,] 2.12026858
## [15,] 0.74616471
## [16,] 0.55993104
## [17,] 0.93708774
## [18,] 1.42110950
## [19,] 0.48381997
## [20,] 1.84839221
## [21,] 1.20791801
## [22,] 1.19703933
## [23,] 2.14257844
## [24,] 1.71842957
## [25,] 1.62774109
## [26,] 0.80337201
## [27,] 1.03111043
## [28,] 1.08036086
## [29,] 1.41662700
## [30,] 1.93491938
## [31,] 2.01753545
## [32,] 1.38178447
## [33,] 1.44174354
## [34,] 1.08957872
## [35,] 1.43720962
## [36,] 1.21597071
## [37,] 0.48293228
## [38,] 0.73855377
## [39,] 1.50377574
## [40,] 1.35808903
## [41,] 1.62413051
## [42,] 0.76144258
## [43,] -0.10680178
## [44,] 1.46196157
## [45,] -0.08829541WrightMap::wrightMap(thetas = mod1$theta, thresholds = mod1$xsi, new.quartz = TRUE)## [,1]
## [1,] -1.8702977
## [2,] -1.6885580
## [3,] -1.3116613
## [4,] -1.1701927
## [5,] -1.0094246
## [6,] -1.0043628
## [7,] -0.9691278
## [8,] -0.9641219
## [9,] -0.8751272
## [10,] -0.7641857
## [11,] -0.1016410
## [12,] 0.4420985
## [13,] 0.6157308
## [14,] 0.7338873
## [15,] 0.8078235
## [16,] 1.1767551- Criando curvas empíricas
dev.new()
gf_matrix %>%
ggplot(aes(y = i03, x = Score)) +
geom_smooth() +
geom_point(
data = {
gf_matrix %>% select(i03, Score) %>%
group_by(Score) %>%
dplyr::summarise(i03 = mean(i03, na.rm=TRUE))
},
mapping = aes(y = i03, x = Score),
stat = "identity"
) +
theme_light() Bônus
- Mapa de construto mais bonito !!
source("http://www.labape.com.br/rprimi/R/utils_construct_maps.R")
dev.new()
person_item_map_v3(
item_tresh = mod1$xsi,
coditem = names(gf_matrix)[2:17],
item_text=names(gf_matrix)[2:17],
pole = rep(1, 16),
theta = mod1$theta,
min = -3,
max = 3,
step = 1,
item_text_max = 28,
binwidth = .5,
size_categ_label = 3,
size_bar = 3,
categ_label = c("1", "2"),
categ_color = c("#DF4949", "#2B82C9"),
intercept=0,
color_hist = "#2B82C9",
probs = c(.25, .50, .75)
)
summary(mod1)## ------------------------------------------------------------
## TAM 3.7-16 (2021-06-24 14:31:37)
## R version 4.0.2 (2020-06-22) x86_64, mingw32 | nodename=DESKTOP-U0L65SJ | login=araec
##
## Start of Analysis: 2021-07-06 16:58:24
## End of Analysis: 2021-07-06 16:58:24
## Time difference of 0.1644681 secs
## Computation time: 0.1644681
##
## Joint Maximum Likelihood Estimation in TAM
##
## IRT Model
## Call:
## tam.jml(resp = gf_matrix[, 2:17])
##
## ------------------------------------------------------------
## Number of iterations = 8
##
## Deviance = 18081.21 | Log Likelihood = -9040.61
## Number of persons = 1182
## Number of items = 16
## constraint = cases
## bias = TRUE
## ------------------------------------------------------------
## Person Parameters xsi
## M = 0
## SD = 1.45
## ------------------------------------------------------------
## Item Parameters xsi
## item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
## i03 i03 1182 0.816 -1.870 -1.870 1
## i02 i02 1182 0.794 -1.689 -1.689 1
## i04 i04 1182 0.740 -1.312 -1.312 1
## i10 i10 1182 0.718 -1.170 -1.170 1
## i09 i09 1182 0.692 -1.009 -1.009 1
## i06 i06 1182 0.691 -1.004 -1.004 1
## i08 i08 1182 0.685 -0.969 -0.969 1
## i01 i01 1182 0.684 -0.964 -0.964 1
## i07 i07 1182 0.669 -0.875 -0.875 1
## i05 i05 1182 0.650 -0.764 -0.764 1
## i12 i12 1182 0.525 -0.102 -0.102 1
## i15 i15 1182 0.420 0.442 0.442 1
## i13 i13 1182 0.387 0.616 0.616 1
## i14 i14 1182 0.365 0.734 0.734 1
## i11 i11 1182 0.351 0.808 0.808 1
## i16 i16 1182 0.287 1.177 1.177 1
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## xsi.label xsi.index xsi se.xsi
## 1 i03 1 -1.870 0.087
## 2 i02 2 -1.689 0.083
## 3 i04 3 -1.312 0.077
## 4 i10 4 -1.170 0.075
## 5 i09 5 -1.009 0.074
## 6 i06 6 -1.004 0.073
## 7 i08 7 -0.969 0.073
## 8 i01 8 -0.964 0.073
## 9 i07 9 -0.875 0.072
## 10 i05 10 -0.764 0.071
## 11 i12 11 -0.102 0.068
## 12 i15 12 0.442 0.069
## 13 i13 13 0.616 0.069
## 14 i14 14 0.734 0.070
## 15 i11 15 0.808 0.070
## 16 i16 16 1.177 0.074- Define identificação pela média de dificuldade dos itens igual a zero (semelhandte ao que o winsteps faz)
mod3 <- tam.jml(gf_matrix[ , 2:17], constraint="items")## ....................................................
## Iteration 1 2021-07-06 16:58:51
## MLE/WLE estimation |--------
## Item parameter estimation |----------
## Deviance= 20497.8906
## Maximum MLE/WLE change: 9.208993
## Maximum item parameter change: 1.304447
## ....................................................
## Iteration 2 2021-07-06 16:58:51
## MLE/WLE estimation |-------
## Item parameter estimation |----------
## Deviance= 18462.1369 | Deviance change: 2035.754
## Maximum MLE/WLE change: 7.982651
## Maximum item parameter change: 0.330129
## ....................................................
## Iteration 3 2021-07-06 16:58:51
## MLE/WLE estimation |-----
## Item parameter estimation |----------
## Deviance= 18219.164 | Deviance change: 242.973
## Maximum MLE/WLE change: 0.763315
## Maximum item parameter change: 0.270605
## ....................................................
## Iteration 4 2021-07-06 16:58:51
## MLE/WLE estimation |---
## Item parameter estimation |----------
## Deviance= 18120.8343 | Deviance change: 98.3297
## Maximum MLE/WLE change: 0.098128
## Maximum item parameter change: 0.186806
## ....................................................
## Iteration 5 2021-07-06 16:58:51
## MLE/WLE estimation |---
## Item parameter estimation |----------
## Deviance= 18092.585 | Deviance change: 28.2493
## Maximum MLE/WLE change: 0.032435
## Maximum item parameter change: 0.117637
## ....................................................
## Iteration 6 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |---------
## Deviance= 18084.9443 | Deviance change: 7.6407
## Maximum MLE/WLE change: 0.012746
## Maximum item parameter change: 0.059013
## ....................................................
## Iteration 7 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |----------
## Deviance= 18082.2648 | Deviance change: 2.6795
## Maximum MLE/WLE change: 0.006922
## Maximum item parameter change: 0.043042
## ....................................................
## Iteration 8 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |--------
## Deviance= 18081.6648 | Deviance change: 0.6
## Maximum MLE/WLE change: 0.006043
## Maximum item parameter change: 0.014715
## ....................................................
## Iteration 9 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |--------
## Deviance= 18081.3974 | Deviance change: 0.2674
## Maximum MLE/WLE change: 0.002768
## Maximum item parameter change: 0.011189
## ....................................................
## Iteration 10 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |--------
## Deviance= 18081.2677 | Deviance change: 0.1297
## Maximum MLE/WLE change: 0.001761
## Maximum item parameter change: 0.007834
## ....................................................
## Iteration 11 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |------
## Deviance= 18081.2425 | Deviance change: 0.0252
## Maximum MLE/WLE change: 0.000994
## Maximum item parameter change: 0.003363
## ....................................................
## Iteration 12 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |------
## Deviance= 18081.225 | Deviance change: 0.0175
## Maximum MLE/WLE change: 0.000548
## Maximum item parameter change: 0.002728
## ....................................................
## Iteration 13 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |------
## Deviance= 18081.2166 | Deviance change: 0.0084
## Maximum MLE/WLE change: 0.000413
## Maximum item parameter change: 0.001991
## ....................................................
## Iteration 14 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |-----
## Deviance= 18081.2149 | Deviance change: 0.0017
## Maximum MLE/WLE change: 0.000257
## Maximum item parameter change: 0.000849
## ....................................................
## Iteration 15 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |----
## Deviance= 18081.213 | Deviance change: 0.0019
## Maximum MLE/WLE change: 0.000137
## Maximum item parameter change: 0.001088
## ....................................................
## Iteration 16 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |---
## Deviance= 18081.2119 | Deviance change: 0.0011
## Maximum MLE/WLE change: 0.000162
## Maximum item parameter change: 0.000529
## ....................................................
## Iteration 17 2021-07-06 16:58:51
## MLE/WLE estimation |-
## Item parameter estimation |---
## Deviance= 18081.2118 | Deviance change: 2e-04
## Maximum MLE/WLE change: 7.6e-05
## Maximum item parameter change: 0.000112
## ....................................................
## Iteration 18 2021-07-06 16:58:51
## MLE/WLE estimation |-
## Item parameter estimation |---
## Deviance= 18081.2113 | Deviance change: 5e-04
## Maximum MLE/WLE change: 6.5e-05
## Maximum item parameter change: 0.000128
## ....................................................
## Iteration 19 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |----
## Deviance= 18081.2124 | Deviance change: -0.0011
## Maximum MLE/WLE change: 0.000167
## Maximum item parameter change: 0.00015
## ....................................................
## Iteration 20 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |---
## Deviance= 18081.211 | Deviance change: 0.0014
## Maximum MLE/WLE change: 0.00017
## Maximum item parameter change: 0.000109
## ....................................................
## Iteration 21 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |----
## Deviance= 18081.2119 | Deviance change: -9e-04
## Maximum MLE/WLE change: 0.000121
## Maximum item parameter change: 0.000123
## ....................................................
## Iteration 22 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |--
## Deviance= 18081.211 | Deviance change: 9e-04
## Maximum MLE/WLE change: 0.000107
## Maximum item parameter change: 8.2e-05
## ....................................................
## Iteration 23 2021-07-06 16:58:51
## MLE/WLE estimation |--
## Item parameter estimation |----
## Deviance= 18081.2117 | Deviance change: -7e-04
## Maximum MLE/WLE change: 9.5e-05
## Maximum item parameter change: 9.1e-05
##
## MLE/WLE estimation |------
## ....................................................
##
## Start: 2021-07-06 16:58:51
## End: 2021-07-06 16:58:51
## Time difference of 0.1549699 secssummary(mod3)## ------------------------------------------------------------
## TAM 3.7-16 (2021-06-24 14:31:37)
## R version 4.0.2 (2020-06-22) x86_64, mingw32 | nodename=DESKTOP-U0L65SJ | login=araec
##
## Start of Analysis: 2021-07-06 16:58:51
## End of Analysis: 2021-07-06 16:58:51
## Time difference of 0.1549699 secs
## Computation time: 0.1549699
##
## Joint Maximum Likelihood Estimation in TAM
##
## IRT Model
## Call:
## tam.jml(resp = gf_matrix[, 2:17], constraint = "items")
##
## ------------------------------------------------------------
## Number of iterations = 23
##
## Deviance = 18081.21 | Log Likelihood = -9040.61
## Number of persons = 1182
## Number of items = 16
## constraint = items
## bias = TRUE
## ------------------------------------------------------------
## Person Parameters xsi
## M = 0.53
## SD = 1.45
## ------------------------------------------------------------
## Item Parameters xsi
## item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
## i03 i03 1182 0.816 -1.373 -1.373 1
## i02 i02 1182 0.794 -1.191 -1.191 1
## i04 i04 1182 0.740 -0.815 -0.815 1
## i10 i10 1182 0.718 -0.673 -0.673 1
## i09 i09 1182 0.692 -0.512 -0.512 1
## i06 i06 1182 0.691 -0.507 -0.507 1
## i08 i08 1182 0.685 -0.472 -0.472 1
## i01 i01 1182 0.684 -0.467 -0.467 1
## i07 i07 1182 0.669 -0.378 -0.378 1
## i05 i05 1182 0.650 -0.267 -0.267 1
## i12 i12 1182 0.525 0.395 0.395 1
## i15 i15 1182 0.420 0.939 0.939 1
## i13 i13 1182 0.387 1.113 1.113 1
## i14 i14 1182 0.365 1.231 1.231 1
## i11 i11 1182 0.351 1.305 1.305 1
## i16 i16 1182 0.287 1.674 1.674 1
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## xsi.label xsi.index xsi se.xsi
## 1 i03 1 -1.373 0.056
## 2 i02 2 -1.191 0.055
## 3 i04 3 -0.815 0.053
## 4 i10 4 -0.673 0.053
## 5 i09 5 -0.512 0.052
## 6 i06 6 -0.507 0.052
## 7 i08 7 -0.472 0.052
## 8 i01 8 -0.467 0.052
## 9 i07 9 -0.378 0.052
## 10 i05 10 -0.267 0.051
## 11 i12 11 0.395 0.050
## 12 i15 12 0.939 0.050
## 13 i13 13 1.113 0.051
## 14 i14 14 1.231 0.051
## 15 i11 15 1.305 0.051hist(mod1$WLE)
hist(mod3$WLE)
hist(mod1$xsi)
hist(mod3$xsi)
mean(mod3$xsi)## [1] -0.1115977dev.new()
person_item_map_v3(
item_tresh = mod3$xsi,
coditem = names(gf_matrix)[2:16],
item_text=names(gf_matrix)[2:16],
pole = rep(1, 15),
theta = mod3$theta,
min = -3,
max = 3,
step = 1,
item_text_max = 28,
binwidth = .5,
size_categ_label = 3,
size_bar = 3,
categ_label = c("1", "2"),
categ_color = c("#DF4949", "#2B82C9"),
intercept=0,
color_hist = "#2B82C9",
probs = c(.25, .50, .75)
) des <- TAM::designMatrices(resp=gf_matrix[ , 2:17])
A1 <- des$A[ , , - ncol(gf_matrix[ , 2:17]) ]
A1[ ncol(gf_matrix[ , 2:17]) , 2 , ] <- 1
A1[,2,]## i03 i02 i04 i10 i09 i06 i08 i01 i07 i05 i12 i15 i13 i14 i11
## Item01 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## Item02 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
## Item03 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
## Item04 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
## Item05 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
## Item06 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
## Item07 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
## Item08 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
## Item09 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0
## Item10 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
## Item11 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0
## Item12 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
## Item13 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
## Item14 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
## Item15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
## Item16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 # estimate model
mod5 <- TAM::tam.mml(
resp=gf_matrix[ , 2:17],
A=A1,
beta.fixed=FALSE ,
control=list(fac.oldxsi=.1)
)## ....................................................
## Processing Data 2021-07-06 16:58:52
## * Response Data: 1182 Persons and 16 Items
## * Numerical integration with 21 nodes
## * Created Design Matrices ( 2021-07-06 16:58:52 )
## * Calculated Sufficient Statistics ( 2021-07-06 16:58:52 )
## ....................................................
## Iteration 1 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 45646.7726
## Maximum item intercept parameter change: 0.644
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.875056
## Maximum variance parameter change: 0.259951
## ....................................................
## Iteration 2 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 28705.6683 | Absolute change: 16941.1 | Relative change: 0.5901658
## Maximum item intercept parameter change: 0.650123
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.174963
## Maximum variance parameter change: 0.173656
## ....................................................
## Iteration 3 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21306.8903 | Absolute change: 7398.778 | Relative change: 0.3472481
## Maximum item intercept parameter change: 0.056383
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.157409
## Maximum variance parameter change: 0.042731
## ....................................................
## Iteration 4 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21172.0253 | Absolute change: 134.865 | Relative change: 0.00636996
## Maximum item intercept parameter change: 0.065762
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.029709
## Maximum variance parameter change: 0.001555
## ....................................................
## Iteration 5 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21136.9617 | Absolute change: 35.0636 | Relative change: 0.00165888
## Maximum item intercept parameter change: 0.041755
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.005295
## Maximum variance parameter change: 0.010457
## ....................................................
## Iteration 6 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21130.854 | Absolute change: 6.1076 | Relative change: 0.00028904
## Maximum item intercept parameter change: 0.03624
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.00059
## Maximum variance parameter change: 0.0066
## ....................................................
## Iteration 7 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21126.3361 | Absolute change: 4.5179 | Relative change: 0.00021385
## Maximum item intercept parameter change: 0.033794
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.000252
## Maximum variance parameter change: 0.002663
## ....................................................
## Iteration 8 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.8526 | Absolute change: 2.4835 | Relative change: 0.00011757
## Maximum item intercept parameter change: 0.011122
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.000122
## Maximum variance parameter change: 0.004901
## ....................................................
## Iteration 9 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.4553 | Absolute change: 0.3973 | Relative change: 1.881e-05
## Maximum item intercept parameter change: 0.005094
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.000242
## Maximum variance parameter change: 0.004287
## ....................................................
## Iteration 10 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.3001 | Absolute change: 0.1552 | Relative change: 7.35e-06
## Maximum item intercept parameter change: 0.004698
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.000135
## Maximum variance parameter change: 0.002957
## ....................................................
## Iteration 11 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.2017 | Absolute change: 0.0984 | Relative change: 4.66e-06
## Maximum item intercept parameter change: 0.00176
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 5.1e-05
## Maximum variance parameter change: 0.002044
## ....................................................
## Iteration 12 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.1799 | Absolute change: 0.0218 | Relative change: 1.03e-06
## Maximum item intercept parameter change: 0.001637
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 3.7e-05
## Maximum variance parameter change: 0.001197
## ....................................................
## Iteration 13 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.1687 | Absolute change: 0.0113 | Relative change: 5.3e-07
## Maximum item intercept parameter change: 0.000578
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2.2e-05
## Maximum variance parameter change: 0.000816
## ....................................................
## Iteration 14 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.1663 | Absolute change: 0.0024 | Relative change: 1.1e-07
## Maximum item intercept parameter change: 0.000599
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1.9e-05
## Maximum variance parameter change: 0.000467
## ....................................................
## Iteration 15 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.1649 | Absolute change: 0.0014 | Relative change: 7e-08
## Maximum item intercept parameter change: 0.000275
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1.2e-05
## Maximum variance parameter change: 0.000314
## ....................................................
## Iteration 16 2021-07-06 16:58:52
## E Step
## M Step Intercepts |---
## Deviance = 21123.1645 | Absolute change: 3e-04 | Relative change: 2e-08
## Maximum item intercept parameter change: 0.000107
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1e-05
## Maximum variance parameter change: 0.000197
## ....................................................
## Iteration 17 2021-07-06 16:58:52
## E Step
## M Step Intercepts |--
## Deviance = 21123.1644 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 9.2e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 6e-06
## Maximum variance parameter change: 0.000116
## ....................................................
## Iteration 18 2021-07-06 16:58:52
## E Step
## M Step Intercepts |--
## Deviance = 21123.1644 | Absolute change: 0 | Relative change: 0
## Maximum item intercept parameter change: 8.8e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 4e-06
## Maximum variance parameter change: 6.1e-05
## ....................................................
## Item Parameters
## xsi.index xsi.label est
## 1 1 i03 -1.3592
## 2 2 i02 -1.1810
## 3 3 i04 -0.8099
## 4 4 i10 -0.6703
## 5 5 i09 -0.5113
## 6 6 i06 -0.5063
## 7 7 i08 -0.4714
## 8 8 i01 -0.4664
## 9 9 i07 -0.3783
## 10 10 i05 -0.2683
## 11 11 i12 0.3909
## 12 12 i15 0.9335
## 13 13 i13 1.1070
## 14 14 i14 1.2250
## 15 15 i11 1.2989
## ...................................
## Regression Coefficients
## [,1]
## [1,] 0.5062
##
## Variance:
## [,1]
## [1,] 1.386
##
##
## EAP Reliability:
## [1] 0.783
##
## -----------------------------
## Start: 2021-07-06 16:58:52
## End: 2021-07-06 16:58:52
## Time difference of 0.1155901 secs summary(mod5)## ------------------------------------------------------------
## TAM 3.7-16 (2021-06-24 14:31:37)
## R version 4.0.2 (2020-06-22) x86_64, mingw32 | nodename=DESKTOP-U0L65SJ | login=araec
##
## Date of Analysis: 2021-07-06 16:58:52
## Time difference of 0.1155901 secs
## Computation time: 0.1155901
##
## Multidimensional Item Response Model in TAM
##
## IRT Model: 1PL
## Call:
## TAM::tam.mml(resp = gf_matrix[, 2:17], beta.fixed = FALSE, A = A1,
## control = list(fac.oldxsi = 0.1))
##
## ------------------------------------------------------------
## Number of iterations = 18
## Numeric integration with 21 integration points
##
## Deviance = 21123.16
## Log likelihood = -10561.58
## Number of persons = 1182
## Number of persons used = 1182
## Number of items = 16
## Number of estimated parameters = 17
## Item threshold parameters = 15
## Item slope parameters = 0
## Regression parameters = 1
## Variance/covariance parameters = 1
##
## AIC = 21157 | penalty=34 | AIC=-2*LL + 2*p
## AIC3 = 21174 | penalty=51 | AIC3=-2*LL + 3*p
## BIC = 21243 | penalty=120.27 | BIC=-2*LL + log(n)*p
## aBIC = 21189 | penalty=66.22 | aBIC=-2*LL + log((n-2)/24)*p (adjusted BIC)
## CAIC = 21260 | penalty=137.27 | CAIC=-2*LL + [log(n)+1]*p (consistent AIC)
## AICc = 21158 | penalty=34.53 | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1) (bias corrected AIC)
## GHP = 0.55936 | GHP=( -LL + p ) / (#Persons * #Items) (Gilula-Haberman log penalty)
##
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.783
## ------------------------------------------------------------
## Covariances and Variances
## [,1]
## [1,] 1.386
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
## [,1]
## [1,] 1.177
## ------------------------------------------------------------
## Regression Coefficients
## [,1]
## [1,] 0.50618
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
## 1 i03 1182 0.816 -1.359 -1.359 1
## 2 i02 1182 0.794 -1.181 -1.181 1
## 3 i04 1182 0.740 -0.810 -0.810 1
## 4 i10 1182 0.718 -0.670 -0.670 1
## 5 i09 1182 0.692 -0.511 -0.511 1
## 6 i06 1182 0.691 -0.506 -0.506 1
## 7 i08 1182 0.685 -0.471 -0.471 1
## 8 i01 1182 0.684 -0.466 -0.466 1
## 9 i07 1182 0.669 -0.378 -0.378 1
## 10 i05 1182 0.650 -0.268 -0.268 1
## 11 i12 1182 0.525 0.391 0.391 1
## 12 i15 1182 0.420 0.934 0.934 1
## 13 i13 1182 0.387 1.107 1.107 1
## 14 i14 1182 0.365 1.225 1.225 1
## 15 i11 1182 0.351 1.299 1.299 1
## 16 i16 1182 0.287 1.667 1.667 1
##
## Item Parameters Xsi
## xsi se.xsi
## i03 -1.359 0.054
## i02 -1.181 0.053
## i04 -0.810 0.051
## i10 -0.670 0.051
## i09 -0.511 0.050
## i06 -0.506 0.050
## i08 -0.471 0.050
## i01 -0.466 0.050
## i07 -0.378 0.050
## i05 -0.268 0.050
## i12 0.391 0.048
## i15 0.934 0.049
## i13 1.107 0.049
## i14 1.225 0.049
## i11 1.299 0.049
##
## Item Parameters in IRT parameterization
## item alpha beta
## 1 i03 1 -1.359
## 2 i02 1 -1.181
## 3 i04 1 -0.810
## 4 i10 1 -0.670
## 5 i09 1 -0.511
## 6 i06 1 -0.506
## 7 i08 1 -0.471
## 8 i01 1 -0.466
## 9 i07 1 -0.378
## 10 i05 1 -0.268
## 11 i12 1 0.391
## 12 i15 1 0.934
## 13 i13 1 1.107
## 14 i14 1 1.225
## 15 i11 1 1.299
## 16 i16 1 1.667mod4 <- tam.mml(gf_matrix[ , 2:17], constraint = "items")## ....................................................
## Processing Data 2021-07-06 16:58:52
## * Response Data: 1182 Persons and 16 Items
## * Numerical integration with 21 nodes
## * Created Design Matrices ( 2021-07-06 16:58:52 )
## * Calculated Sufficient Statistics ( 2021-07-06 16:58:52 )
## ....................................................
## Iteration 1 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 45646.7726
## Maximum item intercept parameter change: 0.904224
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.875056
## Maximum variance parameter change: 0.259951
## ....................................................
## Iteration 2 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 23138.2935 | Absolute change: 22508.48 | Relative change: 0.9727804
## Maximum item intercept parameter change: 0.253972
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.294617
## Maximum variance parameter change: 0.084812
## ....................................................
## Iteration 3 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21193.2149 | Absolute change: 1945.079 | Relative change: 0.09177837
## Maximum item intercept parameter change: 0.323192
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.059875
## Maximum variance parameter change: 0.055257
## ....................................................
## Iteration 4 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21128.1448 | Absolute change: 65.07 | Relative change: 0.00307978
## Maximum item intercept parameter change: 0.046069
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.011496
## Maximum variance parameter change: 0.002784
## ....................................................
## Iteration 5 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21124.9697 | Absolute change: 3.1751 | Relative change: 0.0001503
## Maximum item intercept parameter change: 0.019918
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.002435
## Maximum variance parameter change: 0.004361
## ....................................................
## Iteration 6 2021-07-06 16:58:52
## E Step
## M Step Intercepts |----
## Deviance = 21123.6291 | Absolute change: 1.3406 | Relative change: 6.347e-05
## Maximum item intercept parameter change: 0.008004
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0.000425
## Maximum variance parameter change: 0.0043
## ....................................................
## Iteration 7 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.3495 | Absolute change: 0.2796 | Relative change: 1.324e-05
## Maximum item intercept parameter change: 0.00619
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 5.9e-05
## Maximum variance parameter change: 0.003211
## ....................................................
## Iteration 8 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.2095 | Absolute change: 0.14 | Relative change: 6.63e-06
## Maximum item intercept parameter change: 0.002857
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 4.1e-05
## Maximum variance parameter change: 0.00169
## ....................................................
## Iteration 9 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1791 | Absolute change: 0.0304 | Relative change: 1.44e-06
## Maximum item intercept parameter change: 0.001687
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1.1e-05
## Maximum variance parameter change: 0.001128
## ....................................................
## Iteration 10 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1683 | Absolute change: 0.0108 | Relative change: 5.1e-07
## Maximum item intercept parameter change: 0.000657
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000818
## ....................................................
## Iteration 11 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1663 | Absolute change: 0.0021 | Relative change: 1e-07
## Maximum item intercept parameter change: 0.000275
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 5e-06
## Maximum variance parameter change: 0.000347
## ....................................................
## Iteration 12 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1658 | Absolute change: 4e-04 | Relative change: 2e-08
## Maximum item intercept parameter change: 0.000349
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1.2e-05
## Maximum variance parameter change: 0.00033
## ....................................................
## Iteration 13 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1654 | Absolute change: 4e-04 | Relative change: 2e-08
## Maximum item intercept parameter change: 0.000195
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 3.3e-05
## ....................................................
## Iteration 14 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1651 | Absolute change: 3e-04 | Relative change: 2e-08
## Maximum item intercept parameter change: 0.000216
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 5e-06
## Maximum variance parameter change: 0.000144
## ....................................................
## Iteration 15 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1649 | Absolute change: 2e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000158
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1e-06
## Maximum variance parameter change: 6e-06
## ....................................................
## Iteration 16 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1648 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000187
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 3e-06
## Maximum variance parameter change: 9.3e-05
## ....................................................
## Iteration 17 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1647 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.00015
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1e-06
## Maximum variance parameter change: 2.1e-05
## ....................................................
## Iteration 18 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1647 | Absolute change: 0 | Relative change: 0
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000181
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 3e-06
## Maximum variance parameter change: 9.3e-05
## ....................................................
## Iteration 19 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1646 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000158
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 4.5e-05
## ....................................................
## Iteration 20 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1647 | Absolute change: -1e-04 | Relative change: 0
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000189
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 3e-06
## Maximum variance parameter change: 9.6e-05
## ....................................................
## Iteration 21 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1645 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000107
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 3e-06
## Maximum variance parameter change: 6.9e-05
## ....................................................
## Iteration 22 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1644 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 0.000147
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1e-06
## Maximum variance parameter change: 5e-05
## ....................................................
## Iteration 23 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1645 | Absolute change: 0 | Relative change: 0
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000156
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 4.8e-05
## ....................................................
## Iteration 24 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1647 | Absolute change: -2e-04 | Relative change: 1e-08
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000173
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 3e-06
## Maximum variance parameter change: 0.000102
## ....................................................
## Iteration 25 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1645 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000108
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 7.5e-05
## ....................................................
## Iteration 26 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1644 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 0.000129
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 1e-06
## Maximum variance parameter change: 5.4e-05
## ....................................................
## Iteration 27 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1645 | Absolute change: -1e-04 | Relative change: 0
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000107
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.2e-05
## ....................................................
## Iteration 28 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1644 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 0.000122
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.1e-05
## ....................................................
## Iteration 29 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1645 | Absolute change: -1e-04 | Relative change: 0
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000118
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.3e-05
## ....................................................
## Iteration 30 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1644 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 0.000122
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.3e-05
## ....................................................
## Iteration 31 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1645 | Absolute change: -1e-04 | Relative change: 0
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000124
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.5e-05
## ....................................................
## Iteration 32 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1644 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 0.000126
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.5e-05
## ....................................................
## Iteration 33 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1645 | Absolute change: -1e-04 | Relative change: 1e-08
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000129
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.8e-05
## ....................................................
## Iteration 34 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1645 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 0.00013
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 6.8e-05
## ....................................................
## Iteration 35 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1646 | Absolute change: -1e-04 | Relative change: 1e-08
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000133
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 7e-05
## ....................................................
## Iteration 36 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1645 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000135
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 7e-05
## ....................................................
## Iteration 37 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1646 | Absolute change: -1e-04 | Relative change: 1e-08
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000138
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 7.3e-05
## ....................................................
## Iteration 38 2021-07-06 16:58:53
## E Step
## M Step Intercepts |---
## Deviance = 21123.1645 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.00014
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 7.3e-05
## ....................................................
## Iteration 39 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1646 | Absolute change: -1e-04 | Relative change: 1e-08
## !!! Deviance increases! !!!!
## !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1 !!!!
## Maximum item intercept parameter change: 0.000143
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 2e-06
## Maximum variance parameter change: 7.5e-05
## ....................................................
## Iteration 40 2021-07-06 16:58:53
## E Step
## M Step Intercepts |----
## Deviance = 21123.1645 | Absolute change: 1e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 9.8e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 3e-06
## Maximum variance parameter change: 7.5e-05
## ....................................................
## Item Parameters
## xsi.index xsi.label est
## 1 1 i03 -1.3593
## 2 2 i02 -1.1811
## 3 3 i04 -0.8100
## 4 4 i10 -0.6704
## 5 5 i09 -0.5113
## 6 6 i06 -0.5063
## 7 7 i08 -0.4714
## 8 8 i01 -0.4665
## 9 9 i07 -0.3783
## 10 10 i05 -0.2683
## 11 11 i12 0.3908
## 12 12 i15 0.9334
## 13 13 i13 1.1068
## 14 14 i14 1.2249
## 15 15 i11 1.2987
## ...................................
## Regression Coefficients
## [,1]
## [1,] 0.5062
##
## Variance:
## [,1]
## [1,] 1.386
##
##
## EAP Reliability:
## [1] 0.782
##
## -----------------------------
## Start: 2021-07-06 16:58:52
## End: 2021-07-06 16:58:53
## Time difference of 0.2101989 secssummary(mod4)## ------------------------------------------------------------
## TAM 3.7-16 (2021-06-24 14:31:37)
## R version 4.0.2 (2020-06-22) x86_64, mingw32 | nodename=DESKTOP-U0L65SJ | login=araec
##
## Date of Analysis: 2021-07-06 16:58:53
## Time difference of 0.2101989 secs
## Computation time: 0.2101989
##
## Multidimensional Item Response Model in TAM
##
## IRT Model: PCM2
## Call:
## tam.mml(resp = gf_matrix[, 2:17], constraint = "items")
##
## ------------------------------------------------------------
## Number of iterations = 40
## Numeric integration with 21 integration points
##
## Deviance = 21123.16
## Log likelihood = -10561.58
## Number of persons = 1182
## Number of persons used = 1182
## Number of items = 16
## Number of estimated parameters = 17
## Item threshold parameters = 15
## Item slope parameters = 0
## Regression parameters = 1
## Variance/covariance parameters = 1
##
## AIC = 21157 | penalty=34 | AIC=-2*LL + 2*p
## AIC3 = 21174 | penalty=51 | AIC3=-2*LL + 3*p
## BIC = 21243 | penalty=120.27 | BIC=-2*LL + log(n)*p
## aBIC = 21189 | penalty=66.22 | aBIC=-2*LL + log((n-2)/24)*p (adjusted BIC)
## CAIC = 21260 | penalty=137.27 | CAIC=-2*LL + [log(n)+1]*p (consistent AIC)
## AICc = 21158 | penalty=34.53 | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1) (bias corrected AIC)
## GHP = 0.55936 | GHP=( -LL + p ) / (#Persons * #Items) (Gilula-Haberman log penalty)
##
## ------------------------------------------------------------
## EAP Reliability
## [1] 0.782
## ------------------------------------------------------------
## Covariances and Variances
## [,1]
## [1,] 1.386
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
## [,1]
## [1,] 1.177
## ------------------------------------------------------------
## Regression Coefficients
## [,1]
## [1,] 0.50617
## ------------------------------------------------------------
## Item Parameters -A*Xsi
## item N M xsi.item AXsi_.Cat1 B.Cat1.Dim1
## 1 i03 1182 0.816 -1.359 -1.359 1
## 2 i02 1182 0.794 -1.181 -1.181 1
## 3 i04 1182 0.740 -0.810 -0.810 1
## 4 i10 1182 0.718 -0.670 -0.670 1
## 5 i09 1182 0.692 -0.511 -0.511 1
## 6 i06 1182 0.691 -0.506 -0.506 1
## 7 i08 1182 0.685 -0.471 -0.471 1
## 8 i01 1182 0.684 -0.466 -0.466 1
## 9 i07 1182 0.669 -0.378 -0.378 1
## 10 i05 1182 0.650 -0.268 -0.268 1
## 11 i12 1182 0.525 0.391 0.391 1
## 12 i15 1182 0.420 0.933 0.933 1
## 13 i13 1182 0.387 1.107 1.107 1
## 14 i14 1182 0.365 1.225 1.225 1
## 15 i11 1182 0.351 1.299 1.299 1
## 16 i16 1182 0.287 1.668 1.668 1
##
## Item Parameters in IRT parameterization
## item alpha beta
## 1 i03 1 -1.359
## 2 i02 1 -1.181
## 3 i04 1 -0.810
## 4 i10 1 -0.670
## 5 i09 1 -0.511
## 6 i06 1 -0.506
## 7 i08 1 -0.471
## 8 i01 1 -0.466
## 9 i07 1 -0.378
## 10 i05 1 -0.268
## 11 i12 1 0.391
## 12 i15 1 0.933
## 13 i13 1 1.107
## 14 i14 1 1.225
## 15 i11 1 1.299
## 16 i16 1 1.668hist(mod4$person$EAP)
hist(mod4$xsi$xsi)
mean(mod4$xsi$xsi)## [1] -0.1112181hist(mod5$person$EAP)
hist(mod5$xsi$xsi)
mean(mod5$xsi$xsi)## [1] -0.1111309- Análide da dimensionalidade do teste gf
r_matrix <- tetrachoric(gf_matrix[ , 2:17]) r_matrix$rho %>% view
fa.parallel(gf_matrix[ , 2:17], cor = "tet")
## Parallel analysis suggests that the number of factors = 7 and the number of components = 1 r_matrix$rho %>% data.frame %>%
add_rownames(var = "coditem1") %>%
pivot_longer(cols = 2:17, names_to = "coditem2" ,values_to = "r") %>%
ggplot(
aes(x=r)
) +
geom_histogram(
aes(y=..density..),
binwidth = .10,
color = "white",
fill = "red",
alpha = .5
) +
scale_x_continuous(
breaks = seq(0, 1, .1),
limits = c(0,1)
) +
scale_color_brewer(palette = "Set1") +
theme_minimal()
- Análide da dimensionalidade do ENEM (mat)
score_mt %>% sample_n(size = 1200) %>%
fa.parallel(cor = "tet")
## Parallel analysis suggests that the number of factors = 19 and the number of components = 15score_ch %>% sample_n(size = 1200) %>%
fa.parallel(cor = "tet")
## Parallel analysis suggests that the number of factors = 17 and the number of components = 8r_matrix_mt <- score_mt %>% sample_n(size = 1200) %>% tetrachoricr_matrix_ch <- score_ch %>% sample_n(size = 1200) %>% tetrachoricr_matrix_mt$rho %>% view
r_matrix_ch$rho %>% view
r_matrix_mt$rho %>% data.frame %>%
add_rownames(var = "coditem1") %>%
pivot_longer(cols = 2:46, names_to = "coditem2" ,values_to = "r") %>%
ggplot(
aes(x=r)
) +
geom_histogram(
aes(y=..density..),
binwidth = .10,
color = "white",
fill = "blue",
alpha = .5
) +
scale_x_continuous(
breaks = seq(0, 1, .1),
limits = c(0,1)
) +
scale_color_brewer(palette = "Set1") +
theme_minimal()
r_matrix_ch$rho %>% data.frame %>%
add_rownames(var = "coditem1") %>%
pivot_longer(cols = 2:46, names_to = "coditem2" ,values_to = "r") %>%
ggplot(
aes(x=r)
) +
geom_histogram(
aes(y=..density..),
binwidth = .10,
color = "white",
fill = "cyan",
alpha = .5
) +
scale_x_continuous(
breaks = seq(0, 1, .1),
limits = c(0,1)
) +
scale_color_brewer(palette = "Set1") +
theme_minimal()
r_matrix_mt[["tau"]] %>% viewr_matrix_mt$rho %>% data.frame %>%
add_rownames(var = "coditem1") %>%
pivot_longer(cols = 2:46, names_to = "coditem2" ,values_to = "r") %>%
pull(r) %>% describe## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2025 0.09 0.17 0.07 0.07 0.09 -0.29 1 1.29 3.64 17.82 0r_matrix_ch$rho %>% data.frame %>%
add_rownames(var = "coditem1") %>%
pivot_longer(cols = 2:46, names_to = "coditem2" ,values_to = "r") %>%
pull(r) %>% describe## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2025 0.14 0.16 0.12 0.12 0.09 -0.14 1 1.14 3.67 17.94 0r_matrix$rho %>% data.frame %>%
add_rownames(var = "coditem1") %>%
pivot_longer(cols = 2:17, names_to = "coditem2" ,values_to = "r") %>%
pull(r) %>% describe## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 256 0.38 0.18 0.34 0.34 0.1 0.14 1 0.86 2.32 5.59 0.01fa_mt3 <- fa(r_matrix_mt$rho, nfactors = 3, rotate = "promax", n.obs = 1200 )
print.psych(fa_mt3, digits = 2, sort = TRUE)## Factor Analysis using method = minres
## Call: fa(r = r_matrix_mt$rho, nfactors = 3, n.obs = 1200, rotate = "promax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item MR1 MR2 MR3 h2 u2 com
## mt_3 3 0.63 -0.17 -0.02 0.381 0.62 1.1
## mt_45 45 0.59 -0.09 -0.12 0.309 0.69 1.1
## mt_6 6 0.57 -0.08 0.07 0.345 0.65 1.1
## mt_8 8 0.57 -0.10 -0.01 0.312 0.69 1.1
## mt_9 9 0.54 -0.05 0.15 0.358 0.64 1.2
## mt_43 43 0.52 -0.12 -0.18 0.245 0.75 1.3
## mt_13 13 0.47 -0.04 -0.03 0.211 0.79 1.0
## mt_34 34 0.43 0.08 0.21 0.305 0.70 1.5
## mt_19 19 0.41 -0.04 0.15 0.229 0.77 1.3
## mt_16 16 0.36 -0.16 -0.08 0.126 0.87 1.5
## mt_38 38 0.36 0.10 0.09 0.177 0.82 1.3
## mt_39 39 0.34 -0.04 0.08 0.139 0.86 1.1
## mt_42 42 0.33 -0.08 0.02 0.112 0.89 1.1
## mt_29 29 0.30 0.21 0.03 0.162 0.84 1.8
## mt_33 33 0.30 0.00 0.07 0.107 0.89 1.1
## mt_37 37 0.29 -0.03 0.12 0.121 0.88 1.3
## mt_4 4 0.28 0.07 -0.06 0.082 0.92 1.2
## mt_25 25 0.27 0.25 0.06 0.175 0.83 2.1
## mt_5 5 0.26 -0.03 0.06 0.081 0.92 1.1
## mt_21 21 0.24 0.21 0.11 0.155 0.84 2.4
## mt_28 28 0.24 0.06 -0.05 0.061 0.94 1.2
## mt_26 26 0.24 -0.09 0.02 0.064 0.94 1.3
## mt_12 12 0.21 0.09 -0.04 0.055 0.94 1.4
## mt_27 27 0.21 0.11 0.16 0.113 0.89 2.5
## mt_15 15 0.18 0.05 -0.08 0.035 0.97 1.5
## mt_36 36 0.15 0.12 -0.08 0.039 0.96 2.4
## mt_14 14 -0.26 0.44 0.01 0.227 0.77 1.6
## mt_31 31 0.04 0.32 0.28 0.213 0.79 2.0
## mt_11 11 0.18 -0.31 0.26 0.193 0.81 2.6
## mt_23 23 -0.06 0.25 -0.09 0.069 0.93 1.4
## mt_7 7 -0.02 0.24 0.11 0.073 0.93 1.4
## mt_30 30 0.09 -0.22 0.02 0.052 0.95 1.3
## mt_18 18 0.07 0.22 0.13 0.084 0.92 1.8
## mt_2 2 0.08 0.21 0.01 0.059 0.94 1.3
## mt_1 1 -0.03 0.16 -0.05 0.026 0.97 1.2
## mt_44 44 0.11 0.15 0.03 0.044 0.96 2.0
## mt_10 10 0.02 -0.15 -0.04 0.024 0.98 1.2
## mt_24 24 0.14 0.08 0.42 0.247 0.75 1.3
## mt_40 40 -0.02 -0.32 0.39 0.234 0.77 1.9
## mt_32 32 -0.08 0.13 0.38 0.155 0.85 1.3
## mt_20 20 0.11 -0.06 0.37 0.173 0.83 1.2
## mt_41 41 -0.04 0.01 0.23 0.048 0.95 1.1
## mt_17 17 0.09 -0.03 0.22 0.068 0.93 1.4
## mt_22 22 0.13 -0.12 -0.16 0.044 0.96 2.8
## mt_35 35 0.05 0.08 -0.11 0.018 0.98 2.3
##
## MR1 MR2 MR3
## SS loadings 4.08 1.17 1.30
## Proportion Var 0.09 0.03 0.03
## Cumulative Var 0.09 0.12 0.15
## Proportion Explained 0.62 0.18 0.20
## Cumulative Proportion 0.62 0.80 1.00
##
## With factor correlations of
## MR1 MR2 MR3
## MR1 1.00 0.15 0.33
## MR2 0.15 1.00 0.09
## MR3 0.33 0.09 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 990 and the objective function was 7.66 with Chi Square of 9063.33
## The degrees of freedom for the model are 858 and the objective function was 3.82
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 1200 with the empirical chi square 5982.09 with prob < 0
## The total number of observations was 1200 with Likelihood Chi Square = 4516.9 with prob < 0
##
## Tucker Lewis Index of factoring reliability = 0.476
## RMSEA index = 0.06 and the 90 % confidence intervals are 0.058 0.061
## BIC = -1566.39
## Fit based upon off diagonal values = 0.8
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of (regression) scores with factors 0.92 0.77 0.78
## Multiple R square of scores with factors 0.84 0.59 0.61
## Minimum correlation of possible factor scores 0.69 0.18 0.23- Análise de rasch no MIRT
- Veja http://philchalmers.github.io/mirt/html/00Index.html
mod1 <- mirt(gf_matrix[ , 2:17], model = 1, TOL = .001, itemtype='Rasch')##
Iteration: 1, Log-Lik: -10577.431, Max-Change: 0.15361
Iteration: 2, Log-Lik: -10566.725, Max-Change: 0.09803
Iteration: 3, Log-Lik: -10563.192, Max-Change: 0.05889
Iteration: 4, Log-Lik: -10562.052, Max-Change: 0.03554
Iteration: 5, Log-Lik: -10561.724, Max-Change: 0.01803
Iteration: 6, Log-Lik: -10561.629, Max-Change: 0.00990
Iteration: 7, Log-Lik: -10561.598, Max-Change: 0.00563
Iteration: 8, Log-Lik: -10561.589, Max-Change: 0.00289
Iteration: 9, Log-Lik: -10561.585, Max-Change: 0.00159
Iteration: 10, Log-Lik: -10561.583, Max-Change: 0.00097summary(mod1)## F1 h2
## i03 0.596 0.355
## i02 0.596 0.355
## i04 0.596 0.355
## i10 0.596 0.355
## i09 0.596 0.355
## i06 0.596 0.355
## i08 0.596 0.355
## i01 0.596 0.355
## i07 0.596 0.355
## i05 0.596 0.355
## i12 0.596 0.355
## i15 0.596 0.355
## i13 0.596 0.355
## i14 0.596 0.355
## i11 0.596 0.355
## i16 0.596 0.355
##
## SS loadings: 5.687
## Proportion Var: 0.355
##
## Factor correlations:
##
## F1
## F1 1coef(mod1 , simplify=TRUE, IRTpars=TRUE)## $items
## a b g u
## i03 1 -1.864 0 1
## i02 1 -1.686 0 1
## i04 1 -1.315 0 1
## i10 1 -1.175 0 1
## i09 1 -1.016 0 1
## i06 1 -1.011 0 1
## i08 1 -0.976 0 1
## i01 1 -0.971 0 1
## i07 1 -0.883 0 1
## i05 1 -0.773 0 1
## i12 1 -0.114 0 1
## i15 1 0.428 0 1
## i13 1 0.602 0 1
## i14 1 0.720 0 1
## i11 1 0.794 0 1
## i16 1 1.162 0 1
##
## $means
## F1
## 0
##
## $cov
## F1
## F1 1.385plot(mod1, type = 'trace', facet_items = FALSE)
itemplot(mod1, item = 3)
itemplot(mod1, item = 3, type= "score")
itemplot(mod1, item = 3, type= "infoSE")
plot(mod1, type = 'rxx')
itemfit(mod1, fit_stats = 'infit')## item outfit z.outfit infit z.infit
## 1 i03 0.738 -3.362 0.863 -2.895
## 2 i02 0.729 -3.886 0.847 -3.555
## 3 i04 0.728 -4.889 0.842 -4.380
## 4 i10 0.817 -3.457 0.909 -2.630
## 5 i09 0.860 -2.864 0.916 -2.590
## 6 i06 0.832 -3.502 0.893 -3.326
## 7 i08 0.812 -4.030 0.878 -3.853
## 8 i01 0.949 -1.032 0.948 -1.610
## 9 i07 1.004 0.107 1.019 0.621
## 10 i05 0.805 -4.740 0.880 -4.140
## 11 i12 0.867 -4.049 0.901 -4.088
## 12 i15 0.908 -2.418 0.920 -3.323
## 13 i13 1.036 0.858 1.019 0.739
## 14 i14 0.877 -2.803 0.930 -2.713
## 15 i11 0.967 -0.693 0.972 -1.034
## 16 i16 0.915 -1.447 0.908 -2.979itemfit(mod1, empirical.plot=2)
itemfit(mod1, empirical.plot=16)
theta_se <- fscores(mod1, method = "WLE", full.scores.SE = TRUE)
empirical_rxx(theta_se)## F1
## 0.8045146empirical_plot(gf_matrix[ , 2:17], c(1, 8, 16))
mod2 <- score_mt %>% sample_n(size = 1200) %>%
mirt(model = 1, TOL = .001, itemtype='Rasch')##
Iteration: 1, Log-Lik: -28900.691, Max-Change: 0.58376
Iteration: 2, Log-Lik: -28660.500, Max-Change: 0.10388
Iteration: 3, Log-Lik: -28618.635, Max-Change: 0.04225
Iteration: 4, Log-Lik: -28601.496, Max-Change: 0.02879
Iteration: 5, Log-Lik: -28592.983, Max-Change: 0.02070
Iteration: 6, Log-Lik: -28588.717, Max-Change: 0.01474
Iteration: 7, Log-Lik: -28585.706, Max-Change: 0.00670
Iteration: 8, Log-Lik: -28585.232, Max-Change: 0.00394
Iteration: 9, Log-Lik: -28585.048, Max-Change: 0.00243
Iteration: 10, Log-Lik: -28584.964, Max-Change: 0.00160
Iteration: 11, Log-Lik: -28584.936, Max-Change: 0.00097summary(mod2)## F1 h2
## mt_1 0.232 0.0537
## mt_2 0.232 0.0537
## mt_3 0.232 0.0537
## mt_4 0.232 0.0537
## mt_5 0.232 0.0537
## mt_6 0.232 0.0537
## mt_7 0.232 0.0537
## mt_8 0.232 0.0537
## mt_9 0.232 0.0537
## mt_10 0.232 0.0537
## mt_11 0.232 0.0537
## mt_12 0.232 0.0537
## mt_13 0.232 0.0537
## mt_14 0.232 0.0537
## mt_15 0.232 0.0537
## mt_16 0.232 0.0537
## mt_17 0.232 0.0537
## mt_18 0.232 0.0537
## mt_19 0.232 0.0537
## mt_20 0.232 0.0537
## mt_21 0.232 0.0537
## mt_22 0.232 0.0537
## mt_23 0.232 0.0537
## mt_24 0.232 0.0537
## mt_25 0.232 0.0537
## mt_26 0.232 0.0537
## mt_27 0.232 0.0537
## mt_28 0.232 0.0537
## mt_29 0.232 0.0537
## mt_30 0.232 0.0537
## mt_31 0.232 0.0537
## mt_32 0.232 0.0537
## mt_33 0.232 0.0537
## mt_34 0.232 0.0537
## mt_35 0.232 0.0537
## mt_36 0.232 0.0537
## mt_37 0.232 0.0537
## mt_38 0.232 0.0537
## mt_39 0.232 0.0537
## mt_40 0.232 0.0537
## mt_41 0.232 0.0537
## mt_42 0.232 0.0537
## mt_43 0.232 0.0537
## mt_44 0.232 0.0537
## mt_45 0.232 0.0537
##
## SS loadings: 2.416
## Proportion Var: 0.054
##
## Factor correlations:
##
## F1
## F1 1plot(mod2, type = 'rxx')