| Bock1997 {mirt} | R Documentation |
A 3-item tabulated data set extracted from Table 3 in Chapter Two.
Phil Chalmers rphilip.chalmers@gmail.com
Bock, R. D. (1997). The Nominal Categories Model. In van der Linden, W. J. & Hambleton, R. K. Handbook of modern item response theory. New York: Springer.
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
## No test:
dat <- expand.table(Bock1997)
head(dat)
## Item.1 Item.2 Item.3
## 1 1 1 1
## 2 1 1 1
## 3 1 1 1
## 4 1 1 1
## 5 1 1 1
## 6 1 1 1
itemstats(dat, use_ts=FALSE)
## $overall
## N
## 1 2000
##
## $itemstats
## N mean sd
## Item.1 2000 2.443 1.070
## Item.2 2000 2.666 0.957
## Item.3 2000 2.780 1.059
##
## $proportions
## 1 2 3 4
## Item.1 0.240 0.284 0.267 0.208
## Item.2 0.122 0.314 0.340 0.224
## Item.3 0.141 0.273 0.253 0.334
mod <- mirt(dat, 1, 'nominal')
# reproduce table 3 in Bock (1997)
fs <- round(fscores(mod, verbose = FALSE, full.scores = FALSE)[,c('F1','SE_F1')],2)
fttd <- residuals(mod, type = 'exp')
table <- data.frame(fttd[,-ncol(fttd)], fs)
table
## Item.1 Item.2 Item.3 freq exp F1 SE_F1
## 1 1 1 1 50 46.444027 -1.72 0.68
## 2 1 1 2 32 37.215496 -1.22 0.64
## 3 1 1 3 15 18.069304 -0.95 0.62
## 4 1 1 4 10 8.692424 -0.61 0.61
## 5 1 2 1 54 59.965727 -1.38 0.65
## 6 1 2 2 80 70.000273 -0.91 0.62
## 7 1 2 3 40 41.674601 -0.65 0.61
## 8 1 2 4 24 25.832371 -0.33 0.61
## 9 1 3 1 27 28.065138 -1.07 0.63
## 10 1 3 2 52 46.689631 -0.62 0.61
## 11 1 3 3 33 33.847511 -0.37 0.61
## 12 1 3 4 27 26.935712 -0.04 0.61
## 13 1 4 1 4 3.940514 -0.63 0.61
## 14 1 4 2 13 10.897962 -0.19 0.61
## 15 1 4 3 10 10.571253 0.06 0.61
## 16 1 4 4 10 12.283469 0.40 0.63
## 17 2 1 1 27 20.191927 -1.29 0.64
## 18 2 1 2 19 26.271170 -0.82 0.62
## 19 2 1 3 11 16.603995 -0.57 0.61
## 20 2 1 4 11 11.097212 -0.24 0.61
## 21 2 2 1 30 36.068703 -0.98 0.63
## 22 2 2 2 78 66.604897 -0.53 0.61
## 23 2 2 3 69 51.217364 -0.28 0.61
## 24 2 2 4 48 43.966108 0.05 0.61
## 25 2 3 1 24 22.900098 -0.68 0.61
## 26 2 3 2 48 59.345066 -0.25 0.61
## 27 2 3 3 52 55.428529 0.01 0.61
## 28 2 3 4 53 61.277297 0.34 0.62
## 29 2 4 1 3 4.974192 -0.25 0.61
## 30 2 4 2 21 21.301177 0.19 0.62
## 31 2 4 3 20 26.765813 0.45 0.63
## 32 2 4 4 54 43.946401 0.81 0.65
## 33 3 1 1 9 7.040049 -0.96 0.62
## 34 3 1 2 12 13.275569 -0.51 0.61
## 35 3 1 3 13 10.330678 -0.26 0.61
## 36 3 1 4 7 9.005107 0.06 0.61
## 37 3 2 1 11 16.098345 -0.66 0.61
## 38 3 2 2 29 42.609506 -0.23 0.61
## 39 3 2 3 37 40.289025 0.03 0.61
## 40 3 2 4 44 45.264883 0.36 0.62
## 41 3 3 1 15 12.966052 -0.38 0.61
## 42 3 3 2 62 47.984143 0.06 0.61
## 43 3 3 3 60 55.255840 0.32 0.62
## 44 3 3 4 88 80.660157 0.67 0.64
## 45 3 4 1 4 3.999324 0.05 0.61
## 46 3 4 2 27 24.639934 0.50 0.63
## 47 3 4 3 43 38.630407 0.78 0.65
## 48 3 4 4 73 85.862836 1.17 0.68
## 49 4 1 1 4 2.538215 -0.75 0.62
## 50 4 1 2 8 6.100809 -0.31 0.61
## 51 4 1 3 7 5.455196 -0.06 0.61
## 52 4 1 4 9 5.695962 0.27 0.62
## 53 4 2 1 7 6.816068 -0.46 0.61
## 54 4 2 2 21 22.926076 -0.02 0.61
## 55 4 2 3 25 24.946447 0.23 0.62
## 56 4 2 4 31 33.758294 0.58 0.64
## 57 4 3 1 8 6.427237 -0.17 0.61
## 58 4 3 2 23 30.276410 0.27 0.62
## 59 4 3 3 35 40.293621 0.54 0.63
## 60 4 3 4 73 71.523729 0.90 0.66
## 61 4 4 1 4 2.513701 0.26 0.62
## 62 4 4 2 21 19.940144 0.73 0.65
## 63 4 4 3 36 36.579513 1.02 0.67
## 64 4 4 4 105 101.211362 1.43 0.71
mod <- mirt(dat, 1, 'nominal')
coef(mod)
## $Item.1
## a1 ak0 ak1 ak2 ak3 d0 d1 d2 d3
## par 0.79 0 1.269 2.304 3 0 0.673 0.538 -0.013
##
## $Item.2
## a1 ak0 ak1 ak2 ak3 d0 d1 d2 d3
## par 0.898 0 0.859 1.717 3 0 1.452 1.636 0.647
##
## $Item.3
## a1 ak0 ak1 ak2 ak3 d0 d1 d2 d3
## par 0.908 0 1.289 2.038 3 0 1.495 1.508 1.457
##
## $GroupPars
## MEAN_1 COV_11
## par 0 1
## End(No test)