## Loading required package: sm
## Package `sm', version 2.2-5: type help(sm) for summary information
## Loading required package: ltm
## Loading required package: MASS
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:sm':
## 
##     muscle
## Loading required package: msm
## Loading required package: polycor
## Loading required package: mvtnorm
## Loading required package: sfsmisc

Estimation

##           est       sem  n
## [1,] 1.186119 0.5494026 20
## [2,] 2.324989 0.5415616 20
## [3,] 2.324989 0.5415616 20
## [4,] 2.324989 0.5415616 20
## [5,] 2.324989 0.5415616 20
## [6,] 2.324989 0.5415616 20

Item Parameters

Sort Item Parameters according to Item Discrimination

##     discrimination difficulty guessing
## A18         20.246      1.892    0.038
## A10          2.670      1.498    0.235
## A12          2.194     -1.930    0.007
## A4           1.523      0.018    0.266
## A7           1.447      0.093    0.718
## A11          1.349      9.753    0.067
## A6           1.120     -2.757    0.002
## A15          1.093     -1.149    0.001
## A19          1.004     -2.623    0.000
## A1           0.990     -2.951    0.001
## A13          0.939     -2.874    0.002
## A3           0.836     -2.292    0.001
## A8           0.805     -0.587    0.001
## A9           0.741     -1.953    0.002
## A5           0.704     -3.367    0.006
## A14          0.663     -1.130    0.002
## A17          0.448      1.593    0.007
## A20          0.352     -5.466    0.004
## A2           0.010     66.186    0.318
## A16         -1.808     -8.468    0.152

Most difficult to easiest items

##     discrimination difficulty guessing
## A2           0.010     66.186    0.318
## A11          1.349      9.753    0.067
## A18         20.246      1.892    0.038
## A17          0.448      1.593    0.007
## A10          2.670      1.498    0.235
## A7           1.447      0.093    0.718
## A4           1.523      0.018    0.266
## A8           0.805     -0.587    0.001
## A14          0.663     -1.130    0.002
## A15          1.093     -1.149    0.001
## A12          2.194     -1.930    0.007
## A9           0.741     -1.953    0.002
## A3           0.836     -2.292    0.001
## A19          1.004     -2.623    0.000
## A6           1.120     -2.757    0.002
## A13          0.939     -2.874    0.002
## A1           0.990     -2.951    0.001
## A5           0.704     -3.367    0.006
## A20          0.352     -5.466    0.004
## A16         -1.808     -8.468    0.152

Total item 1

There are several different patterns all with a score of 17
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 score theta
11 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
12 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
13 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 17 1.184
14 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 17 1.778
15 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 17 1.995
16 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 17 2.323
17 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
18 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 17 1.037
19 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 17 1.037
20 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 17 1.991
21 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
22 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
23 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
24 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 17 2.323
25 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 17 2.172
26 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 17 0.952
27 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 17 2.172
28 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 17 0.796
29 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 17 2.172
30 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 17 2.172
31 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
32 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 17 2.172
33 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 17 1.184
34 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
35 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
36 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
37 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 17 1.326
38 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 17 1.037
39 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186
40 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 17 0.796
41 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 17 1.184
42 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 17 1.186

Total item 18

There is a single scoring pattern (all answered only item 2 incorrectly) for a grade of 18
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 score theta
2 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
3 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
4 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
5 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
6 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
7 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
8 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
9 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325
10 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 18 2.325