TARLE 10.4

34; ｾ＠

TARLE 10.4 TARLE 10.4

Ilem Inrormalion

I 2 5 6 K 9 10

0.50 0.66 0.0.1 0.19 0.1 R 1.()6 OAK

---.---

II I.l 0.4.') O. 16

hem 9 has the highest infonnation at e

=

^0.45. It is administered nexl.

1 1

Future Directions of ltetTI Response Theory

We hope that Dr. Testmaker and other applied measurement specialists will find the contents of this book helpful. Many important concepts.

models. features, and applications were introduced. and many examples were provided; this material should prepare our readers for the next steps in the learning process. No book, hy itself, can prepare measurement specitdists to use IRT models successfully in their work. Applied work with various data sets and IRT computer programs is an essential compo- nent of training in IRT. The practitioner must be ready to handle the many problems that arise in practice.

Although IRT provides solutions to many testing prohlems that pre- viously were unsolved, it is not a magic wand that can be waved to overcome such deficiencies as poorly written test items and poor test designs. In the hands of careful test developers, however, IRT models and methods can become powerful tools in the design and construction of sound educational and psychological instruments, and in reporting and interpreting test results.

Research on JRT models and their applications is being conducted at a phenomenal rate (see Thissen & Steinberg, 1986, for a taxonomy of models). Entire issues of several journals huve been devoted to devel- opments in IRT. For the future, two directions for research appear to be especially important: polytomous unidimensional response models and both dichotomous and polytomous multidimensional response models.

Research in hoth directions is well underway (Bock, 1972; Masters &

Wright, 1984; Samejima, 1969, 1972, 1973, 1974). With the growing interest in "authentic measurement," special attention must be given to I RT models that can handle polytomolls scoring, since authentic mea- surement is linked to performance testing and to nondichotomous scor- ing of examinee performance.

I'D

154 ｉｬｬｊｎｉＩａｍｉｾｎｬＧａｌｓ＠ OF ITliM RESPONSE TIIEORY

Multidimensional IRT models were introduced originally by Lord and Novick (1968) and Samejima (1974) and, more recently. by Embret- son (1984) and McDonald (1989). Multidimensional mmJcls offer the prospect of better filling current test data and providing multidimen- sional representations of both items and examinee abilities. It remains to be seen whether parameters for these multidimensional models call be estimated properly and whether multidimensional representations of items and examinees are useful to practitioners.

Goldstein and Wood (1989) have argued for more IRT model building in the future but feel that more attention should be given to placing IRT models within an explicit linear modeling framework. Advantages, aQcording to Goldstein and Wood, include model parameters that are silnpler to understand, easier to estimate, and that have well-known shltistical properties.

'In addition to the important IRT applications addressed in earlier chapters, three others are likely to draw special attention from educators and psychologists in the coming years. First, large-scale state, national, and international assessments are attracting considerable attention and will continue to do so for the foreseeable future. Item response models are being used at the all-important reporting stages in these assess- ments. It will be interesting to see what technical controversies arise from this type of application. One feature that plays an important role in reporting is the ICC. Are ICCs invariant to the nature and amounts of instruction? The assumption is that ICCs are invariant, but substan- tially more research is needed to establish this point.

Second. cognitive psychologists such as Embretson (1984) arc inter- ested in using IRT models to link examinees' task performances fo their abilities through complex models that attempt to estimate parameters for the cognitive components needed to complete the fasks. This line of research is also consistent with Goldstein and Wood's (1989) goal of seeking more meaningful psychological models that help explain exam- inee test perrormance. Much or the IRT research to date has emphasi7.ed the use of mathematical models that provide little in the way of psycho- logical interpretations of examinee item lind test performance.

Third, educators and psychologists are making the argument for using test scores to do more than simply rank order examinees on their abilities or determine whether they have met n particular achievement level or standard. Diagnostic inrormation is becoming increasingly important to users of test scores. Inappropriateness mea.mrement de- veloped by M. Levine and F. Drasgow (see, for example, Drasgow

f'u/llrl' Oi't'Clitl/u ollll'm R",'IWIU(! l'h"(}I'Y 155 el aI., 1987), which incorporales IRT models, provides a framework for idenlifying aherranl responses of examinees and special groups of examinees on individual items and groups of items. Such information may he helpful in successful diagnoslic work. Gretl1er use of IRT models in providing diagnostic inrormation is anlicipafed in the coming years.

Appendix A ..

Classical and IRT Parameter Estimates for the New Mexico State Proficiency Exam

TABLE A.I Classical and IRT Item ParHtncler ESlimates for IIIC Olle-, Two-, lind Three-Parameter Models

ＭＭｾＭＭＭＭＭｾ＠

1'1.'111 P"raml.'la E.,lilllille.'

ｾ＠... "-.-'-- ＭｾＮ＠

ＭＭＮＭＮｾＢＭＭＭＮ＠

^JP

llelll P ^r

"

^{b 1I I>} ＭＭＭＭＮｾｾｾＭＭＭＭｾＭＭ ^{a c}

1 0.45 OAI 0.22 (121 0.61 ｏＮｾｒ＠ 0.R4 0.17

2 0.70 0.45 LOU -U-fn 0.1l2 0.51 ()QI 0.1"

:\ 0.65 0,50 ·0.75 {),(,O {),1)2 lUll 1 . III n,17

4 0.77 n.20 -IA5 --2,25 11.14 ·1,69 IU7 n,17

5 0.75 0.:\7 -1.34 -1.25 0,66 -0.97 n,M n,17

6 0.]9 n.27 n.52 0.71 O,W 1.11 O,M 0.17

7 0.76 OAO ^{' 1.3(,} ｾ＠ 1.67 0.75 -II.')() 0.79 0,17

R 0.60 0,35 -11.52 -O,S6 (),52 . n,o'J 0.67 0,17

9 0.78 0.29 -1.51 -1.70 050 -U6 O.S] 1l.1'I

10 0.55 0.32 ,-0.27 -0,32 !l47 O.IQ 0,62 0.17

II 0.61 0.37 -0.53 -U.S5 0.56 ·n.14 O.6S 017

12 0.59 0,21 ··0,4 7 -(l,R I (1,29 -0. II IU7 0.17

D 055 0,30 n.25 -0 .. 10 0,4.1 0,22 1),56 n,17

14 0.73 0.44 I.IR -0.97 O,R2 ··(J,67 O.RR 0.17

IS 0.38 0.54 O.5X O,4Q 0,75 0,76 UO n.IS

16 0.62 0.54 -0.51\ -0.45 1.04 -0,04 I.:'i.l 0,21

17 0.80 0.34 -1.67 -1.5] 0.67 ,1..12 0.06 0.17

18 0.65 0.45 -0.74 -0.78 0,5<1 ·(1.32 O.M 0.17

19 0.49 OA3 0.04 O,OJ 0,6R 0.51 1.2J 0,22

20 0.64 OAO -0.7n n.M 0.65 - 0.31 O.7:l 0.17

1:'i6

'1

,/

Ap/)I'I/(UX A \57

TABU': A.I continued

. _ . _ - - _ ... - lP

/tt'm P ^r b b a b a ^('

21 0.69 0.34 ｾＮＹＹ＠ -1.07 0.53 ｾＮＶＸ＠ 0.59 0.17

22 0.67 0.41 ｾＮＸＵ＠ ｾＮＷＸ＠ 0.68 4).46 0.74 0.10

23 0.46 0.35 0.18 0.20 0.50 0.63 0.74 0.17

24 0.74 0.52 -1.26 -0.89 1.15 -0.64 1.25 0.17

25 0.61 0.47 ｾＮＵＶ＠ -0.48 0.80 -0.12 0.98 0.17

26 0.34 0.30 0.78 0.97 0.44 1.18 0.65 0.12

27 0.70 0.50 -1.05 -O.RO 0.99 -0.52 1.08 0.17

2R 0.6\ OA4 -0.56 ＭｾＱＮＵＰ＠ 0.71 () 12 0.91 0.17

19 0.73 0.35 -1.23 -1.24 O.5R -H.91 0.62 0.17

3() _{0.74 0.44 -1.28 -1.0:1 0.85 --O.R I} 0.R6 0.17

."

^{0.57 (U2 -0.35 0.41 OA6 O.OR (I.5R 0.17}

32 0.74 O.3R -1.20 1.17 ＨＩｈｾ＠ 0.'10 0.6R 0.17

.H 0.44 OYi 0.29

o.n

051 O.7R 0.R7 0.19

.14 0.60 OA5 -0.52 OAt. n.7S (UI.l UO 0.20

35 02R 0.29 1.14 1.'17 OAt. lAO 1'<)4 n.IS

30 O.M 0.46 -0.99 -n.R2 II.R3 · n . .'III 0.94 n.l7

n 1129 n.27 1.11 1.46 nAI 1.54 n.63 0.10

JR 0.77 (US -1.4 \ '.19 II"'L 1111 OM 0.17

'"

^{0.(,0 (UK -0.50 n.51 051 · not) 0.69 0.17}

40 043 OAR 03J n.26 (1.111 O.5K UO 0.17

41 n.4:1 OAI 0.:1:1 IU O.fi2 O."R 0.99 n.17

41 n.()(1 0.46 -0.51 ·11.45 ^{(U.') · (I.ot) ().')]} 0.17

41 O.4() (),l7 0.17 11.1 R ^0:')6 (1.70 I.H 0.25

44 (1.52 n.2l -0.12 -0.19 (U2 0.44 0.4 , 0.17

4.'\ 0.26 0.2R 1.24 1.53 OA5 1.46 1.14 0.15

46 O.M 0.44 ｾＩＮＶｒ＠ -0.61 O.D - 11.2:') 0.R4 0.17

47 (US OAO -J.J4 --1.16 n.74 {1.R9 O.7R n.17

4R 079 0.39 -1.57

-un

^{0.79 ·I.OR O.RO} 0.17

49 0.76 (U6 -1.:17 -1.2R OM -1.00 O.oK 0.17

:')0 n.57 ^(U() 4).34 ｾＩＮＴＳ＠ OA! O.!O 0.51 0.17

51 OA9 IU5 0.04 (1.115 053 (1..'\7 0.94 0.20

52 (U4 n.n n.R 1 (un 11.59 1.01 1.06 0.14

53 O,,'\() 0.39 4).114 ·OA! n.59 0.5] I.Ol 0.23

:')4 0.74 IUJ -1.26 -1.32 (J.55 ·0.94 0.01 0.17

55 OAR 0.61 0.12 0.0:') 1.21 n.n 1.41 0.08

158 FUNDAMENTALS OF ITEM RESPONSE THEORY TAIILE A.I conlinut!d

__ ｾ＠______ JIl-I ｬｴｦｮｾｦ｡ＬＮＬＡＢＡＮ･Ａ･Ａｾ＠ E.I!inlllleJ

Cla.uiml IP 2P 3P

_ _ _ _ _ • _ _ _ _ _ " _ _ c

111'/1/ p r h b a b ^{(I ('}

56 0.51 0.34 -0.03 -0.03 0.48 0.43 0.67 0.17

57 0.64 0.32 -0.71 -0.82 0.49 -0.37 O:5ti 0.17

58 0.50 0.43 -0.02 -{J.03 0.66 0.35 0.85 0.17

59 <-O.l!:tl 0.26 -1.1\8 -2.18 0.48 1.82 0.52 0.17

60 0.47 0.35 0.15 0.18 0.49 0.61 0.70 0.17

61 0.71 0.35 -1.09 -1.13 0.56 0.77 0.62 0.17

62 0.73 0.38 -1.21 -1.15 0.64 -0.85 0.68 0.17

63 0.79 0.30 -1.57 -1.69 0.53 -1.37 0.56 0.17

64 0.63 0.23 -0.63 -0.97 0.33 --0.34 0.40 0.17

65 0.59 0.47 -0.43 -0.38 0.77 -0.05 0.89 0.17

66 0.77 0.16 -·1.45 -2.85 0.26 1.97 0.31 0.17

67 0.54 0.52 -0.20 -0.17 0.90 0.17 1.22 O. I 7

68 0.66 0.41 ·-0.80 -0.75 0.65 ·-0.40 0.74 0.17

69 0.72 0.37 -1.12 -1.10 0.61 -1-1.77 0.66 0.17

70 0.53 0.21 -0.14 {J.26 0.26 0.46 0.35 0.17

71 0.78 0.41 ^{.. 1.49} .. 1.21 0.83 0.911 0.114 0.17

72 0.78 0.37 -1.53 -1.34 0.72 -1.06 0.76 0.17

73 0.64 0.53 -0.68 -0.53 0.98 0.23 1.14 0.17

74 0.60 0.28 -0.48 -0.62 0.41 -0.1l7 0.52 0.17

75 0.46 0.23 0.17 0.3\ 0.30 0.91 1.41 0.17

76 1.26

77 -1.47

78 -1.61

79 0.60

80 0.63

81 -1.45

82 -0.91

83 -0.69

84 Ll5

85 1.02

86 0.91

87 -0.39

88 2.11

89 1.78

90 1.96