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NAEP Analysis and Scaling → Estimation of NAEP Score Scales → NAEP Assessment Item Response Theory Parameters → Mathematics Assessment Item Response Theory Parameters → IRT Parameters for the Algebra and Functions Scale, by Block and Item, Grade 8 Mathematics Combined National and State Main Assessment: 2003

NAEP Technical DocumentationIRT parameters for items in the algebra and functions scale, by block and item, grade 8 mathematics combined national and state main assessment: 2003

Block	Item	NAEP ID	aj	bj	cj	dj1	dj2	dj3	dj4
M3	5	M066201	0.69	-1.82	0.06	†	†	†	†
	10	M067401	1.07	1.25	0.19	†	†	†	†
	11	M086101	0.85	0.55	0.20	†	†	†	†
	12	M047701	1.16	1.24	0.25	†	†	†	†
	13	M067301	1.15	0.17	0.21	†	†	†	†
	15	M093701	1.31	1.84	0.19	†	†	†	†
M4	3	M067701	0.73	-2.06	0.06	†	†	†	†
	10	M066601	0.36	-0.88	†	-0.34	0.34	†	†
	11	M067201	0.48	0.87	†	-1.18	1.18	†	†
	20	M086301	0.24	-1.98	†	-2.08	2.08	†	†
M5	6	M019701	0.49	-2.35	†	†	†	†	†
	11	M066501	0.53	-0.86	†	-0.46	0.46	†	†
	13	M066301	0.30	-1.95	†	-3.51	3.51	†	†
	14	M067901	0.68	-0.67	†	-1.42	1.42	†	†
M6	8	M020401	0.56	-0.72	†	†	†	†	†
	13	M018301	0.89	-0.90	0.06	†	†	†	†
	20	M018701	1.59	0.00	0.26	†	†	†	†
	24	M021201	0.87	0.28	0.00	†	†	†	†
	26	M018801	1.12	0.16	0.27	†	†	†	†
	27	M019301	1.51	0.65	0.21	†	†	†	†
M7	12	M013231	0.76	1.44	0.09	†	†	†	†
	17	M075501	1.31	0.07	0.18	†	†	†	†
	18	M047601	1.56	0.27	0.10	†	†	†	†
	19	M092001	0.36	1.10	†	-0.64	-0.73	-0.40	1.77
M8	1	M012231	0.63	-2.77	0.12	†	†	†	†
	10	M052501	1.32	0.75	0.20	†	†	†	†
	16	M067001	1.61	0.66	0.36	†	†	†	†
	17	M051701	1.33	0.07	0.19	†	†	†	†
M9	2	M0757CL	0.43	-1.19	†	2.46	-0.63	-1.82	†
	4	M091701	1.25	-0.73	0.24	†	†	†	†
	10	M075301	1.26	-0.29	†	1.19	-1.19	†	†
	14	M013731	1.09	0.91	0.11	†	†	†	†
M10	3	M068101	1.00	-0.91	0.11	†	†	†	†
	11	M091801	1.21	0.49	0.14	†	†	†	†
	12	M093001	0.78	0.32	0.16	†	†	†	†
	13	M093501	1.00	1.31	0.00	†	†	†	†
	15	M052101	1.13	0.38	0.00	†	†	†	†
	17	M086201	0.95	0.58	0.16	†	†	†	†
	18	M093301	1.20	0.55	0.14	†	†	†	†
M11	2	M105801	0.51	-0.98	0.13	†	†	†	†
	6	M106201	0.82	-0.43	0.30	†	†	†	†
	11	M106701	1.47	1.46	0.12	†	†	†	†
	15	M107101	0.67	0.66	0.17	†	†	†	†
	18	M107501	0.70	-1.17	0.00	†	†	†	†
M12	3	M110101	1.45	0.74	0.19	†	†	†	†
	10	M110801	0.23	2.16	0.07	†	†	†	†
	13	M111201	0.36	-0.31	0.11	†	†	†	†
	14	M111301	0.60	-1.76	0.16	†	†	†	†
	17	M111601	1.57	0.60	0.28	†	†	†	†
† Not applicable; c parameters are not estimated for generalized partial credit models. NOTE: For item j, aj represents the discriminatory power of the item, bj represents a location parameter related to item difficulty, cj represents the guessing parameter, and dji is the category threshold parameter for category i. The c parameter value is exactly zero for items scaled with the two-parameter logistic model. For item j, dji may not sum to zero because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 Mathematics Assessment.

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