An approach was developed based on item-response models defined at the level of salient subject groups rather than at the level of individuals, designed for use with multiple-matrix sampling designs. In each of three National Assessment of Educational Progress (NAEP) mathematics subtopics, Reiser's group-effects latent trait model was fitted to the proportions of correct response to items as observed in the cells of a design. Item parameters and contrasts among demographic groups were estimated in each of four data sets: 1972-73 and 1977-78 data for 13-year-olds and 17-year-olds. Based on items common to two or more data sets, results were linked across ages and over time in each subtopic. Item parameters and group averages were obtained on scales common across ages and years. Successful calibration and linking in all subtopics demonstrates the feasibility of applying item-response methods to sparse sampling designs. However, scaling must be accomplished within fairly narrowly-defined skill areas, such as the NAEP subtopics, if the integrity of scales is to be maintained. Item response scaling of NAEP test booklets as a whole is discouraged. Primary type of information provided by the report: Results (Secondary Analysis). (Author/CM)