The Null Distribution of Person-Fit Statistics for Conventional and Adaptive Tests

Abstract

Several person-fit statistics have been proposed to detect item score patterns that do not fit an item response theory model. To classify response patterns as misfitting, the distribution of a person-fit statistic is needed. The theoretical null distributions of several fit statistics have been derived for paper-and-pencil (P&P) tests. However, it is unknown whether these distributions also hold for computerized adaptive tests (CAT). A three-part simulation study was conducted. In the first study, the theoretical distribution of the l z statistic across trait. θlevels for CAT and P&P tests was investigated. The distribution of the l* z statistic proposed by Snijders (in press) was also investigated. Results indicated that the distribution of both l z and l* z differed from the theoretical distribution in CAT. The second study examined the distributions of l z and l* z using simulation. These simulated distributions, when based on O [UNKNOWN], were found to be problematic in CAT. In the third study, the detection rates of l* z and l z were compared. The rates for both statistics were found to be similar in most cases.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 81 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.