The Use Of Log-linear Model In CTT Equating

When measuring the same trait in measurement research, if the tests are differentthe raw scores can’t be compared directly, while equating can put the comparison intoeffect. However random errors are unavoidable during the process of equating. Someresearches imply that smoothing tests scores before equating reduced the equatingerror. In order to prove the function of smoothing on the equating error, this researchused log-linear model to smooth the scores before equating and compare the randomerrors of before-smoothing and after-smoothing.This research uses the log-linear model to smooth the scores of different tests, onone hand the log-linear model is efficient; on the other hand the log-linear model isfitting with the frequency of the test scores. The log-linear model is flexible to dealwith the wide range of the test scores. The article used the log-linear model to smooththe tests scores before equating and then calculates the equating error by using thefrequency percentile equivalents and the chain equivalent methods, and compares theequivalent errors before and after smoothing the scores. The hypothesis of this paperas follows:1. Smooth the complete simulative scores and then calculate the equating errorsbefore smoothing the scores and after smoothing the scores by using thefrequency percentile equivalents and the chain equivalent methods. Theequating error after smoothing is smaller than the error before smoothing.2. Smooth the missing high， middle and low simulative scores and then calculatethe equating errors by using two equivalent methods, then compare the equatingerrors before smoothing the scores and after smoothing the scores. The equatingerror after smoothing is smaller than before smoothing.3. Smooth the real test scores and calculate the equivalent error by using twoequivalent methods, then compare the equating error before smoothing thescores and after smoothing the scores. The equating error after smoothing issmaller than before smoothing.The result shows that no matter using the frequency percentile equivalents or thechain equivalent methods, the equating errors after smoothing are smaller than theerrors before smoothing. And most of all, the errors after smoothing by using thefrequency percentile equivalents are smaller than the errors by using the chainequivalent methods.