A Two-Parameter Partial Credit Model for the Ordered-Response Data

Abstract

本文旨在提出步驟鑑別度以改進Masters於1982年所提的「（一個參數）部份計分模式」，而成為「兩個參數部份計分模式」，並探索它的存在可能性。本文作者自行設計的電腦程式，TPPCM，使用最大近似值估計法去估計模式參數與能力參數，並驗証各種參數之適合度，及提供訊息函數，並舉例說明與討論，獲四項結論：（一）兩個參數部份計分模式的存在性獲得肯定；（二）步驟鑑別度能提供區別受試者表現水準之參考；（三）步驟訊息函數獨由每個試題的步驟鑑別度所決定，對試題的選擇與試卷的編輯很有貢獻；（四）除了「明確客觀性」與「參數可分離性」外，兩個參數部份計分模式與一個參數部份計分模式分享共同的基本假設與特性。

The purpose of this paper is to expand Masters` (1982) (one-parameter) partial credit model to be a two-parameter partial credit model. A FORTRAN 77 computer program, TPPCM. developed by present author, which uses maximum likelihood estimation solutions, is used to calibrate model parameters, test goodness-of- fit, and provide information functions of a dataset. From the analysis and discussion of findings of this research, four conclusions cam be drawn as follows: (a) The existence of the two-parameter partial credit model is confirmed. This model becomes an alternative model to score persons` partial knowledge or calibrate any questionnaire or test with ordered-response formats, (b) Step discriminations provide a good help in partitioning persons` performance levels, (c) Step information functions are uniquely and differently determined from step discriminations of each item. Hence it implies potentials for item and test design, selection, and construction. (d) The two-parameter partial credit model shares the same features of the one-parameter partial credit model, except that of specific objectivity and parameter separability.