有獎徵答-- an IRT (Rasch) question （含審查意見與回覆）

ADL CAT 稿件的審查意見：
依據 difficulty parameter, why is playing chess/cards more difficult than gainful work? It seems to me that the result of this analysis suffered from a common problem with Rasch analysis, namely that frequency of performance is confused with difficulty of performance.  Please see Whiteneck G, Dijkers MP. Difficult to measure constructs: conceptual and methodological issues concerning participation and environmental factors. Arch Phys Med Rehabil. 2009 Nov;90(11 Suppl):S22-35 on the limitations of Rasch analysis in the context of participation (or instrumental ADL).

如下圖：依據 Rasch analysis 分析結果， Reading 的難度 > Work > Preparing meal > Heavy housework 這似乎違背邏輯/經驗！！

請以中文解釋之，含其臨床意義。
9/26日之前提出。
可單獨或團隊提出。

image source: https://encrypted-tbn3.google.com/images?q=tbn:ANd9GcR-MLm6Mt_SX9T30vZrnUDcpR7dRotc6vbVBMn-qVW3g9pflovl

Comment: The results of table 2 are intriguing. Why is playing chess/cards more difficult than gainful work? The same for art activities? It seems to me that the result of this analysis suffered from a common problem with Rasch analysis, namely that frequency of performance is confused with difficulty of performance.  Please see Whiteneck G, Dijkers MP. Difficult to measure constructs: conceptual and methodological issues concerning participation and environmental factors. Arch Phys Med Rehabil. 2009 Nov;90(11 Suppl):S22-35 on the limitations of Rasch analysis in the context of participation (or instrumental ADL).

* Response: It was our mistake to state that “The items are largely listed in increasing level of difficulty.” We have deleted the statement. The items’ level of difficulty cannot be simply determined by their order (or parameter of step difficulty) for two reasons. The first is that there are various steps of difficulty (various numbers of item response categories). The second is that the discrimination parameter also affects the hierarchy of item difficulty. That is, some items might be more difficult at certain level of function, but they might be easier at another level of function. This is a potential drawback of the 2-parameter model. We have addressed this issue as follows:

 “We used the GPCM (a type of 2-paramter IRT model, including discrimination and difficulty parameters)³⁴ to fit the patients’ responses and estimate the item parameters for the ADL item bank. The GPCM is a flexible model from the parametric, unidimensional, polytomous-response IRT models. Because GPCM allows discrimination to vary from item to item, it generally fits response data better than a 1-parameter model (e.g., Rasch model).³⁵ However, using a 2-parameter IRT model may have made the results difficult to interpret. For example, an item’s level of difficulty cannot be simply determined by its “difficulty” parameter (i.e., step threshold) because the discrimination parameter (i.e., slope) also affects the hierarchy of item difficulty. That is, some items might be more difficult at certain levels of function, but they might be easier at other levels of function. This is a potential drawback of the 2-parameter model. Nevertheless, the 2-parameter IRT model is suggested due to its flexibility and is adopted by several health-related CATs.^{12, 15, 36}” 

Furthermore, “Even if the discrimination parameter is fixed, explanations of an item’s value of “difficulty” parameter have to be cautious. For example, our results showed that the value (3.54) of difficulty parameter of “volunteer work” was unexpectedly higher than that (2.53) of “gainful work” (Table 2). The value of difficulty parameter is commonly interpreted as the “level of difficulty or challenge” of a task. The difficulty parameter of an item is influenced by how often patients perform the task.²² Appendix 1 shows that only a small proportion of the patients had been working (gainful work (7.1%) and volunteer work (3.1%)). However, that frequency might not necessarily indicate the level of difficulty of a task. Particularly, the patients tested were all outpatients, who were unlikely to seek and do volunteer work. On the other hand, gainful employment is often an obligation or responsibility. Thus, the value of difficulty parameter is not equal to the level of challenge of an ADL task.³⁷ In addition, as aforementioned, we used a 2-parameter model, not the 1-parameter IRT model. Due to these issues, our data are not sufficient to determine whether an item with a low value of difficulty (e.g., doing gainful work) is less challenging than an item with a high value of difficulty (e.g., doing volunteer work).” 

Your further comments are appreciated!