Academic journal article Social Behavior and Personality: an international journal

Fuzzy Partial Credit Scaling: A Valid Approach for Scoring the Beck Depression Inventory

Academic journal article Social Behavior and Personality: an international journal

Fuzzy Partial Credit Scaling: A Valid Approach for Scoring the Beck Depression Inventory

Article excerpt

In this study a new scaling method was proposed and validated, fuzzy partial credit scaling (FPCS), which combines fuzzy set theory (FST; Zadeh, 1965) with the partial credit model (PCM) for scoring the Beck Depression Inventory (BDI-ll; Beck, Steer, & Brown, 1996). To achieve this, the Chinese version of the BDI-ll (C-BDI-ll) was administered to a clinical sample of outpatients suffering depression, and also to a nonclinical sample. Detailed FPCS procedures were illustrated and the raw score and FPCS were compared in terms of reliability and validity. The Cronbach alpha coefficient showed that the reliability of C-BDI-ll was higher in FPCS than in raw score. Moreover, the analytical results showed that, via FPCS, the probability of correct classification of clinical and nonclinical was increased from 73.2% to 80.3%. That is, BDI scoring via FPCS achieves more accurate depression predictions than does raw score. Via FPCS, erroneous judgments regarding depression can be eliminated and medical costs associated with depression can be reduced. This study empirically showed that FST can be applied to psychological research as well as engineering. FST characterizes latent traits or human thinking more accurately than does crisp binary logic.

Keywords: fuzzy partial credit scaling, fuzzy set theory, Rasch model, depression, Beck Depression Inventory.

Depression is among the most pervasive psychological problems in primary healthcare settings, accounting for 10.4% of all patients seen in such settings globally (Endler, Macrodimitris, & Kocovski, 2000). Self-reported measures of depression are most straightforward and important tools in various healthcare settings in the diagnosis and classification of different levels of depression. Therefore, a valid scoring schema is essential to accurately reflect the severity of depressive symptoms. The most popular scoring schema applied in psychological inventories is raw score, or "method of successive integral". In this scoring schema, alternatives listed in the scale are scored at equally spaced intervals. For example, a score of 4, 3, 2, or 1 is given if the alternatives strongly agree, agree, disagree, or strongly disagree respectively, are chosen. However, this approach has been criticized on the grounds that it is too simplistic (Nunnally & Bernstein, 1994; Yu, 2005).

First, raw score fails to achieve "meaningful measurement" for nonlinearity, and sample and test dependence (Wright, 1999). By contrast, item response theory (LRT) approach. Rasch models (Rasch, 1960) transform raw score into linear measures and, consequently, achieve a more objective and meaningful psychological measurement. Second, the options used in the rating scales, without clear and mutually exclusive distinctions, could be viewed as "linguistic variables". Linguistic variables, as defined in fuzzy set tiieory (FST; Zadeh, 1965), are variables of which the values are not numbers but words or sentences in a natural or artificial language (Klir & Yuan, 1995; Zimmermann, 1996). For instance, "sadness", a question adapted in the Beck Depression Inventory II (BDI-II; Beck, Steer, & Brown, 1996), is a linguistic variable if it takes a value such as "I felt sad all the time", or "I felt sad much of the time". Moreover, these terms are not clearly defined and no definite boundaries exist between, for example, "much of the time" and "all the time". Lacking clear definitions for the variables, the arithmetic performed on linguistic variables is beyond the capability of traditional binary crisp logic. Therefore, the newly developed fuzzy logic is the preferred solution for measurement.

Furthermore, the distinctions between two adjacent alternatives may be so polarized or extreme that none of the alternatives can reflect an individual's mental state exactly. Considering the example quoted above, the discrepancy between two adjacent alternatives such as "I did not feel sad," and "I felt sad much of the time" seems so strong that examinees who felt sad only occasionally would not be easily able to select an alternative. …

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