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研究生(外文):Syu, Jia Jia
論文名稱:Person-fit偵測作假之效用- 非參數試題反應理論的模擬與應用
論文名稱(外文):Applying person-fit in faking detection- The simulation and practice of non-parametric item response theory
指導教授(外文):Yu, Min Ning
外文關鍵詞:Nonparametric item response theoryfakingsample sizeperson-fitR
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本研究使用模擬資料及實際資料進行研究假設的檢驗。在研究一中,依據不同的樣本數、樣本能力分配、作假動機以及題目的異常率,以R產生模擬作答並求出person-fit數值,進而比較參數型與非參數型各person-fit指標的偵測率(detection rate),作為效用判斷之依據。研究二則將此技術應用於實際資料中,以社會期許量表與一份興趣量表進行本研究所採用之三種統計數(lz, U3p與Guttman errors)的偵測檢證,以瞭解其在實際情境中的實用性。
研究結果指出,較佳的person-fit統計數需視不同的情境而定。Guttman errors最適合用於當樣本數小於100人,受試者能力值為常態分配及低闊峰,而作答異常率僅為部分的情況。當作答異常率達到100%,受試者能力分配為負偏態及低闊峰,且作假程度嚴重時,以U3p的偵測效果較佳。而lz則最適用於各種中等程度的作假情境。從實際資料的分析結果,指出不論是大樣本或小樣本,能力分配為常態性的假設皆不容易被滿足,且應用person-fit統計數於作假偵測是可行的,特別是使用非參數型的U3p指標。

Faking detection is a crucial issue because of the effect on the hypothesized relation among variables, model testing, and test fairness. Aside from the Social Desirable Scale, which has often been used in detecting faking, we explored the possibility of an alternative method, which is the person-fit statistics of nonparametric item response theory (NIRT). In the scope of parametric item response theory (PIRT), the person-fit technique has been used in faking detection. Although the PIRT assumptions such as large sample size, normal distribution, and number of items are difficult to achieve, numerous researchers still adopt conventional methods, leading to inaccurate results and implications. Using NIRT person-fit may be more flexible and closer to the practical condition based on NIRT features, and are therefore the focus of this study.

We used both simulated and real data to test the hypothesis. In Study 1, the data were simulated and varied in sample size, distribution, faking motivation, and aberrant rate, to investigate the accuracy of person-fit estimating between PIRT and NIRT. In Study 2, the technique using person-fit as a faking detection tool was applied to empirical data to evaluate its use in a practical context.

The results indicate that superior person-fit statistics are conditional. The Guttman error detection rate was higher when the sample size was less than 100, when partial item-faking existed in the scale, and in normal and platykurtic distributions. When the aberrant rate is 100% with severe faking, U3p outperformed other indicators in the negatively skewed and platykurtic distribution. Comparatively, lz could be adopted in all median-faking conditions. Our empirical study found that the normal distribution of ability is not easy to satisfy across a small and large sample size. Adopting person-fit statistics for faking detection is feasible, particularly for U3p.

Chapter 1 Introduction 1
1.1 Background 1
1.2 Statement of the Problem 6
1.3 Limitations of the Study 7
1.4 Glossary 7
1.4.1 Parametric item response theory 7
1.4.2 Nonparametric item response theory 8
1.4.3 Person-fit 8
Chapter 2 Literature Review 9
2.1 Person-fit 9
2.1.1 lz 14
2.1.2 Guttman errors 16
2.1.3 U3p 18
2.2 Person-fit and faking 20
2.3 Sample Size and Distribution 25
2.4 The comparisons of PIRT and NIRT 31
2.4.1 The limitations of PIRT 31
2.4.2 NIRT 32
2.5 Nonparametric Estimation 35
2.5.1 The comparison between parametric and non-parametric methods 35
2.5.2 The assumptions of NIRT models 36
Chapter 3 Method 44
3.1 Study 1: Simulation study 45
3.1.1 Simulation design and variables 46
3.1.2 Data Generation 51
3.2 Study Two: Empirical-data application 54
Chapter 4 Results 56
4.1 Simulation study 57
4.1.1 Detection rate of three indicators under different distributions and sample sizes. 57
4.1.2 Detection rate of three indices under different distributions and aberrant rates 70
4.1.3 Detection rate of three indices under different distributions and faking degrees 79
4.2 Study 2: Empirical study 88
4.2.1 Distribution under the given sample size 89
4.2.2 Social desirability scale and person-fit statistics 91
Chapter 5 Discussion and Conclusion 95
5.1 Discussion on major findings 95
5.1.1 Sample size 95
5.1.2 Faking degree 97
5.1.3 Aberrant rate 98
5.1.4 The superior indicator 99
5.1.5 The methods of data simulation 100
5.2 Discussion on Empirical Study 101
5.3 Suggested steps for application 103
5.4 Limitations of Research 105
5.5 Suggestions for Future Research 107
References 109
Appendix 120

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