臺灣博碩士論文加值系統

問卷調查一直是最為廣泛使用且最具彈性的行銷研究方法，根據研究目的不同，問卷設計可以不同尺度呈現，以蒐集最豐富之資訊。而在眾多問卷尺度中，李克特量表最常用來衡量受訪者對個別問項的態度及傾向。雖然，問卷資料多為間斷型資料或順序型資料，但大多數的問卷資料仍以常態分配為基礎的多變量分析工具，進行資料分析與解讀。本研究認為，在分析問卷資料時，研究者會面對三大挑戰:第一、當資料與分析方法的統計假設不符合時，可能會造成分析結果有偏差的情況。第二、問卷資料為橫斷性資料，一個受訪者只有一組資料，任何統計方法都無法針對個別受訪者的異質性做分析探討。第三、研究者多希望了解某一組問項對另一組問項的解釋能力。針對上述問題，本研究提出貝氏Ordered Probit Model的解決方案，並使用蒙地卡羅馬可夫鏈模擬技術估計模式參數，並將本研究提出的模型與估計方法，實際應用於分析美國啤酒消費問卷中。初步分析結果顯示，受訪者對於尺度選擇的偏好具異質性，亦即每位受訪者皆有自己專屬的一組尺度區間；研究結果亦顯示在李克特分數越低時，其所對應之尺度的變異程度越小，這個發現驗證了固定區間假設的不合理性。本研究的實證結果也發現，具有某些人格特質的啤酒消費者如：樂於與人溝通交流內心話，卻很有自己想法、不容易受他人影響的消費者較喜愛嘗試不同品牌的啤酒，對於新產品的接受程度較高，且在挑選啤酒時會傾向注意特殊品牌。

In survey research, itemized rating scale, such as Likert scale, is commonly used to determine a degree of agreement or disagreement with each of a series of statements about an object, such as customer satisfaction measurement and purchase intention. Even though itemized rating scale has been widely applied in survey method, researchers may encounter the following problem in data anlysis. First, ignoring the discrete aspect of these data can cause estimation biases in statistical inferences. Second, consumer heterogeneity cannot be studied because data collected from a questionnaire is cross-sectional. Third, researchers often want to study the relationship between two different sets of variables in a questionnaire. To address these issues, a Bayesian ordered probit model is proposed in this research to analyze itemized rating-scale data. The estimation procedure of Markov Chain Monte Carlo is also developed to estimate the proposed model. The proposed model is illustrated by a beer survey data. The empirical result shows that each respondent has different scale usage behavior. The smaller Likert score has the small variance of the scale cut-off value. This finding invalidates the assumption of equal spacing of cut-off values in conventional data analysis method. In addition, it also shows that respondents who talk about things philosophically when they drink with their friends and who tend to buy different brands than their friends have greater tendency to try new or special beer brands.

摘要 i
ABSTRACT ii
誌謝 iii
目錄 iv
圖目錄 v
表目錄 vi
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究範圍 3
1.4 研究架構 4
第二章 文獻探討 5
2.1 間斷型資料統計分析方法 5
2.1.1 相關分析 6
2.1.2 迴歸分析 6
2.1.3 評等量尺模式 7
2.2 貝氏統計 8
2.3 蒙地卡羅-馬可夫鏈演算法 9
2.3.1 Gibbs抽樣法 11
2.3.2 Random-walk Metropolis-Hastings演算法 12
2.4 資料擴增演算法和潛在變數模型 12
第三章 研究方法 15
3.1 模型建構 15
3.2 參數估計 17
3.3 模擬實驗 21
第四章 實證分析 26
4.1 研究樣本與資料來源 26
4.2 貝氏模式分析 28
4.3 模型比較 37
第五章 結論與建議 40
參考文獻 41

英文文獻
[1] Andrich, D. (1978), "A rating formulation for ordered response categories, "Psychometrika, 43, 561-573.
[2] Allenby, G. M. and P. E. Rossi (1999), "Marketing Models of Customer Heterogeneity," Journal of Economtrics, Vol. 89, pp.57-78.
[3] Bond, T. G., & Fox, C. M. (2007). Applying the Rasch model：Fundamental measurement in the human sciences (2nd ed.), Mahwah, N.J.：Erlbaum.
[4] Embretson, S. E., & Reise, S. P. (2000).Item response theory for psychologists. Mahwah, NJ：Erlbaum.
[5] Gelfand, A. E., and Smith, A. F. M. (1990), "Sampling-Based Ap-proaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.
[6] Gelman, Andrew, Carlin, John B., Stern, Hal S., and Rubin, Donald B (2003) Bayesian Data Analysis, Second Edition. Chapman & Hall/CRC.
[7] G. Fennell and G. M. Allenby(2006), "Multiple Perspectives：Marketing Needs to Unambiguously Articulate its Role as a Business and Societal Function, " Marketing Research, vol.18, no.4, pp.26-31.
[8] Hastings, W. K. (1970), "Monte Carlo Sampling Methods Using Markov Chains and Their Applications," Biometrika, 57, pp.97-109.
[9] I.J.Good. (1980) "Some history of the hierarchical Bayesian methodology, "In Bayesian Statistics：Proceedings of the First International Meeting held in Valencia, pp.489-504.
[10] Likert, R. (1932), "A Technique for the Measurement of Attitudes" Archives of Psychology, Vol. 140, pp. 1-55.
[11] Metropolis, N., Rosenbluth,A. W., Rosenbluth,M. N. , Teller,A. H., and Teller, E. (1953), "Equations of State Calculations by Fast Compution Machines, " Journal of chemical Physics, 21, pp.1087-1091.
[12] Muller, P. (1993). "A Generic Approach to Posterior Integration and Gibbs Sampling," Technical Report 91-09, Department of Statustucs, Purdue University.
[13] McCulloch, Robert, Nicholas Polson, Peter Rossi, (2000) "Bayesian analysis of the multinomial probit model with fully identified parameters, " J. Econometrics 99 173-193.
[14] Marshall, Pablo, Eric T. Bradlow, (2002) "A unified approach to conjoint analysis models," Journal of the American Statistical Association, vol. 97, pp. 674-682.
[15] Nummelin, E. (1984) "General Irreducible Markov Chains and Non-Negative Operator, " Cambridge Univ. Press.
[16] Rasch, G. (1960), "Probabilistic models for some intelligence and attainment tests," Copenhagen：Institute of Educational Research. (Expanded edition, 1980. Chicago：The University of Chicago Press.)
[17] Rossi, Peter E., Zvi Gilula, and Greg M. Allenby, (2001) "Overcoming Scale Usage Heterogeneity: A Bayesian Hierarchical Approach," Journal of the American Statistical Association, vol. 96, no. 453, pp. 20-31.
[18] Rossi, Peter E. and Greg M. Allenby (2003), "Bayesian Statistics and Marketing", Marketing Science, Vol. 22, pp. 304-328.
[19] Rossi, P.E., Allenby, G.M., and McCulloch (2005), Bayesian Statistics and Marketing, New York : John Wiley & Sons.
[20] Robert, Christian P. and Casella, George (2010), Monte Carlo Statistical Methods. Springer.
[21] Stevens, S. S. (1951). Mathematics, measurement and psychophysics. In Handbook of Experimental Psychology (S. S. Stevens, ed.) New York: Wiley.
—(1958).Problems and methods of psychophysics. Psychol. Bull. 55, 177-196.
—(1968).Measurement, statistics and the schemaparic view. Science, 161,849-856.
[22] Smith, A. F. M., and Gelfand, A. E. (1992), "Bayesian Statistics Without Tears: A Sampling-Resampling Perspective, " The American Statistician, 46, 84-88.
[23] Tanner, M.A and Wong.W.H (1987), " The calculation of posterior distributions by data augmentation (wira discussion), " J.Amer. Statist. Assoc.82, 528-550.
[24] Tierney, L. (1994). "Markov Chains for Exploring Posterior Distributions", Annals of Statistics, 22, pp.1701-1762.

中文文獻
[25] 廖子毅，應用層級貝氏模型在顧客異質性暨產品異質性之解讀，碩士論文，國立臺北科技大學，台北，2005。
[26] 王仕茹，整合層級貝氏聯合區隔與定位分析模式：來源國效應評價、品牌權益衡量與新產品設計之應用，碩士論文，國立臺灣大學國際企業學研究所，台北，1998。