在進行順序變項的結構方程模型分析時，一個常用的方法是先將資料以列聯表的方式表徵，利用列聯表的配對細格機率求得資料的多元類別關聯，再將此多元類別關聯做為共變異數矩陣進行結構方程模型分析。在實務應用上實徵資料的研究常會面臨遺漏值的問題，雖然在連續變項的結構方程模型的遺漏值已經有了完善的發展，然而在以結構方程模型分析順序變項時的遺漏值處理法卻尚未有一個好的流程。本研究試圖使用階層對數模型結合 Poisson 廣義線性模型提出一個求得列聯表配對細格機率估計值的方法，並推導其漸進估計標準誤，做為一個處理順序變項結構方程模型的遺漏值問題的初探。本研究亦以一個模擬資料比較此方法和列刪除法、配對刪除法於偏誤值、變異數與 95% 信賴區間覆蓋率之表現，結果顯示最大概似法在整體的表現上優於其他兩者，不但具有較小的偏誤和變異數，同時 95% 信賴區間覆蓋率的表現也符合預期，本文亦於最後說明如何將此法應用於結構方程模型方法。

When using structural equation modeling (SEM) to analyze ordinal data, analysts first obtain a polychoric correlation matrix and the data then treat it as covariance matrix in SEM. Once the original ordinal data has missing values, the modification of the process
of estimating polychoric correlation correctly may be an issue. The quality of polychoric correlation estimates relies on the quality of pairwise contingency table cell probability estimates. This article proposed a procedure of maximum likelihood (ML) method of obtaining the estimates of contingency table cell probabilities and derived the of asymptotic covariance matrix of contingency table cell probability estimates. The article also conducted a simulation research to compare the performances of the proposed method, listwise deletion and pairwise deletion. The results suggested that when data is missing completely at random, all of the three methods performed well. On the contrary, only maximum likelihood method had an acceptable performance when the data is missing at random.

Agresti, A. (2002). Categorical Data Analysis.
Allison, P. D. (2003). Missing data techniques for structural equation modeling. Journal of Abnormal Psychology; Journal of Abnormal Psychology, 112(4), 545.
Arbuckle, J. L. (1996). Full Information Estimation in the Presence of Incomplete Data. In Advanced structural equation modeling: Issues and techniques. New Jersey.
Bollen, K. A. (1989). Structural equations with latent variables.
Carter, R. L. (2006). Solutions for Missing Data in Structural Equation Modeling. Assessment, 1(1), 1–6.
Christensen, R. (1990). Log-Linear Models. New York: Springer.
Enders, C. K. (2001a). The impact of nonnormality on full information maximum-likelihood estimation for structural equation models with missing data. Psychological methods, 6(4),352–70.
Enders, C. K. (2001b). A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling, 8(1), 128–141.
Enders, C. K., & Bandalos, D. L. (2001). The Relative Performance of Full Information Maximum Likelihood Estimation for Missing Data in Structural Equation Models Equation Models. Educational Psychology Papaers and Publications, 430–457.
Friendly, M. (2000). Note on“Obtaining the Maximum Likelihood Estimates in Incomplete R × C Contingency Tables Using a Poisson Generalized Linear Model”. Journal of Computational and Graphical Statistics, 9(1), 158–166.
Glasser, M. (1964). Linear Regression Analysis With Missing Observations Among the Independent Variables. Journal of the American Statistical Association, 59(307), 834–844.
Harding, T., & Tusell, F. (2012). cat: Analysis of categorical-variable datasets with missing values.
Jöreskog, K. G. (1973). A General Method for Estimating a Linear Structural Equation System.
Lipsitz, S. R., Parzen, M., & Molenberghs, G. (1998). Obtaining the Maximum Likelihood Estimates in Incomplete R × C Contingency Tables Using a Poisson Generalized Linear Model. Journal of Computational and Graphical Statistics, 7(3), 356.
Little, J., & Rubin, D. (1987). Statistical analysis with missing data.
MacCallum, R. C. (2003). 2001 Presidential Address: Working with Imperfect Models.Multivariate Behavioral Research, 38(1), 113–139.
MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual review of psychology, 201–226.
Magder, L. S. (2003). Simple approaches to assess the possible impact of missing outcome information on estimates of risk ratios, odds ratios, and risk differences. Controlled Clinical Trials, 24(4), 411–421.
Meng, X. L., & Rubin, D. B. (1993). Maximum likelihood estimation via the mbox{ECM} algorithm: a general framework. Biometrika, 80, 267–278.
Muthén, B. O., du Toit, S. H., & Spisic, D. (1997). Robust Inference using Weighted Least Squares and Quadratic Estimating Equations in Latent Variable Modeling with Categorical and Continuous Outcomes.
Newman, D. A. (2003). Longitudinal Modeling with Randomly and Systematically Missing Data: A Simulation of Ad Hoc, Maximum Likelihood, and Multiple Imputation Techniques. Organizational Research Methods, 6(3), 328–362.
Olsson, U. (1979a). Maximum Likelihood Estimation of the Polychoric. Psychometrika, 44(4), 443–460.
Olsson, U. (1979b). On the robustness of factor analysis against crude clasifications of the observations.pdf. Multivariate Behavioral Research, 13(4), 485–500.
Poon, W.-Y., & Lee, S.-Y. (1987). Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients. Psychometrika, 52(3), 409–430.
Raymond, M. R., & Roberts, D. M. (1987). A Comparison of Methods for Treating Incomplete Data in Selection Research. Educational and Psychological Measurement, 47(1), 13–26.
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York: Wiley.
Savalei, V., & Bentler, P. M. (2009). A Two-Stage Approach to Missing Data: Theory and Application to Auxiliary Variables. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 477–497.
Savalei, V., & Falk, C. F. (2014). Robust two-stage approach outperforms robust full information maximum likelihood with incomplete nonnormal data. Structural Equation Modeling: A Multidisciplinary Journal, 21(2), 280–302.
Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data.
Schafer, J. L., & Graham, J. W. (2002). Missing data: our view of the state of the art.Psychological methods, 7(2), 147–177.
Schafer, J. L., & Schenker, N. (2000). Inference with imputed conditional means. Journal of the American Statistical Association, 95(449), 144–154.
van Dyk, D. A., Meng, X.-L., & Rubin, D. B. (1995). Maximum likelihood estimation via the ECM algorithm: computing the asymptotic variance. Statistica Sinica, 5, 55–75.
Wothke, W. (2000). Longitudinal and multigroup modeling with missing data. Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples., 219–240, 269–281.
Zhu, X. (2014). Comparison of Four Methods for Handing Missing Data in Longitudinal Data Analysis through a Simulation Study. Open Journal of Statistics, 4, 933–944.