Unlike multilevel data with a purely nested structure, data that are cross-classified not only may be clustered into hierarchically ordered units but also may belong to more than one unit at a given level of a hierarchy. In a cross-classified design, students at a given school might be from several different neighborhoods and one neighborhood might have students who attend a number of different schools. In this type of scenario, schools and neighborhoods are considered to be cross-classified factors, and cross-classified random effects modeling (CCREM) should be used to analyze these data appropriately. A common problem in any type of multilevel analysis is the presence of missing data at any given level. There has been little research conducted in the multilevel literature about the impact of missing data, and none in the area of cross-classified models. The purpose of this study was to examine the effect of data that are missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR), on CCREM estimates while exploring multiple imputation to handle the missing data. In addition, this study examined the impact of including an auxiliary variable that is correlated with the variable with missingness (the level-1 predictor) in the imputation model for multiple imputation. This study expanded on the CCREM Monte Carlo simulation work of Meyers (2004) by the inclusion of studying the effect of missing data and method for handling these missing data with CCREM. The results demonstrated that in general, multiple imputation met Hoogland and Boomsma’s (1998) relative bias estimation criteria (less than 5% in magnitude) for parameter estimates under different types of missing data patterns. For the standard error estimates, substantial relative bias (defined by Hoogland and Boomsma as greater than 10%) was found in some conditions. When multiple imputation was used to handle the missing data then substantial bias was found in the standard errors in most cells where data were MNAR. This bias increased as a function of the percentage of missing data.

在處理具遺失值之類別資料時，傳統的方法是將資料捨棄，但是這通常不是明智之舉，這些遺失某些分類訊息的資料通常還是可以提供其它重要的訊息，尤其當這類型資料的個數佔大多數時，將其捨棄可能使得估計的變異數增加，甚至影響最後的決策。如何將這些遺失某些訊息的資料納入考慮，作出完整的分析是最近幾十年間頗為重要的課題。本文主要整理了五種分析這類型資料的方法，分別為單樣本方法、多樣本方法、概似方程式因式分解法、EM演算法，以上四種方法可使用在資料遺失呈隨機分佈的條件成立下來進行分析。第五種則為樣本遺失不呈隨機分佈之分析方法。 / Traditionally, the simple way to deal with observations for which some of the variables are missing so that they cannot cross-classified into a contingency table simply excludes them from any analysis. However, it is generally agreed that such a practice would usually affect both the accuracy and the precision of the results. The purpose of the study is to bring together some of the sound alternatives available in the literature, and provide a comprehensive review. Four methods for handling data missing at random are discussed, they are single-sample method, multiple-sample method, factorization of the likelihood method, and EM algorithm. In addition, one way of handling data missing not at random is also reviewed.