長期性資料(longitudinal data)，是指對同一個觀察個體(subject)或實驗單位(experiment unit)，在不同時間點上重複觀察或測量一個或多個變數。雖然觀察個體之間互相獨立，但就同一個個體而言，不同時間的觀察或測量常常是有相關性的。且觀察的個體之間可能由於一些無法測量的環境因素造成個體之間有差異，因此在傳統橫斷面分析中，假設其有相同迴歸係數的邊際模型可能不合理。隨機效果模型可以解決長期資料分析的相關，並假設每個個體的迴歸係數不同；此模型不但可以說明橫斷面資料的cohort效果，也可直接解釋長期資料的age效果；更可以區分個體之間與個體之內的變異。 本研究以1995年至2000年台灣11個產業中的100家公司之每股盈餘與各財務比率，作為實證分析的資料；分別配適每股盈餘與時間、產業別、時間產業別交互作用及財務比率及排除每股盈餘有異常值後之邊際效果模型(一般迴歸分析)及隨機效果模型，並比較其參數估計之異同。實證結果顯示，一般迴歸分析與假設誤差不相關且等變異下的隨機效果模型參數估計相似，但後者能區分變異為個體之間(between-subjects)與個體之內(within-subject)的變異。而假設誤差不相關且不等變異與假設誤差服從AR(1)且不等變異下的隨機效果模型估計相近。實證結果並顯示，在排除異常值後的模型參數估計，一般迴歸分析不論是估計值及顯著性大多沒有很大差別；而隨機效果模型的估計在排除異常值前後較有差別。特別是現金流量比率(CFR)原本為不顯著變數，在排除異常值後的模型配適全部變顯著性變數。 / The defining characteristic of a longitudinal study is that individuals are measured repeatedly through time. Although it is independent between subjects, the set of observations on one subject tends to be inter-correlated. Because there is some natural heterogeneity due to unmeasured factors between subjects, it is not corrected to assume they have the same regression coefficients. A random effect model is a reasonable description about the different regression coefficients, and it can resolve the inter-correlation of the observations on one subject. The major advantages of the random effect model are its capacity to separate what in the context of population studies are called cohort and age effects, and it can distinguish the variations between subjects and within subjects. This study describes the marginal model and random effect model, and shows their difference by real data analysis. We apply these models to the earnings per share (EPS) and other financial ratios of one hundred companies in Taiwan, which are distributed in eleven industries. The results show that the parameter estimates of the marginal model and random effect model are similar when error structure is independent and of equal variance. Furthermore, the latter can distinguish the variations between subjects and within subjects. However, the residual analysis reveals that the error structure may not be constant. Therefore, we consider heteroscedasticity error in random effect model. We also assume that error follows an autoregressive process (e.g. AR(1) model), which leads to the optimum among our results in terms of residual analysis. There are some observations that appear to be outlying from the majority of data. The results show little difference in the marginal models no matter whether those outliers are included. However, we obtain different results in the random effect models. Especially, the variable of “cash flow ratio” becomes significant once those potential outliers have been excluded, while it is not significant when all cases are fitted in the model.

長期性資料(longitudinal data)的最主要特徵是為對多個被觀測個體在不同的時間點上重複測量一個或多個反應變數。而在分析長期性資料的方法中，Laird & Ware(1982)建議以線性混合效果模型(linear mixed effects model，LME)來進行估計分析，此模型方法中，資料可以允許遺失值，並可將受測個體間與個體內的變異分開說明。 另在配適最小平方法(OLS)的迴歸模型中，係數估計經常會受到異常值的影響，而Rousseeuw & Leroy(1987)提出最小消去平方法(least trimmed squares，LTS)的穩健迴歸模型，即是解決最小平方法中對於異常值敏感的問題。 本研究主要針對台灣股票預期報酬之三種模型：資本資產定價模型、特徵模型、因子模型分別以OLS、LTS、LME三種估計方法做配適，並比較配適模型之適當與否，樣本資料為民國七十年七月至九十年六月共252個月516家上市公司股票報酬。實證結果顯示，不論是採用OLS、LTS、LME的估計方法，股票報酬解釋變數：系統風險、公司規模、帳面權益對市值比、SMB、HML皆為股票報酬的顯著解釋因子；而在模型比較方面，不論是配適資本資產定價模型、特徵模型或因子模型，LME都較OLS為較適當配適模型。這顯示了在分析長期性資料時，LME的確是一個較佳的統計分析模型。