| Abstract: | 以潛在類別模型資料分析時，在模型中加入共變項或解釋變項可以增加對於各個潛在類別分類的預測力和解釋力。而在多層次潛在類別模型（MLCM）的設定中，可以選擇在第一層和第二層結構中分別或是同時加入共變項或解釋變項在結構設定中。Pirani（2013）的研究運用第一層和第二層的共變項來研究歐洲人對社會排斥的經驗和看法的研究中，即為MLCM研究中使用共變項的一個實際研究例子。過去文獻中，設定和估計共變項效果加入於混合模型(Mixture Model)主要有兩種方法：單一步驟法和三步驟法。以單一步驟法估計共變項效果時，共變項效果的估計和潛在類別結構的確認是同時進行。也就是模型的其他參數和共變項效果是同時估計。而三步驟法則是把模型的其他參數及潛在模型結構的確認和共變項效果的估計於不同階段估計，亦即是以反覆疊代來分別順序性的處理。一般來說，順序性估計的三步驟法較不易因為共變項的加入而有使潛在類別結構產生扭曲(class distortion)的狀況。然而，三步驟法的共變項參數估計可能會有被嚴重低估的狀況。為了修正這個缺點，Bolck等人（2004）提出了Boltz-Croon-Hagenaars法（BCH方法）的修正方法，即在原本的三步驟法中的第三步驟使用重新加權頻率表（reweighted frequency table）來進行參數校正。另外，Vermunt（2010）也提出了「最大概似三步驟法」來校正估計參數的標準誤（SE）。目前研究在共變項或解釋變項的參數估計和分析大多以單一資料結構為主。而對於多層次結構資料的部分，除Bennink et al. (2015) 研究外，仍缺乏對此一議題之系統性的研究和探討；另外，Bennink et al. (2015) 的研究也僅著重第二層共變項直接或間接對第二層潛在類別結構的影響，而非同時探討各別對不同階層的影響。因此，此所提出的研究計畫將同時針對兩階層性資料於各層中共變項參數的設定和估計方式進行系統化的探討，以一系列的模擬研究來探討單一步驟法，三步驟法，以及校正的三步驟法（最大概似三步驟法）對於共變項參數的估計效果進行模擬研究及評量。計畫中針對：樣本大小（組數目，組大小），共變項效果量大小，潛在類別間的關連度（同質性和歧異性）等因素對於以不同方法估計共變項效果量的影響做探討。
The inclusion of covariates in the model improves the prediction of class memberships and facilitates the identification of the latent classes in latent class analysis (LCA). For the Multilevel Latent Class Model (MLCM), covariates can be introduced at level-1 and level-2 separately, or simultaneously at both levels. An empirical example of demonstrating the use of covariates in MLCM is Pirani's (2013) study of incorporating level-1 and -2 covariates to investigate Europeans' experiences and perceptions of social exclusion.Two main approaches of incorporating and estimating covariates effects in the literature are the one-step method and the three-step method. The one-step method assesses the covariate effect at the same stage of identifying the latent class structure. This means that the parameters defining the structure of the latent classes and the covariate effects are estimated simultaneously. The three-step method, in contrast, examines the covariate effects in a stepwise manner. The main advantage of the three-step method over the one-step method is that the class solutions are not distorted by the inclusion of covariates (Bakk et al., 2013; Bakk & Vermunt, 2016; Vermunt, 2010). Despite these advantages, a potential problem of the classical three-step method is that the covariate parameters are severely underestimated (Bolck et al., 2004). To address this shortcoming, Bolck et al. (2004) developed a correction method, the three-step Bolck-Croon-Hagenaars method (BCH method), in which the third step of the classical three-step method was modified using the reweighted frequency table. Vermunt (2010) also suggested an alternative bias-adjusted three-step method, the maximum likelihood three-step method, making it possible to obtain corrected standard errors (SEs) and accommodate continuous covariates.A number of studies have explored the usages of these methods for evaluating covariate effects at the individual level but not in a multilevel framework (e.g., Bakk et al., 2013; Bakk, Oberski, & Vermunt, 2014; Bolck et al., 2004; Vermunt, 2010). One exception is Bennink et al. (2015)’s work, but their work focused only on the situation where level-2 covariates are expected to affect the level-2 outcome directly or indirectly through a level-2 latent class only. The case that level-1 and level-2 covariates predict class membership at each level simultaneously is not yet been systematically examined. The proposed proposal aims to fill this gap and therefore focuses on investigating the performance of three methods for estimating covariate effects when both level-1 and level-2 covariates are simultaneously incorporated into the nonparametric MLCM to predict latent class membership at each level. A series of simulation study are planned to explore and compare the three methods of evaluating covariate effects: the one-step method, the classical three-step method, and the ML method. Factors investigated in the proposed simulation studies include: sample sizes at level-1 and level-2, magnitude of covariate effects, classes separation, and class distinctness. |
