潛在異質性的變與不變：隨機截距潛在轉移模型的分類校正與輔助變數分析之蒙地卡羅模擬與實徵研究

State and Change of Latent Heterogeneity: Monte Carlo Simulation and Empirical Study on Bias Correction of Classification with Auxiliary Variables in Random Intercept Latent Transition Analysis

觀察資料的重複測量帶有個體內變異與個體間變異，導致潛在異質性的縱貫分析必須兼顧潛在類別的變動與個別差異的估計，並以多階段程序控制分類誤差，在確保分類穩定的前提下，進行異質性轉移機率的估計與輔助變數效果的分析。本研究利用蒙地卡羅模擬探討不同強度的隨機截距（random intercepts, RI）與分類誤差校正的加權策略對於潛在轉移模型參數與輔助變數效果的影響，發現即使重複測量中僅有微弱強度的個體間變異或中度的觀察變數跨時相關，RI項的導入對於轉移機率與異質分類即有顯著影響，以及在模式設定正確下的Bolck—Croon—Hagenaars（BCH）權數估計與加權，可以維持異質分類的穩定不偏，從而獲得有效的輔助變數效果估計。透過KIT（Kids in Taiwan: National Longitudinal Study of Child Development & Care）資料庫不同月齡幼兒調查下的父職參與異質性分析，本研究具體檢視不同的BCH加權影響，以及不同型態的輔助變數在多階段估計程序的執行策略，提供帶有隨機截距的潛在轉移分析具體實徵案例。

Repeated measures data contain both within-subject and between-subject variation. Longitudinal analyses of latent heterogeneity must therefore simultaneously account for transitions in latent classes and estimation of individual differences. A multi-stage procedure is required to control for classification errors, ensure stable classification when estimating the probabilities of heterogeneity transitions, and analyze the effects of auxiliary variables. This study employed Monte Carlo simulations to investigate the impact of random intercepts (RI) with varying magnitudes and weighting strategies for classification error correction on the parameters of latent transition models and the effects of auxiliary variables. Results revealed that under a weak between-subject effect or a moderate level of temporal correlation, introduction of RI significantly influences transition probabilities and latent heterogeneous classification. The Bolck–Croon–Hagenaars (BCH) weighting with correct model specifications can maintain stable and un-shifted classification, producing effective estimates of auxiliary variable effects. Using the empirical data on father involvement in the KIT (Kids in Taiwan: National Longitudinal Study of Child Development & Care) dataset as an example, this study investigated the impact of BCH weighting on heterogeneity analysis with auxiliary variables in multi-stage estimation procedures, providing a concrete empirical example of latent transition analysis with random intercept.