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Evaluating the Performance of Standard Latent Class Analysis Compared to Tree-Based Latent Class Analysis

Thu, April 24, 5:25 to 6:55pm MDT (5:25 to 6:55pm MDT), The Colorado Convention Center, Floor: Meeting Room Level, Room 302

Abstract

Purpose
This study investigates how Latent Class Tree Analysis (LCTA) and LCA sensitivity to local independence assumptions impact the accuracy and reliability of class membership identification in complex data structures. While LCA's sensitivity to local independence is known, its impact on accuracy and reliability in class membership is under-researched, as are comparisons between LCA and LCTA. This study addresses these gaps through extensive simulations.

Theoretical Framework
LCA is used to identify unobserved subgroups within a population based on observed categorical variables, assuming local independence within each class (Goodman, 1974; McCutcheon, 1987). LCTA is a recent advancement that extends LCA by allowing hierarchical classification, better capturing complex data structures. While LCTA still assumes local independence at each level, it models dependencies within nested subgroups more flexibly. Based on this, we hypothesized that:
ยท LCTA provides more accurate class membership identification in complex data structures compared to LCA.

Methods/Data Sources
We will generate multiple datasets under various conditions: (1) Local independence and (2) violation of local independence with varying sample sizes (500, 1000, 2000). We looked at different numbers of latent classes (i.e. 3, 4-true classes) with 10 indicators. Then we introduced a level of local dependency among observed dichotomous variables to evaluate the impact on model accuracy and reliability. That is, we set the correlation among the variables to be 0.3 and 0.2 for the 3-class model and 4-class model respectively. There are unequal class sizes for each model. For the 3-class model, the probabilities for class memberships are 0.3, 0.4, and 0.3, respectively. For the 4-class model, the probabilities for class memberships are 0.3, 0.2, 0.2, and 0.3.
Results
Tables 1 and 2 show results for latent class (LC) and latent class tree (LCT) models under no local independence violations. BIC values are generally similar, but LCT models sometimes have slightly higher BIC values, indicating a marginally poorer fit. For the 3-True Class with a sample size of 500, the LC model has a lower classification error (0.053) than the LCT model (0.111). For the 4-true class with the same sample size, the LC model outperforms LCT in higher-cluster scenarios. Overall, LC models perform better in class membership identification.
Tables 3 and 4 show results under local independence violations. LCT models are slightly more robust, with lower classification errors and comparable BIC values. Both models show increased errors and BIC values with more clusters and larger sample sizes. LCT models may offer a slight edge in classification accuracy under these conditions.

Scholarly Significance
This study advances latent class modeling by comparing LCA and LCT in handling complex data. By examining their sensitivity to local independence assumptions, it provides insights into their accuracy and reliability in class membership identification. The research highlights LCT's advantages in capturing hierarchical relationships and dependencies within data, which LCA might overlook. These findings are crucial for researchers and practitioners in selecting the most appropriate approach, leading to more robust outcomes.

Authors