Bayesian SEM in AMOS

[Neeraj Kaushik]

Dear Friends

Traditional CB-SEM is used when:

1. Data is strictly continuous and normal: Your indicators are interval/ratio scales (like 7-point Likert scales treated as continuous) with zero skewness or kurtosis issues. Data must be normally distributed.

2. Sample size is large: You have hundreds of responses to support asymptotic large-sample theory. Typically use the thumb rule formula:

Sample size = 10 * No of items in the scale

3. Theory testing is the primary goal: Your main objective is to establish global model fit indices (CFI > 0.95, RMSEA < 0.06) to confirm or reject an established theory.

But when these assumptions are not met, we can use BAYESIAN SEM.

Use Bayesian SEM approach when:

1. Analyzing ordinal or categorical data: Traditional MLE struggles with binary or ordered-categorical variables. AMOS Bayesian estimation seamlessly handles categorical data by treating thresholds as parameters.

2. Sample sizes are small: When you lack the sample size required for stable MLE estimation, Bayesian estimation protects against the bias typically introduced by small sample constraints.

3. Complex models fail to converge (including Heywood Cases): If your traditional model suffers from non-positive definite matrices or Heywood cases (negative variance estimates), the MCMC sampling algorithm can bypass these mathematical roadblocks.

4. Incorporating historical knowledge: You want to apply "priors" derived from previous literature or pilot studies to influence the current model's posterior distribution.

I've explained this concept in this video:
AMOS-32. Bayesian SEM: https://youtu.be/cXJDUzrvCME

Happy Learning

Neeraj