Estimating Standardized SEM Parameters Given Nonnormal Data and Incorrect Model: Methods and Comparison

Abstract

When both model misspecifications and nonnormal data are present, it is unknown how trustworthy various point estimates, standard errors (SEs), and confidence intervals (CIs) are for standardized structural equation modeling parameters. We conducted simulations to evaluate maximum likelihood (ML), conventional robust SE estimator (MLM), Huber–White robust SE estimator (MLR), and the bootstrap (BS). We found (a) ML point estimates can sometimes be quite biased at finite sample sizes if misfit and nonnormality are serious; (b) ML and MLM generally give egregiously biased SEs and CIs regardless of the degree of misfit and nonnormality; (c) MLR and BS provide trustworthy SEs and CIs given medium misfit and nonnormality, but BS is better; and (d) given severe misfit and nonnormality, MLR tends to break down and BS begins to struggle.

Keywords:

• incorrect model
• nonnormal data
• robust methods
• standard errors
• standardized model parameters

Notes

¹ MLM stands for maximum likelihood with robust standard errors and mean-adjusted model chi-square statistic. MLMV and MLMVS stand for maximum likelihood with robust standard errors and mean- and variance-adjusted model chi-square statistic.

² Nevitt and Hancock (2001) also studied the case of a slightly misspecified CFA model, but the results were almost identical to those based on the correct model. Thus they reported only the results based on the correct model.

³ The model in Finch et al. (1997) has structural coefficients but the model is equivalent to a CFA model.

⁴ We chose these values for because they correspond to an RMSEA of .05, .08, and .11. Because the model remains the same across all misfit conditions, the model degrees of freedom is always df = 163. Based on the definition of population RMSEA, we have . Given the values of df, we can calculate the values.