Path Analysis with Nonnormal Continuous Data: A Monte Carlo Simulation

The impact of nonnormality on parameter estimates and model-data fit has been extensively evaluated in confirmatory factor analysis models, but comparatively less attention has been given to path models, where nonnormality may occur in different combinations across exogenous, endogenous, and mediating variables. This simulation study examined the effects of varying degrees and configurations of nonnormality on path coefficient estimation, standard errors, statistical power, and model fit under five estimation methods: maximum likelihood (ML), robust maximum likelihood (MLR), mean-adjusted maximum likelihood (MLM), mean- and variance-adjusted maximum likelihood (MLMV), and bootstrap maximum likelihood (MLB). Sample size and severity of nonnormality were systematically varied across 21 distributional configurations. Results showed that relative bias of path coefficients was generally small and approached zero as sample size increased, although coefficients involving severely nonnormal variables showed larger bias and root mean squared error when samples were small. Robust estimators (MLR, MLM, MLMV, and MLB) produced more accurate standard error estimates than ML under nonnormal conditions, with MLB showing the smallest standard error bias in the smallest samples. Statistical power increased primarily as a function of the magnitude of the path coefficient and sample size, though severe nonnormality reduced power at small sample sizes. Fit index results indicated that CFI and TLI remained very high in most conditions, even when variables were severely nonnormal. SRMR was relatively unaffected by nonnormality and sample size, whereas RMSEA was more sensitive to both factors and improved markedly with larger samples. Overall, the findings suggest that robust estimators are preferable for path analysis with nonnormal data, particularly when sample sizes are small to moderate.