Robust Maximum Likelihood

Robust maximum likelihood is used to adjust the model fit test statistic and standard errors when estimating structural equation with non-normally distributed data. A major assumption of normal theory maximum likelihood estimation is that the data follow a multivariate normal distribution. When data violate this assumption, commonly through measures of skewness and kurtosis, statistics based on normal theory maximum likelihood estimation can be misleading. While the parameter estimates under normal theory maximum likelihood estimation remain relatively robust to violations of normality, the test statistics and standard errors break down under normal theory maximum likelihood estimation and correction is required through use of robust maximum likelihood.

After providing some background information, this entry details the assumptions needed to determine whether the data are multivariate normal, the statistical ...