Small sample corrections for Wald tests in latent variable models

Latent variable models are commonly used in psychology and increasingly used for analysing brain imaging data. Such studies typically involve a small number of participants (n<100), where standard asymptotic results often fail to control the type 1 error appropriately. The paper presents two corrections improving the control of the type 1 error of Wald tests in latent variable models estimated by using maximum likelihood. First, we derive a correction for the bias of the maximum likelihood estimator of the variance parameters. This enables us to estimate corrected standard errors for model parameters and corrected Wald statistics. Second, we use a Student t-distribution instead of a Gaussian distribution to account for the variability of the variance estimator. The degrees of freedom of the Student t-distributions are estimated by using a Satterthwaite approximation. A simulation study based on data from two published brain imaging studies demonstrates that combining these two corrections provides superior control of the type 1 error rate compared with the uncorrected Wald test, despite being conservative for some parameters. The methods proposed are implemented in the R package lavaSearch2, which is available from https://cran.r-project.org/web/packages/lavaSearch2.