  Latent variable models (LVMs) are commonly used in psychology and
increasingly used for analyzing brain imaging data. Such studies typically
involve a small number of participants (n<100), where standard asymptotic
results often fail to appropriately control the type 1 error. This paper
presents two corrections improving the control of the type 1 error of Wald
tests in LVMs estimated using maximum likelihood (ML). First, we derive a
correction for the bias of the ML 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's t-distribution instead of
a Gaussian distribution to account for the variability of the variance
estimator. The degrees of freedom of the Student's t-distributions are
estimated 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 to the
uncorrected Wald test, despite being conservative for some parameters. The
proposed methods are implemented in the R package lavaSearch2 available at
https://cran.r-project.org/web/packages/lavaSearch2.
