Improper solutions in structural equation models - Causes, consequences, and strategies

In this article, the authors examine the most common type of improper solut ions: zero or negative error variances. They address the causes of conseque nces of; and strategies to handle these issues. Several hypotheses are eval uated using Monte Carlo simulation models, including two structural equatio n models with several misspecifications of each model Results suggested sev eral unique findings. First, increasing numbers of omitted paths in the mea surement model were associated with decreasing numbers of improper solution s. Second, bias in the parameter estimates,vas higher in samples with impro per solutions than in samples including only proper solutions. Third invest igation of the consequences of using constrained estimates in the presence of improper solutions indicated that inequality constraints helped some sam ples achieve convergence. Finally, the use of confidence intervals as well as four other proposed tests yielded similar results when testing whether t he error variance,vas greater than or equal to zero.