The use of item parcels in structural equation modelling: non-normal data and small sample sizes.

Maximum likelihood estimation in confirmatory factor analysis requires large sample sizes, normally distributed item responses, and reliable indicators of each latent construct, but these ideals are rarely met. We examine alternative strategies for dealing with non-normal data, particularly when the sample size is small. In two simulation studies, we systematically varied: the degree of non-normality; the sample size from 50 to 1000; the way of indicator formation, comparing items versus parcels; the parcelling strategy, evaluating uniformly positively skews and kurtosis parcels versus those with counterbalancing skews and kurtosis; and the estimation procedure, contrasting maximum likelihood and asymptotically distribution-free methods. We evaluated the convergence behaviour of solutions, as well as the systematic bias and variability of parameter estimates, and goodness of fit.