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Pairwise maximum likelihood (PML) estimation method is developed for factor analysis models with ordinal data and tted both in an exploratory and conrmatory set-up. The performance of the method is studied via simulations

Normal-distribution-based maximum likelihood (ML) and multiple imputation (MI) are the two major procedures for missing data analysis. This article compares the two procedures with respects to bias and efficiency of parameter estimates. It also compares formula-based standard errors (SEs) for each procedure against the corresponding empirical SEs. The results indicate that parameter estimates by MI tend to be less efficient than those by ML; and the estimates of variance-covariance parameters by MI are also more biased. In particular, when the population for the observed variables possesses heavy tails, estimates of variance-covariance parameters by MI may contain severe bias even at relative large sample sizes. Although performing a lot better, ML parameter estimates may also contain substantial bias at smaller sample sizes. The results also indicate that, when the underlying population is close to normally distributed, SEs based on the sandwich-type covariance matrix and those based on the observed information matrix are very comparable to empirical SEs with either ML or MI. When the underlying distribution has heavier tails, SEs based on the sandwich-type covariance matrix for ML estimates are more reliable than those based on the observed information matrix. Both empirical results and analysis show that neither SEs based on the observed information matrix nor those based on the sandwich-type covariance matrix can provide consistent SEs in MI. Thus, ML is preferable to MI in practice, although parameter estimates by MI might still be consistent.

In the investigation of the effect of attention deficit hyperactivity disorder (ADHD) symptoms on school careers there is a need to study the role of adolescent and childhood ADHD symptoms and academic achievement, and to incorporate measures that include the individual's perspective. Our aim was to gain an overview of the long-term development of school careers in relation to ADHD symptoms. We studied associations between ADHD symptoms and academic achievement at different time-points and future orientation at the end of high school, and assessed the role of self-perceptions of academic competence in these associations. Participants were 192 children (47% girls) with a range of ADHD symptoms taken from a community sample. Collecting data at three time points, in 6th, 11th and 12th grade we tested a structural equation model. Results showed that ADHD symptoms in 6th grade negatively affected academic achievement concurrently and longitudinally. ADHD symptoms in 11th grade negatively affected concurrent academic achievement and academic self-perception and future orientation in 12th grade. Academic achievement had a positive influence on academic self-perception and future orientation. Given the other factors, self-perception of academic competence did not contribute to outcomes. We concluded that early ADHD symptoms may cast long shadows on young people's academic progress. This happens mainly by way of stability in symptoms and relations to early low academic achievement.

The problem of penalized maximum likelihood (PML) for an exploratory factor analysis (EFA) model is studied in this paper. An EFA model is typically estimated using maximum likelihood and then the estimated loading matrix is rotated to obtain a sparse representation. Penalized maximum likelihood simultaneously fits the EFA model and produces a sparse loading matrix. To overcome some of the computational drawbacks of PML, an approximation to PML is proposed in this paper. It is further applied to an empirical dataset for illustration. A simulation study shows that the approximation naturally produces a sparse loading matrix and more accurately estimates the factor loadings and the covariance matrix, in the sense of having a lower mean squared error than factor rotations, under various conditions.