On the use of likert-type scales in multilevel data:Influence on aggregate variables

In multilevel analyses, problems may arise when using Likert-type scales at the lowest level of analysis. Specifically, increases in variance should lead to greater censoring for the groups whose true scores fall at either end of the distribution. The current study used simulation methods to examine the influence of single-item Likert-type scale usage on ICC(1), ICC(2), and group-level correlations. Results revealed substantial underestimation of ICC(1) when using Likert-type scales with common response formats (e.g., 5 points). ICC(2) and group-level correlations were also underestimated, but to a lesser extent. Finally, the magnitude of underestimation was driven in large part to an interaction between Likert-type scale usage and the amounts of within- and between-group variance. © Sage Publications.

The method of fundamental solutions for free surface Stefan problems

In this paper, free surface problems of Stefan-type for the parabolic heat equation are investigated using the method of fundamental solutions. The additional measurement necessary to determine the free surface could be a boundary temperature, a heat flux or an energy measurement. Both one- and two-phase flows are investigated. Numerical results are presented and discussed.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.