[[EQUATION]]-optimal Designs for Hierarchical Linear Models: an Equivalence Theorem and a Nature-inspired Meta-heuristic Algorithm

Hierarchical linear models are widely used in many research disciplines and estimation issues for such models are generally well addressed. Design issues are relatively much less discussed for hierarchical linear models but there is an increasing interest as these models grow in popularity. This paper discusses [[EQUATION]] -optimality for predicting individual parameters in such models and establishes an equivalence theorem for confirming the [[EQUATION]] -optimality of an approximate design. Because the criterion is non-differentiable and requires solving multiple nested optimization problems, it is much harder to find and study [[EQUATION]] -optimal designs analytically. We propose a nature-inspired meta-heuristic algorithm called competitive swarm optimizer (CSO) to generate [[EQUATION]] -optimal designs for linear mixed models with different means and covariance structures. We further demonstrate that CSO is flexible and generally effective for finding the widely used locally [[EQUATION]] -optimal designs for nonlinear models with multiple interacting factors and some of the random effects are correlated. Our numerical results for a few examples suggest that [[EQUATION]] and [[EQUATION]] -optimal designs may be equivalent and we establish that [[EQUATION]] and [[EQUATION]] -optimal designs for hierarchical linear models are equivalent when the models have only a random intercept only. The challenging mathematical question whether their equivalence applies more generally to other hierarchical models remains elusive.

A multilevel analysis of factors affecting kindergartners’ creative dispositions in relations to child-level variables and teacher-level variables

Kindergarteners’ creative dispositions are not only affected by their individual characteristics, but also by the organizational creative climate of their kindergartens. Using the Hierarchical Linear Models (HLM), this study examined a correlation between a 5-year-old child’s variables (e.g. child’s creativity and their perceptions of creative classroom climate), teacher’s variables (e.g. the types of kindergarten, teacher’s perceptions of organizational creative climate, and teacher’s creative dispositions) and child’s creative dispositions. The study sample included a total number of 20 kindergarten teachers who teach 5-year-old children and a total number of 195 kindergarteners selected from 10 exemplary kindergartens (i.e. kindergartens recognized by the Ministry of Education in Korea for their outstanding curriculum) and 10 average kindergartens of similar size. The findings of the study are as follows. First, the levels of children’s creative thinking and their creative dispositions both were higher in the exemplary kindergartens than those in the average kindergartens. Furthermore, in terms of the levels of teachers’ creative dispositions and their perceptions of the organizational creative climate, teachers working in the exemplary kindergartens scored higher than those in the average kindergartens. Next, despite that no direct correlations existed between kindergarteners’ creative dispositions and teachers’ creative dispositions, kindergarteners’ creative dispositions were affected by the types of the kindergartens (e.g. the outstanding curriculum of the exemplary kindergartens) and teachers’ perceptions of organizational creative climate. In conclusion, this study indicates the significance of building an organizational creative climate of kindergartens not only for the children but for the teachers to foster children’s creative dispositions.

Environmental Concern and Destination Choices of Tourists: Exploring the Underpinnings of Country Heterogeneity

This article analyzes the main determinants of pro-environmental concern of European tourists when they make holiday decisions. Tourist environmental concern depends not only on individual and travel-related attributes, but also on the characteristics of the tourists’ place of residence. Thus, this article simultaneously applies micro and macro approaches using hierarchical linear models, which can estimate variations in tourists’ environmental concern because of between-country and within-country differences. Specifically, the heterogeneous pattern across European countries in the level of environmental concern is mainly explained by between-country economic, cultural, and environmental differences. Within-country variability in the level of pro-environmental concern is mainly explained by individual and travel-related variables, and particularly by the characteristics of the destination. The results demonstrate that environmental concern varies depending on whether the destination is booked via a last-minute offer or not, whether it is a traditional or emergent destination, and whether the trip is abroad or domestic.

Exploring the Factors Controlling Nighttime Lights from Prefecture Cities in Mainland China with the Hierarchical Linear Model

Nighttime light data have been proven to be valuable for socioeconomic studies. However, they are not only affected by anthropogenic factors but also by physical factors, and previous studies have rarely examined these diverse variables in a systematic way that explains differences in nighttime lights across different cities. In this paper, hierarchical linear models at two levels of city and province were developed to investigate the nighttime lights effect on cross-level factors. An experiment was conducted for 281 prefecture cities in Mainland China using orbital satellite data in 2016. (1) There exist significant differences among city average lights, of which 49.9% is caused at the provincial level, indicating the factors at the provincial level cannot be ignored. (2) Economy-energy-infrastructure and demography factors have a significant positive lights effect. Meanwhile, industry-information and living-standard factors at the provincial level can further significantly increase these differences by 18.30% and 29.01%, respectively. (3) The natural-greenness factor displayed a significant negative lights effect, and its interaction with natural-ecology will continue to decrease city lights by 11.99%. However, artificial-greenness is an unreliable city-level factor explaining lights variations. (4) As for the negative lights effect of elevation and latitude, these become significant in a multivariate context and contribute lights indirectly. (5) The two-level hierarchical linear models are statistically significant at the level of 10%, and compared with the null model, the explained variances on city lights can be improved by 70% at the city level and 90% at the provincial level in the final mixed effect model.

The Right Fit? Classroom Mismatch in Middle School and Its Inconsistent Effect on Student Learning

Research on college admissions shows that all students tend to benefit from overmatching, but high-status students are most likely to be overmatched, and low-status students are most likely to be undermatched. This study examines whether mismatching takes place when students are sorted into classrooms in middle school. Given prior research on effectively maintained inequality, we theorize that classroom sorting acts as an opportunity for privileged parents to obtain a qualitative advantage for their children. Our research uses administrative data from Indiana and hierarchical linear models to analyze classroom mismatch in sixth through eighth grades. We find that privileged students are more likely to be overmatched in both math and English language arts (ELA) classrooms but that overmatching is beneficial in math but detrimental in ELA. This suggests that inequality can be effectively maintained only if parents have an accurate understanding of what constitutes an advantage.