scholarly journals G-optimal designs for hierarchical linear models: an equivalence theorem and a nature-inspired meta-heuristic algorithm

2021 ◽  
Author(s):  
Xin Liu ◽  
RongXian Yue ◽  
Zizhao Zhang ◽  
Weng Kee Wong
2021 ◽  
Author(s):  
Xin Liu ◽  
RongXian Yue ◽  
Zizhao Zhang ◽  
Weng Kee Wong

Abstract 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.


2020 ◽  
Vol 41 (2) ◽  
pp. 61-67
Author(s):  
Marko Tončić ◽  
Petra Anić

Abstract. This study aims to examine the effect of affect on satisfaction, both at the between- and the within-person level for momentary assessments. Affect is regarded as an important source of information for life satisfaction judgments. This affective effect on satisfaction is well established at the dispositional level, while at the within-person level it is heavily under-researched. This is true especially for momentary assessments. In this experience sampling study both mood and satisfaction scales were administered five times a day for 7 days via hand-held devices ( N = 74 with 2,122 assessments). Several hierarchical linear models were fitted to the data. Even though the amount of between-person variance was relatively low, both positive and negative affect had substantial effects on momentary satisfaction on the between- and the within-person level as well. The within-person effects of affect on satisfaction appear to be more pronounced than the between-person ones. At the momentary level, the amount of between-person variance is lower than in studies with longer time-frames. The affect-related effects on satisfaction possibly have a curvilinear relationship with the time-frame used, increasing in intensity up to a point and then decreasing again. Such a relationship suggests that, at the momentary level, satisfaction might behave in a more stochastic manner, allowing for transient events/data which are not necessarily affect-related to affect it.


1994 ◽  
Vol 39 (5) ◽  
pp. 475-476
Author(s):  
Paula L. Woehlke

Sociology ◽  
2016 ◽  
Vol 51 (5) ◽  
pp. 1011-1033 ◽  
Author(s):  
James Laurence

Extensive research has demonstrated that neighbourhood ethnic diversity is negatively associated with intra-neighbourhood social capital. This study explores the role of segregation and integration in this relationship. To do so it applies three-level hierarchical linear models to two sets of data from across Great Britain and within London, and examines how segregation across the wider-community in which a neighbourhood is nested impacts trust amongst neighbours. This study replicates the increasingly ubiquitous finding that neighbourhood diversity is negatively associated with neighbour-trust. However, we demonstrate that this relationship is highly dependent on the level of segregation across the wider-community in which a neighbourhood is nested. Increasing neighbourhood diversity only negatively impacts neighbour-trust when nested in more segregated wider-communities. Individuals living in diverse neighbourhoods nested within integrated wider-communities experience no trust-penalty. These findings show that segregation plays a critical role in the neighbourhood diversity/trust relationship, and that its absence from the literature biases our understanding of how ethnic diversity affects social cohesion.


Statistics ◽  
1996 ◽  
Vol 27 (3-4) ◽  
pp. 267-278 ◽  
Author(s):  
Rainer Schwabe

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