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With clustered data, such as where students are nested within schools or employees are nested within organizations, it is often of interest to estimate and compare associations among variables separately for each level. While researchers routinely estimate between-cluster effects using the sample cluster means of a predictor, previous research has shown that such practice leads to biased estimates of coefficients at the between level, and recent research has recommended the use of latent cluster means with the multilevel structural equation modeling framework. However, the latent cluster mean approach may not always be the best choice as it (a) relies on the assumption that the population cluster sizes are close to infinite, (b) requires a relatively large number of clusters, and (c) is currently only implemented in specialized software such as Mplus. In this paper, we show how using empirical Bayes estimates of the cluster means can also lead to consistent estimates of between-level coefficients, and illustrate how the empirical Bayes estimate can incorporate finite population corrections when information on population cluster sizes is available. Through a series of Monte Carlo simulation studies, we show that the empirical Bayes cluster-mean approach performs similarly to the latent cluster mean approach for estimating the between-cluster coefficients in most conditions when the infinite-population assumption holds, and applying the finite population correction provides reasonable point and interval estimates when the population is finite. The performance of EBM can be further improved with restricted maximum likelihood estimation and likelihood-based confidence intervals. We also provide an R function that implements the empirical Bayes cluster-mean approach, and illustrate it using data from the classic High School and Beyond Study. [ABSTRACT FROM AUTHOR]

The prevalence of outdoor sports tourism has posed certain threats to the natural environment. In recent years, incidents of outdoor sports enthusiasts damaging ecological environments and historical sites have become increasingly common. Thus, it is imperative to encourage these enthusiasts to protect environmental ecosystems, and sustainability has become a priority consideration for those participating in outdoor sports tourism. This paper explores the multiple mediating roles of environmental knowledge and attitudes in the relationship between sustainable values and the pro-environmental behaviours of outdoor sports tourism enthusiasts. The study aims to provide references and suggestions for promoting environmentally responsible behaviours in outdoor sports tourism and to support the sustainable development of sports tourism in China and globally. The research targets outdoor sports tourism enthusiasts, analysing data from 1079 survey responses. Structural Equation Modeling (SEM) is used to test the direct and indirect effects between variables. The results indicate that sustainable values have a positive impact on environmental attitudes, environmental knowledge, and pro-environmental behaviours. Furthermore, environmental attitudes and knowledge play a positive mediating role between sustainable values and pro-environmental behaviours. Lastly, this paper offers substantial suggestions to promote the sustainable development of outdoor sports tourism. [ABSTRACT FROM AUTHOR]