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Chapter 3 52 the discrete latent group engagement scores. Finally, based on the output test statistics, the study’s hypotheses can be confirmed or rejected. 3.2.3 Limitations of Bathtub Modeling Micro-macro analysis in general and bathtub modeling in particular are innovative and well-performing approaches to examine how micro-level mechanisms influence the relationship between macro-level variables. However, there are several limitations. For example, it is unclear how sample size influences the performance of bathtub models. Although Bennink (2014) demonstrates that the method generally outperforms the traditional aggregation and disaggregation approaches, the more complex bathtub models with indirect or interaction effects can provide equally inaccurate estimates when applied to small macro-level samples. While a sample of 200 groups should be sufficient to provide accurate results for complex models (Bennink, 2014), this number is quite large. The minimum sample size to establish accurate results is unknown and seems to differ from one model to the next. Furthermore, to date, no research has been conducted regarding power in bathtub models with continuous latent variables. Additionally, it is unknown how missing values impact the performance of bathtub models. Although the standard approach to handling missing values in multi-level research is listwise deletion, multiple imputation is currently undergoing heavy development for the classical top-down effects (Van Buuren, 2011). The impact of missing values and the best way of handling them in multi-level research with bottom-up effects, such as bathtub models, has yet to receive empirical attention. A further consideration lies in the person-as-variable approach, which considers the employees within a group as interchangeable. This approach implies that each individual within a group contributes equally to the estimation of the latent score for that group. For constructs like engagement, this seems theoretically sound as each employee’s engagement can be considered equally important to the team’s latent score. However, there may be HRM research questions in which the data of certain employees can be considered more important to or representative of the group’s latent score. For example, when accounting for differences in employment type (e.g., full-/part-time or temporary/fixed contracts) or when scores follow specific distributions within subgroups of employees (e.g., forced distributed performance evaluations). Although bathtub modeling clearly outperforms traditional aggregation and disaggregation approaches (Bennink, 2014; Bennink et al., 2013, 2015; Croon & Van Veldhoven, 2007), multi-level structural equation models (SEM) may function as an alternative. When the outcome variable resides at the micro-level, multi-level SEM can be preferable to bathtub models (Lüdtke et al., 2008). However, similar to the traditional micro-macro analysis (Croon & Van Veldhoven, 2007), a multi-level SEM only works with continuous data and is unable to handle categorical predictors. Additionally, multi-level SEM on continuous data frequently provides more biased estimates of the bottom-up effects than the latent bathtub model advocated by this paper (Onrust, 2015). On a final note, bathtub models are very flexible and they run in most statistical software developed for latent variable modeling, including Mplus (Muthén & Muthén, 1998-2016) and Latent GOLD (Vermunt & Magidson, 2013). They can be conducted in R