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Expanding the methodological toolbox of HRM researchers 49 micro-level responses to the macro-level while taking into account both within-group variance and sampling variability. Subsequently, the latent variable can be used as a regular predictor in the macro-level model. Applied to employee engagement, bathtub modeling provides an opportunity to examine how HRM policies and practices influence organizational performance through the behaviors of employees. This analysis can be conducted without ignoring the possibility that employee engagement is personal and individually determined (Macey & Schneider, 2008), and without inflating statistical power (Bennink et al., 2013, Krull & MacKinnon, 1999). The following illustrates the modeling process step-by-step. First, the data requirements are described, followed by the two parts of the model and their respective interpretation. Afterwards, several limitations to bathtub modeling are presented. 3.2.1 Data Requirements Before conducting a bathtub model, the sample size and the data format need to be considered. The power of a bathtub model largely depends on the sample size at all levels of analysis. Hence, researchers should not only gather data of multiple groups but they should also ensure high response rates within the groups. Bennink (2014) demonstrates that a sample of as small as 40 groups with ten respondents per group can already result in nearly unbiased parameter estimates in case of a bottom-up, micro-macro effect (e.g., engagement on organizational performance). In order to detect more complex effects like interactions or indirect effects, larger sample sizes at the macro-level are required. Simulations demonstrate that 200 groups with ten respondents per group should be enough to detect most effects (Bennink, 2014), suggesting that increasing the macro-level sample size should be the focus for researchers seeking to examine small and/or complex effects. After data collection, the bathtub modeling requires the data to be structured according to its multi-level nature. Depending on the statistical software used, the model can be estimated on a dataset with either a long or a wide format. For long datasets, each row would represent a micro-level case (e.g., employee) and one of the columns would identify the macro-level unit this micro-level case belongs to (e.g., team or work group). Subsequently, a bathtub model can be applied using a multi-level regression approach. For wide datasets, the format is more peculiar: each row needs to represent a macro-level unit whereas, for each micro-level case, each measurement should be stored in a separate column. This format is commonly referred to as the persons-as-variable approach and it does not work in all software packages (e.g., Mplus). 3.2.2 Bathtub Model A bathtub model consists of two parts: a measurement model and a structural model. The measurement model describes the relationship between the observed micro- level (individual) variable(s) and the macro-level latent variable(s) based on them. Because this part of the model is primarily concerned with raising the individual-level scores to the group-level, it is often referred to as the within-group part. Next, the structural model describes the relationship between the variables at the macro-level. By relating the latent variable, derived from the measurement part, to the other macro-level
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