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Chapter 3 50 variables of interest, the bathtub model takes the individual variation that occurs at the micro-level into account. The below elaborates on both parts in more detail. The measurement part of a bathtub model uses a multi-level latent variable model to raise the observed individual data to the level of the group. Here, the format of the individual, micro-level data is quite important. The latent variable approach was initially proposed by Croon and Van Veldhoven (2007), who demonstrated how treating individual scores as exchangeable indicators for a continuous latent variable makes it possible to predict a group-level outcome with lower-level independent variables. It works by estimating an unobserved continuous score at the group-level based on the observed individual data. Because the resulting latent group score reflects the underlying individual data and its variance, it takes the measurement and sampling errors that occur at the micro-level into account. However, this approach was developed specifically for raising continuous variables to the group-level using a normally distributed latent variable and, while very useful, the approach has the limitation that it cannot treat categorical variables adequately. Bennink, Croon, and Vermunt (2015) therefore propose an extension of this latent variable approach, which makes it possible to raise categorical variables to the group- level using a generalized latent variable modeling framework (Skrondal & Rabe-Hasketh, 2004). This extended model allows micro-level discrete variables to be raised to the macro-level using a categorical latent variable, called a latent class variable. Using this approach, the unobserved heterogeneity at group-level can be estimated using a latent class variable that clusters together groups that are more similar to each other. In this way, individual data can be raised to the group-level by creating clusters of macro-level groups (i.e., latent classes) based on the similarity of their micro-level scores. Although it is common practice to have as many latent classes at the macro-level as there are discrete categories at the micro-level (Bennink, 2014), the optimal number of classes may also be estimated based on fit measures like BIC, AIC or χ 2 . The strength of the measurement model can be assessed using the entropy (R 2 ), with values above .70 reflecting a strong model where classes are adequately distinguished (Vermunt, 2010). This latent class approach is especially useful in the social sciences. For example, in HRM research, the effects of categorical variables are often of interest (e.g., gender and educational level) whereas employee behaviors are often measured with categorical, ordinal measures (e.g., Likert-type items). Once the measurement model is specified, the structural part of the model can be estimated. As the individual scores have been elevated in the measurement model, the structural model occurs completely at the macro-level and this is where the actual hypothesis testing takes place. Because it occurs on a single level, the interpretation of the structural model is comparable to that of a regular regression model, with direct, indirect and/or interaction effects depending on the specified model. The measurement scale of the dependent variable determines the type of regression model that applies (i.e., logistic, linear or ANOVA).

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