Coalition research increasingly emphasizes party-level explanations of coalition outcomes. However, this work does not account for the complex multilevel structure between parties and governments: many parties participate in multiple governments and governments often comprise multiple parties. In this paper, I demonstrate that this crisscrossing structure creates dependencies among observations both across and within governments. If ignored, these dependencies lead to downward-biased regression coefficients and standard errors, which cluster-robust standard errors do not correct. I then introduce a model that extends the multiple-membership multilevel model to represent the multilevel structure of coalition government data. The model accounts for dependencies across governments by including party effects in all coalitions they participate and for dependencies within governments by modeling the total party effect on a government as the weighted sum of each coalition party’s effect. By allowing party weights to vary based on covariates describing their interrelationships, the model enables researchers to examine the interdependent nature of coalition outcomes. Through simulation and an empirical application to coalition government survival, I validate the proposed model and show that ignoring the crisscrossing multilevel structure can lead to erroneous conclusions at all levels of analysis. The R package ‘rmm’ is provided to estimate the model.
- R&R at Political Analysis.
Beyond coalition research
Most multilevel analyses examine how lower-level units, such as persons, are affected by their embedding in contextual/aggregate units at a higher level (macro-to-micro link). The generalized multiple-membership multilevel model (MMMM) conceptually reverses this multilevel setup. It allows studying how the effects of units at lower levels propagate to a higher level (micro-to-macro link).
Previous studies examining micro-to-macro links either aggregated or disaggregated the data. These approaches obstruct the inherent aggregation problem, cannot separate micro-level and macro-level variance, and ignore dependencies among observations, thus inducing excessive Type-I error.
The MMMM overcomes these problems by explicitly modeling the aggregation from the micro to the macro level by including an aggregation function in the regression model. It is a theoretically and statistically sound solution to the study of micro-to-macro links with regression analysis.
The R package “rmm” provides an interface to fit the MMMM with Bayesian MCMC using JAGS from within R for a variety of outcomes (linear, logit, conditional logit, Cox, Weibull).
Next to aggregation regessions, the MMMM can be used
- to model spatial structures. Level-1 units, in this case, would be the neighborhoods in the influence sphere of the focal neighborhood, and level-2 units would be the focal neighborhoods. The benefit of using MMMM over other spatial regression models is that the weight matrix can be endogenized, which is not currently possible with other methods
- to model network structures. While this possibility has been explored in other work (Tranmer et al. 2014), the MMMM allows to endogenize the weight matrix, which is not currently possible with other multiple membership multilevel software, such as brms or MLWiN.