Attributed graph kernels using the Jensen-Tsallis q-differences

We propose a family of attributed graph kernels based on mutual information measures, i.e., the Jensen-Tsallis (JT) q-differences (for q  ∈ [1,2]) between probability distributions over the graphs. To this end, we first assign a probability to each vertex of the graph through a continuous-time quantum walk (CTQW). We then adopt the tree-index approach [1] to strengthen the original vertex labels, and we show how the CTQW can induce a probability distribution over these strengthened labels. We show that our JT kernel (for q  = 1) overcomes the shortcoming of discarding non-isomorphic substructures arising in the R-convolution kernels. Moreover, we prove that the proposed JT kernels generalize the Jensen-Shannon graph kernel [2] (for q = 1) and the classical subtree kernel [3] (for q = 2), respectively. Experimental evaluations demonstrate the effectiveness and efficiency of the JT kernels.

The MIMIC model and formative variables:problems and solutions

The use of the multiple indicators, multiple causes model to operationalize formative variables (the formative MIMIC model) is advocated in the methodological literature. Yet, contrary to popular belief, the formative MIMIC model does not provide a valid method of integrating formative variables into empirical studies and we recommend discarding it from formative models. Our arguments rest on the following observations. First, much formative variable literature appears to conceptualize a causal structure between the formative variable and its indicators which can be tested or estimated. We demonstrate that this assumption is illogical, that a formative variable is simply a researcher-defined composite of sub-dimensions, and that such tests and estimates are unnecessary. Second, despite this, researchers often use the formative MIMIC model as a means to include formative variables in their models and to estimate the magnitude of linkages between formative variables and their indicators. However, the formative MIMIC model cannot provide this information since it is simply a model in which a common factor is predicted by some exogenous variables—the model does not integrate within it a formative variable. Empirical results from such studies need reassessing, since their interpretation may lead to inaccurate theoretical insights and the development of untested recommendations to managers. Finally, the use of the formative MIMIC model can foster fuzzy conceptualizations of variables, particularly since it can erroneously encourage the view that a single focal variable is measured with formative and reflective indicators. We explain these interlinked arguments in more detail and provide a set of recommendations for researchers to consider when dealing with formative variables.