Latent Variable Models and Networks: Statistical Equivalence and Testability.

Networks are gaining popularity as an alternative to latent variable models for representing psychological constructs. Whereas latent variable approaches introduce unobserved common causes to explain the relations among observed variables, network approaches posit direct causal relations between observed variables. While these approaches lead to radically different understandings of the psychological constructs of interest, recent articles have established mathematical equivalences that hold between network models and latent variable models. We argue that the fact that for any model from one class there is an equivalent model from the other class does not mean that both models are equally plausible accounts of the data-generating mechanism. In many cases the constraints that are meaningful in one framework translate to constraints in the equivalent model that lack a clear interpretation in the other framework. Finally, we discuss three diverging predictions for the relation between zero-order correlations and partial correlations implied by sparse network models and unidimensional factor models. We propose a test procedure that compares the likelihoods of these models in light of these diverging implications. We use an empirical example to illustrate our argument.

Deviations of rational choice: an integrative explanation of the endowment and several context effects.

People's choices are often found to be inconsistent with the assumptions of rational choice theory. Over time, several probabilistic models have been proposed that account for such deviations from rationality. However, these models have become increasingly complex and are often limited to particular choice phenomena. Here we introduce a network approach that explains a broad set of choice phenomena. We demonstrate that this approach can be used to compare different choice theories and integrates several choice mechanisms from established models. A basic setup implements bounded rationality, loss aversion, and inhibition in a natural fashion, which allows us to predict the occurrence of well-known choice phenomena, such as the endowment effect and the similarity, attraction, compromise, and phantom context effects. Our results show that this network approach provides a simple representation of complex choice behaviour, and can be used to gain a better understanding of how the many choice phenomena and key theoretical principles from different types of decision-making are connected.

Estimating psychopathological networks: Be careful what you wish for.

Network models, in which psychopathological disorders are conceptualized as a complex interplay of psychological and biological components, have become increasingly popular in the recent psychopathological literature (Borsboom, et. al., 2011). These network models often contain significant numbers of unknown parameters, yet the sample sizes available in psychological research are limited. As such, general assumptions about the true network are introduced to reduce the number of free parameters. Incorporating these assumptions, however, means that the resulting network will lead to reflect the particular structure assumed by the estimation method-a crucial and often ignored aspect of psychopathological networks. For example, observing a sparse structure and simultaneously assuming a sparse structure does not imply that the true model is, in fact, sparse. To illustrate this point, we discuss recent literature and show the effect of the assumption of sparsity in three simulation studies.

Three representations of the Ising model.

Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense.