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A review of the literature suggests that few studies use formative indicator measurement models, even though they should. Therefore, the purpose of this research is to (a) discuss the distinction between formative and reflective measurement models, (b) develop a set of conceptual criteria that can be used to determine whether a construct should be modeled as having formative or reflective indicators, (c) review the marketing literature to obtain an estimate of the extent of measurement model misspecification in the field, (d) estimate the extent to which measurement model misspecification biases estimates of the relationships between constructs using a Monte Carlo simulation, and (e) provide recommendations for modeling formative indicator constructs. It has been more than two decades since Churchill (1979), Bagozzi (1980), Peter (1981), and Anderson and Gerbing (1982), among others, criticized the field of marketing for failing to pay enough attention to construct validity and associated measurement issues. A good example of this concern

This paper uses Bayesian network models for that investigation. Bayesian networks, or directed acyclic graph (DAG) models have proved very useful in representing both causal and statistical hypotheses. The nodes of the graph represent vertices, directed edges represent direct influences, and the topology of the graph encodes statistical constraints. We will consider features of such models that can be determined from data under assumptions that are related to those routinely applied in experimental situations:

The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuous-valued data linear acyclic causal models with additive noise are often used because these models are well understood and there are well-known methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the data-generating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true data-generating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1

this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. There are a number of problems associated with structural equation modeling. These problems include:

This paper estimates models of the evolution of cognitive and noncognitive skills and explores the role of family environments in shaping these skills at different stages of the life cycle of the child. Central to this analysis is identification of the technology of skill formation. We estimate a dynamic factor model to solve the problem of endogeneity of inputs and multiplicity of inputs relative to instruments. We identify the scale of the factors by estimating their effects on adult outcomes. In this fashion we avoid reliance on test scores and changes in test scores that have no natural metric. Parental investments are generally more effective in raising noncognitive skills. Noncognitive skills promote the formation of cognitive skills but, in most specifications of our model, cognitive skills do not promote the formation of noncognitive skills. Parental inputs have different effects at different stages of the child’s life cycle with cognitive skills affected more at early ages and noncognitive skills affected more at later ages.

A Bayesian approach to model selection for structural equation models is outlined. This enables us to compare individual models, nested or non-nested, and also to search through the (perhaps vast) set of possible models for the best ones. The approach selects several models rather than just one, when appropriate, and so enables us to take account, both informally and formally, of uncertainty about model structure when making inferences about quantities of interest. The approach tends to select simpler models than strategies based on multiple P-value-based tests. It may thus help to overcome the criticism of structural

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errors-in-variables model.

Brain imaging methods, such as positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), provide a unique opportunity to study the neurobiology of human memory. Since these methods can measure most of the brain, it is possible to examine the operations of large-scale neural systems and their relation to cognition. Two neuroimaging studies, one concerning working memory and the other episodic memory retrieval, serve as examples of application of two analytic methods that are optimized for the quantification of neural systems, structural equation modeling and partial least squares. Structural equation modeling was used to explore shifting prefrontal and limbic interactions from the right to the left hemisphere in a delayed match-to-sample task for faces. A feature of the functional network for short delays was strong right hemisphere interactions between hippocampus, inferior prefrontal, and anterior cingulate cortices. At longer delays, these same three areas were strongly linked, but in the left hemisphere, which was interpreted as reflecting change in task strategy from perceptual to elaborate encoding with increasing delay. The primary manipulation in the memory retrieval study was different levels of retrieval success. Partial least squares was used to determine whether the image-wide pattern of covariances of Brodmann areas 10 and 45/47 in right prefrontal cortex (RPFC) and the left hippocampus (LGH) could be mapped on to retrieval levels. Area 10 and LGH showed an opposite pattern of functional connectivity with a large expanse of bilateral limbic cortices that was equivalent for all levels of retrieval as well as the baseline task. However, only during high retrieval area 45/47 was included in this pattern. The results suggest that activ...

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