What are the differences between factors in SEM and PSEM?
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Structural Equation Models (SEM):Formative and reflective factors are two kinds of measurement models that represent two different causal assumptions. [*:3qsaqbdo]Reflective construct: the latent (factor) variable [latex:3qsaqbdo]\xi[/latex:3qsaqbdo] is the hidden common cause of its associated manifest variables [latex:3qsaqbdo]x_i[/latex:3qsaqbdo]. Changing the value of a manifest variable does not have any impact on the latent (factor) variable.[/*:m:3qsaqbdo][*:3qsaqbdo]Formative construct: the manifest variables are the causes of the associated latent variable. Changing the value of a manifest does change the value of the latent.[/*:m:3qsaqbdo]Probabilistic Structural Equation Models (PSEM):PSEM development, as implemented in BayesiaLab, is based on the following workflow:[list=1:3qsaqbdo][*:3qsaqbdo]Unsupervised Structural Learning is performed to find the relationships between the manifest variables.[/*:m:3qsaqbdo][*:3qsaqbdo]Variable Clustering finds manifests to be grouped into factor constructs.[/*:m:3qsaqbdo][*:3qsaqbdo]For each cluster of manifests, Data Clustering formally induces factor nodes from the factor constructs. This consists of using Naive Bayes structures for creating probabilistic summaries of the Joint Probability Distribution of all the manifests associated with each factor node. Expectation Maximization estimates the probability distributions of these networks. Each of these manifest/factor structures are reflective. [/*:m:3qsaqbdo][*:3qsaqbdo]Finally, Unsupervised Structural Learning is used to find relationships between the target variable(s) and the factor variables.[/*:m:3qsaqbdo][/list:3qsaqbdo]
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Is it correct to infer from this response that manifest variables that supply very little information about a factor could be deleted from the model without changing the outcome of the final unsupervised learning step? Having for years deleted variables with high VIF values during multiple regression refinement, I have a hard time passively retaining all the variables that BayesiaLab says are part of a network--especially when the consensus of the process experts is that no effect should exist.
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Dan
If you delete these variables from the original dataset, the network you will obtain with the unsupervised learning algorithm will have a different structure, and chances are that you will not get the exact same clusters of variables (Factors).If these variables do not bring information to your target, it should not harm to keep them in your network. However, if the experts know for sure that these variables are absolutely useless, it’s probably good not to include them in the model.Hope this helps,-Dan
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