Chapter 23: Structural Equation Mixture Modeling

Conor V. Dolan

Structural equation mixture modeling Applications of structural equation modeling (SEM) are often based on the assumption that the sampled data are identically and independently distributed (IID), according to the multivariate normal distribution. Letting y i denote the vector of observed variables of subject i, we express this as IID y i  N(μ,Σ), where μ and Σ represent the population mean vector and covariance matrix, respectively. This expression implies that the population is homogeneous, in the sense that IID y i  N(μ,Σ) should hold for every possible vector y i . Alternatively, if we view yi as the outcome of some (psychological) process, we may state that the observed vectors y i (i = 1,2,…,N) are independent outcomes of one and the same process, which gives rise to IID N(μ,Σ) data. Violations of the assumption IID y i  N(μ,Σ) come in many forms. Given the heavy reliance per ...

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