# Two domains of structural equation modeling (SEM)

SEM is a general multivariate framework for examining the theory-driven relationships between observed variables and constructs. Constructs are mental abstractions that describe the ideas, objects, people, events, or phenomena that we wish to measure or understand.

In SEM, there have been two statistical representations of constructs based on scientific theory — (common) factors and components. If a researcher considers a construct an external reality being independent of observed variables, which solely produces the correlation pattern of the observed variables, a factor may be used to represent this construct in a statistical model [1]. Observed variables derived from factors are called effect or reflective indicators [2]. Conversely, if a researcher theoretically defines a construct as a summary or an index of observed variables, so that the observed variables’ correlational pattern forms the construct, a weighted composite of the observed variables (i.e., a component) may be used to represent the construct in the model. Observed variables determining a component are referred to as composite indicators [3].

Depending on whether a construct is represented by a factor or a component, SEM has emerged into two domains — factor-based vs. component-based [4-6]. Methodologically, covariance structure analysis (CSA) [7] is a standard statistical method for factor-based SEM, although other methods are also available, including model-implied instrumental variable approach (MIIV) [8,9], consistent partial least squares (PLSc) [10], and generalized structured component analysis with measurement errors incorporated (GSCA_M) [11]. On the other hand, generalized structured component analysis (GSCA) [12,13] and partial least squares (PLS) [14,15] are the most flexible methods for component-based SEM.

Researchers have increasingly recognized that the two representations of constructs are theoretically incompatible with each other and that models with factors only should be estimated by factor-based SEM methods (e.g., CSA) and those with components only should be estimated by component-based SEM methods (e.g., GSCA), otherwise resulting in biased solutions [16-18].