20231115 - CCA

Author: isaactpetersen

04-Constructs.Rmd

@@ -119,7 +119,7 @@ Linear composite approaches are likely more defensible for [formative constructs
 
 To estimate a [reflective construct](#reflectiveConstruct), a latent variable modeling approach is necessary, such as [structural equation modeling](#sem), [factor analysis](#factorAnalysis), or [item response theory](#irt).\index{construct!reflective}\index{latent variable}\index{structural equation modeling}\index{factor analysis}\index{item response theory}
 
-To estimate a [formative construct](#formativeConstruct), one may estimate an average or sum score across items (which gives each item equal weight), estimate a weighted average, use [principal component analysis](#pca), or use [structural equation modeling](#sem).\index{construct!formative}\index{linear composite}\index{structural equation modeling}\index{principal component analysis}
+To estimate a [formative construct](#formativeConstruct), one may estimate an average or sum score across items (which gives each item equal weight), estimate a weighted average, use [principal component analysis](#pca), use confirmatory composite analysis, or use [structural equation modeling](#sem).\index{construct!formative}\index{linear composite}\index{structural equation modeling}\index{principal component analysis}\index{confirmatory composite analysis}
 
 Thus, it is important to think about the nature of the construct before deciding how to estimate it.\index{construct}
 The nature of a construct is a theoretical question.\index{construct}
@@ -130,8 +130,9 @@ In sum, although empiricism is relevant, theory is necessary to inform our under
 
 ## Latent Variable Modeling: IRT, SEM, and CFA {#latentVariableModeling}
 
-[Item response theory](#irt) (IRT), [structural equation modeling](#sem) (SEM), and [confirmatory factor analysis](#cfa) (CFA) are all approaches to latent variable modeling.\index{latent variable}\index{structural equation modeling}\index{factor analysis}\index{factor analysis!confirmatory}\index{item response theory}
+[Item response theory](#irt) (IRT), [structural equation modeling](#sem) (SEM), confirmatory composite analysis (CCA), and [confirmatory factor analysis](#cfa) (CFA) are all approaches to latent variable modeling.\index{latent variable}\index{structural equation modeling}\index{factor analysis}\index{factor analysis!confirmatory}\index{item response theory}\index{confirmatory composite analysis}
 [CFA](#cfa) and [IRT](#irt) most commonly estimate [reflective](#reflectiveConstruct) latent variables rather than [formative](#formativeConstruct) latent variables.\index{construct!reflective}\index{construct!formative}\index{latent variable}\index{factor analysis!confirmatory}\index{item response theory}
+CCA estimates [formative](#formativeConstruct) latent variables.\index{construct!formative}\index{latent variable}\index{confirmatory composite analysis}
 [SEM](#sem) can estimate both [reflective](#reflectiveConstruct) and [formative](#formativeConstruct) latent variables.\index{construct!reflective}\index{construct!formative}\index{latent variable}\index{structural equation modeling}
 [IRT](#irt) is essentially a form of [CFA](#cfa) with [categorical](#nominalData), binary, or [ordinal](#ordinalData) data.\index{latent variable}\index{factor analysis!confirmatory}\index{item response theory}
 As we discuss in Chapter \@ref(sem), [SEM](#sem) is [CFA](#cfa) with regression paths that specify hypothesized causal relations between the latent variables (the structural component of the model).\index{latent variable}\index{structural equation modeling}\index{factor analysis!confirmatory}

09-Structural-Equation-Modeling.Rmd

@@ -357,6 +357,7 @@ fitMeasures(formativeModel2Fit, "df")
 
 Thus, [formative constructs](#formativeConstruct) are challenging to use in a SEM framework.\index{construct!formative}\index{structural equation modeling!model identification}
 To estimate a [formative construct](#formativeConstruct) in a SEM framework, the [formative construct](#formativeConstruct) must be used in the context of a model that allows some constraints.\index{construct!formative}\index{structural equation modeling!model identification}\index{structural equation modeling!degrees of freedom}
+However, emerging techniques such as confirmatory composite analysis allow estimation of [formative](#formativeConstruct) latent factors [@Schuberth2023; @Yu2023].\index{construct!formative}\index{confirmatory composite analysis}
 
 ## Additional Types of SEM {#additionalSEMmodels}