20260114 - cross-reference

Author: isaactpetersen

factor-analysis-pca.qmd

@@ -2478,7 +2478,7 @@ cor.test(
 
 #### Internal Consistency Reliability {#sec-reliability-cfa}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 [Coefficient omega ($\omega$)](#sec-coefficientOmega) is an example of *composite reliability*.\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}
 
 ```{r}
@@ -2586,7 +2586,7 @@ modificationindices(cfaModel1Fit, sort. = TRUE)
 
 ###### Internal Consistency Reliability {#sec-classExamplesModel1reliability-cfa}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(cfaModel1Fit)
@@ -2686,7 +2686,7 @@ modificationindices(cfaModel1Fit, sort. = TRUE)
 
 ###### Internal Consistency Reliability {#sec-classExamplesModel2reliability-cfa}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(cfaModel2Fit)
@@ -2830,7 +2830,7 @@ modificationindices(cfaModel3BFit, sort. = TRUE)
 
 ###### Internal Consistency Reliability {#sec-classExamplesModel3reliability-cfa}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(cfaModel3AFit)
@@ -3081,7 +3081,7 @@ modificationindices(cfaModel4EFit, sort. = TRUE)
 
 ###### Internal Consistency Reliability {#sec-classExamplesModel4reliability-cfa}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(cfaModel4AFit)
@@ -3410,7 +3410,7 @@ modificationindices(cfaModelBifactorFit, sort. = TRUE)
 
 ##### Internal Consistency Reliability {#sec-bifactorModelReliability}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{factor analysis!bifactor}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{factor analysis!bifactor}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(cfaModelBifactorFit)
@@ -3699,7 +3699,7 @@ modificationindices(cfaModelMTMMFit, sort. = TRUE)
 
 ##### Internal Consistency Reliability {#sec-mtmmCFAreliability}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{multitrait-multimethod matrix}\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{multitrait-multimethod matrix}\index{factor analysis!confirmatory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(cfaModelMTMMFit)
@@ -3863,7 +3863,7 @@ modificationindices(esemModelFit, sort. = TRUE)
 
 ##### Internal Consistency Reliability {#sec-esemModelReliability}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{structural equation modeling!exploratory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{structural equation modeling!exploratory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(esemModelFit)
@@ -3985,7 +3985,7 @@ modificationindices(esem_fit, sort. = TRUE)
 
 ##### Internal Consistency Reliability {#sec-esemModelReliability2}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{structural equation modeling!exploratory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{structural equation modeling!exploratory}\index{reliability!internal consistency}\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(esem_fit)

reliability.qmd

@@ -1676,6 +1676,15 @@ summary(
 AVE(latentFactorModel_fit)
 ```
 
+#### Maximal Reliability {#sec-maximalReliability}
+
+Maximal reliability was estimated using a [confirmatory factor analysis](#sec-cfa) model using the `lavaan` [@R-lavaan] and `semTools` [@R-semTools] packages.\index{reliability!internal consistency}\index{reliability!internal consistency!maximal reliability}
+The [confirmatory factor analysis](#sec-cfa) model was fit above in @sec-averageVarianceExtracted.
+
+```{r}
+maximalRelia(latentFactorModel_fit)
+```
+
 #### Split-Half Reliability {#sec-splitHalf-reliability}
 
 When estimating split-half reliability, we randomly take half of the items on the measure and relate scores on these items to the score on the other half of items.\index{reliability!internal consistency}\index{reliability!internal consistency!split-half}\index{split-half reliability!zzzzz@\igobble|seealso{reliability}}

structural-equation-modeling.qmd

@@ -1122,7 +1122,7 @@ measurementModelFit_factorScores <- lavPredict(measurementModelFit)
 
 ### Internal Consistency Reliability {#sec-measurementModelReliability-sem}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(measurementModelFit)
@@ -1297,7 +1297,7 @@ cfaModelFit_factorScores <- lavPredict(cfaModelFit)
 
 ### Internal Consistency Reliability {#sec-cfaModelReliability-sem}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(cfaModelFit)
@@ -1704,7 +1704,7 @@ semModelFit_factorScores <- lavPredict(semModelFit)
 
 ### Internal Consistency Reliability {#sec-semModelReliability-sem}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(semModelFit)

test-bias.qmd

@@ -2788,7 +2788,7 @@ In other words, configural invariance held.\index{structural equation modeling!m
 
 #### Internal Consistency Reliability {#sec-measurementInvarianceReliability}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(configuralInvarianceModel_fit)
@@ -3070,7 +3070,7 @@ In other words, metric invariance held.\index{structural equation modeling!measu
 
 #### Internal Consistency Reliability {#sec-measurementInvarianceMetricModelReliability}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(metricInvarianceModel_fit)
@@ -3352,7 +3352,7 @@ In other words, scalar invariance failed.\index{structural equation modeling!mea
 
 #### Internal Consistency Reliability {#sec-measurementInvarianceScalarModelReliability}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(scalarInvarianceModel_fit)
@@ -3640,7 +3640,7 @@ The *p*-values are non-significant, indicating that the model did not fit signif
 
 #### Internal Consistency Reliability {#sec-measurementInvarianceResidualModelReliability}
 
-[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and maximal reliability, was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
+[Internal consistency reliability](#sec-internalConsistency-reliability) of items composing the latent factors, as quantified by [omega ($\omega$)](#sec-coefficientOmega), [average variance extracted](#sec-averageVarianceExtracted) (AVE), and [maximal reliability](sec-maximalReliability), was estimated using the `semTools` package [@R-semTools].\index{reliability!internal consistency!omega}\index{reliability!internal consistency!average variance extracted}
 
 ```{r}
 compRelSEM(residualInvarianceModel_fit)