20241111 - local fit

08-Structural-Equation-Modeling.Rmd

@@ -843,12 +843,14 @@ However, good model fit does not necessarily indicate a true model.\index{struct
 
 In addition to global fit indices, it can also be helpful to examine evidence of local fit, such as the residual covariance matrix.\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
 The residual covariance matrix represents the difference between the observed covariance matrix and the model-implied covariance matrix (the observed covariance matrix minus the model-implied covariance matrix).\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
+These difference values are called *covariance residuals*.\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
 Standardizing the covariance matrix by converting each to a correlation matrix can be helpful for interpreting the magnitude of any local misfit.\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
-This is known as a residual correlation matrix.\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
+This is known as a residual correlation matrix, which is composed of *correlation residuals*.\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
 Correlation residuals greater than |.10| are possible evidence for poor local fit [@Kline2023].\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
 If a correlation residual is positive, it suggests that the model underpredicts the observed association between the two variables (i.e., the observed covariance is greater than the model-implied covariance).\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
 If a correlation residual is negative, it suggests that the model overpredicts their observed association between the two variables (i.e., the observed covariance is smaller than the model-implied covariance).\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
 If the two variables are connected by only indirect pathways, it may be helpful to respecify the model with direct pathways between the two variables, such as a direct effect (i.e., regression path) or a covariance path.\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
+For guidance on evaluating local fit, see @Kline2024.\index{structural equation modeling!fit index}\index{structural equation modeling!residual}
 
 ## Correlation Matrix {#correlationMatrix-sem}