Merge pull request #95 from maugavilla/master

added mod indices reference/paper to the mod indices vignette

vignettes/mod_indices.Rmd

@@ -17,7 +17,7 @@ There are a couple of common methods for this, (a) testing for high residual cor
 
 ### Modification Indices
 
-Modification indices present different **indices** to quantify the effect of each parameter, and we will focus on two here. These are (a) the modification index (MI) or Lagrange multiplier, which estimates the extent to which the model’s chi-square ($\chi^2$) test statistic would decrease if a parameter were added to the model and freely estimated, and (b) standardized expected parameter change (SEPC), which is the approximated standardized value of the parameter if it were to be estimated in the model [@whittaker_using_2012]. 
+Modification indices present different **indices** to quantify the effect of each parameter, and we will focus on two here. These are (a) the modification index (MI) or Lagrange multiplier, which estimates the extent to which the model’s chi-square ($\chi^2$) test statistic would decrease if a parameter were added to the model and freely estimated, and (b) standardized expected parameter change (SEPC), which is the approximated standardized value of the parameter if it were to be estimated in the model [@whittaker_using_2012; @garniervillarreal_evaluating_2024]. 
 
 MI presents the possible effect on the overall model, and SEPC presents the effect size for the missed parameter. 
 
@@ -114,12 +114,15 @@ And you can check if the added parameter has the expected impact on overall fit
 
 It is important to consider also the theoretical relevance of the suggested parameters, and to ensure that they make sense, instead of just adding parameters until having **good** fit.
 
+
 ### Summary
 
+You can see more details about the application an test  of these indices in Bayesian SEM in @garniervillarreal_evaluating_2024.
+
 In this tutorial we show how to calculate the MI and SEPC across posterior distributions, and evaluate which parameters can be added. 
 
 With the ```ppmc()``` function we are able to calculate relevant information after model estimation, and build posterior distributions of them. 
 
-The general recommendations are to use MI to identify the most likely parameter to add, and SEPC as the effect size of the new parameter. 
+The general recommendations are to use MI to identify the most likely parameter to add, and SEPC as the effect size of the new parameter [@garniervillarreal_evaluating_2024]. 
 
 ### References

vignettes/refs.bib

@@ -441,4 +441,16 @@ @Manual{tarchetypes
     author = {William Michael Landau},
     year = {2021},
     note = {{https://docs.ropensci.org/tarchetypes/, https://github.com/ropensci/tarchetypes}},
+}
+
+
+@article{garniervillarreal_evaluating_2024,
+	title = {Evaluating {Local} {Model} {Misspecification} with {Modification} {Indices} in {Bayesian} {Structural} {Equation} {Mo}},
+	doi = {10.1080/10705511.2024.2413128},
+	abstract = {Model evaluation is a crucial step in SEM, consisting of two broad areas: global and local fit, where local fit indices are used to modify the original model. In the modification process, the modification index (MI) and the standardized expected parameter change (SEPC) are used to select the parameters that can be added to improve the fit. The purpose of this study is to extend the application of MI and SEPC to Bayesian SEM. We present how researchers can estimate posterior distributions of MI and SEPC using a posterior predictive model check (PPMC). We evaluated the effectiveness of these PPMCs with a simulation and found that MI can be used to detect the most relevant added parameters and that SEPC can be used as an effect size. Similar to maximum-likelihood estimation, the SEPC can over­ estimate the population value. Lastly, we present an example application of these indices.},
+	language = {en},
+	journal = {Structural Equation Modeling: A Multidisciplinary Journal},
+	author = {Garnier-Villarreal, Mauricio and Jorgensen, Terrence D},
+	year = {2024},
+	pages = {1--15},
 }