To run, type in the RStudio console:
Invariance explorer helps to find groups that might demonstrate measurement invariance of latent factors. Instead of repeatedly running the models to test invariance, one may plot the group measures and visually select the ones that are closer to each other.
Usually, assessment of measurement invariance is based on a measurement model (which is assumed to be a true model). However, one may employ completely exploratory approach, using covariances between observed variables to find groups with the most similar structures. This is the default (and the quickest) option in the
Measurement invariance explorer. Of course, at some point one has to specify a measurement model, but it may be done after finding a set of groups with similar covariance structures.
If, or when, a measurement model is given, one can use it in
Measurement invariance explorer to find sets of groups that are closer to each other using either model parameters or model fit indices.
First, one has to specify measurement model using lavaan syntax. When you add a code,
Measurement invariance explorer will automatically compute a common measurement invariance tests based on
semTools package. Please, insert only ready-to-use model code, as computation may take a long time.
Measurement invariance explorer computes configural model to compare factor loadings and metric model (with fixed factor loadings) to compare intercepts. It is recommended first be sure that you found a set of groups that have similar loadings before comparing intercepts.
When using fit indices as a measure of group proximity,
Measurement invariance explorer computes for each pair of groups either configural and metric models , or metric and scalar models, and plots the groups based on difference between less and more restricted models, as it was suggested by Chen, 2007. Chen also suggested a threshold of .01. For convenience, a rectangle .01x.01 is added to the plot. If all the groups are inside this rectangle, it is very likely that measurement invariance holds for these groups. When using this approach please pay attention to the actual fit indices, as the implied model is assumed to be true.
Measurement invariance exploreris exploratory. The plots are based basically on averaging a bunch of information, so it doesn't guarantee that closer groups have measurement invariance.
First column should include a group identifier, all the other columns should include indicators. Covariances are computed for all the indicators. When a model is implied, the data file might include any number of variables. However, it is recommended to keep file shorter to enhance a computation time. For example:
Here's a sample code to create data for the app in R from the data.frame:
write.csv(mydata[,c("country", "v1", "v2", "v3", "v4", "v5", "v6")], "fileforMIE.csv", row.names = F)
This app is very useful when there are either clusters of groups or outlier groups (in terms of implied model/correlations). The app is not very suitable for finding model misspecifications.
For the more sophisticated model-based clustering see https://ppw.kuleuven.be/okp/_pdf/DeRoover2017MSFAF.pdf However this method is limited to differences in factor loadings only, does not provide information on specific between-group distances, and is heavly dependent on a single model fit index (BIC). In practive this method is available only with proprietary software.
cmdscale. Inputs are Eucledean distances for covariances, correlations, and parameters, and raw increments in fit indices for the increment options.
kmeans, it is added for convienience only in order to get more dimensions to the two dimensional plot.
This program is free software distributed under the terms of the GNU General Public License v.3
Rudnev M. (2018) Measurement Invariance Explorer. Retrieved from: https://github.com/MaksimRudnev/MIE