Learn how to read structural equation model results in R using summary(). Loadings above 0.3 show strong relationships between variables and latent constructs. Model fit indices like CFI and TLI should be above 0.9, while RMSEA and SRMR should stay below 0.1. A model can have good loadings but poor overall fit.
Chapters
Now that we've run our first model, let's discuss how to interpret our model findings and use options within the summary function to get more information about our model. To examine our model further, we will focus on two key parts. First is the loadings which indicate the strength of the relationship between the manifest and latent variables like a regression coefficient or a factor loading. In the parameter estimates section we can examine our loadings of the manifest variables on the latent variable. The estimate column shows us the coefficients in the scale of the data, but it's often difficult to know what to think of the scale marker variable. Therefore, the completely standardized solution is often used which uses z scores of both the latent and manifested variables for easier interpretation. To get the standardized solution, you can include standardized equals true as an argument in the summary function. The completely standardized solution is here on the right. Under STD all you should look for values close to 1 as values close to 1 indicate a strong relationship to the latent variable. In this example we see good values of our manifest variables in relation to the latent where x2 has the lowest loading. Std LV is the solution if you had set the scaling to the latent variable. These loadings may help identify parts of your model that do not behave as expected, such as a bad item on the scale. While there is no one rule, people often use a criterion of 0.3 as an acceptable loading. After the loadings we can explore the model fit which indicates how well the model and the data match. We can use goodness of fit statistics like the TLI or cfi or badness of fit statistics like the rem C or SRMR to help determine if our model is good. For goodness of fit measures. We want these values to be close to 1 and above 0.9, which indicates that our model and the data match nearly identically. For badness of fit measures, we want the values to be very close to zero, usually below 0.1 as they indicate a mismatch of the model and the data. For more information on goodness and badness of fit measures, check out David A. Kinney's website on measuring model fit to see the most common fit indices. Use fit measures true in the summary function. These values will appear after our overall model summary and before the loadings output. You will see more output when running this in RStudio, but the relevant sections are shown here. In this example we find that the values on CFI and TLI range from 0.5 to 0.7 and the REM, C and SRMR values are over 0.1, indicating a poor fitting model. Models with acceptable coefficients may still fit poorly, indicating that both components are key to understanding models. Let's continue with the exercises and examine more information about our models from the last exercise to see how well these models fit our data.
