1. Model Assessment
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.
2. Standardized Loadings
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 manifest 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 dot 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 dot 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.
3. Fit Indices
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 RMSEA 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 .90, which indicates that our model and the data match nearly identically. For badness of fit measures, we want values very close to zero, usually below .10, 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 Kenny's website on measuring model fit.
4. Fit Indices
To see the most common fit indices, use fit dot measures equals 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 .5 to .7 and the RMSEA and SRMR values are over .10, indicating a poor fitting model. Models with acceptable coefficients may still fit poorly, indicating that both components are key to understanding models.
5. Let's practice!
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.