1. Modification Indices
In this section, you will learn how to assess modification indices to improve your model.
2. Updating Poor Models
Let's look at the fit indices for our two-factor model of intelligence. In our goodness of fit indices, CFI and TLI, we see that they are below the desired criterion of 0.90. The badness of fit indices also indicate a poor fitting model, where the RMSEA is higher than our criterion of 0.10, and the SRMR is OK.
3. Updating Poor Models (2)
What can we do to improve our model? First, we should examine the loadings and variances to determine if any of the manifest variables are not related to our latent variables or they have improbable error values.
By looking at the standardized solution, it appears that each manifest variable is related to the latent variable, as each loading is over 0.30.
4. Updating Poor Models (3)
By looking at the variances, we see values that are appropriate for the scale of the data. We do not expect these values to match exactly match the variance of the real data, but you can use the var() function to get an idea of the expected range of the variance. Generally, when something goes wrong with a model, the estimated variance will be very large in comparison to the data.
5. Modification Indices
A second step is to explore modification indices. Modification indices indicate the improvement on a model if the suggested estimate is added to the model. You can view these values by using the modificationindices() function with the model fit as the main argument. In addition, you can use the sort equals TRUE argument to show you the biggest changes for a model on top, which is useful for complex models with lots of possible changes.
LHS and RHS stand for left and right hand side, respectively, of the model specification code. OP stands for operator, which we explored in the last section as correlation with double tildes or latent predictions with equals tilde. MI stands for modification index, which is a chi-square value. This value represents the amount the chi-square index will decrease when added to the model. This chi-square value is used to calculate the fit indices. The last four columns indicate the expected parameter change or the estimation of that parameter if added to the model.
We can use this table to determine if we want to add any estimates to our model. These parameters should be added one at a time to a model and be selected for their theoretical implications. For example, it may be useful to say that the visual latent variable is predictive of X9, as this variable measures discrimination of capital letters. X7 and X8 are speeded addition and counting, and we could expect those two variables to be correlated as well.
6. Updating the Model
To update the model, you would add the path as a new line in the model specification, and rerun the cfa() and summary() functions. The fit indices for this model are drastically improved in comparison to our previous model. In the next section, we will cover how to directly compare two models.
7. Let's practice!
Let's try estimating modification indices on your models and updating the model specification based on that output.