Investigating model fit
1. Model fit
Now that you can run multidimensional EFAs, it's time to learn how to interpret various model fit statistics.2. Absolute vs. relative model fit
When thinking about model fit, there are two different types of fit statistics you can consider. Absolute fit statistics are useful for making a judgment about whether or not a model fits adequately. These fit statistics have set ranges and meanings, and they have established cutoff values that are commonly used to determine whether a model has good fit. Examples include the chi-square test, TLI, and RMSEA. Relative fit statistics don't have set ranges or meanings, and they are only useful when comparing nested models estimated from the same dataset. We'll focus on the BIC in this course.3. Absolute fit statistics
When it comes down to it, all of the absolute fit statistics attempt to quantify the discrepancy between the observed data and the data that would be expected given the model. These three common fit statistics represent this difference on different scales and are calculated differently. Ideally, the chi-square test would have a non-significant result, meaning the observed and expected data aren't significantly different. However, since the value of this test is affected by sample size, this rarely occurs for large datasets. Both TLI and RMSEA range from 0 to 1. The TLI, or Tucker-Lewis Index, is also known as the penalized non-normal fit index, meaning that more complex models are penalized for adding additional parameters. This can be roughly understood as how well the observed data match the expected data. Larger TLI values are better: a model can be considered to have good fit if the value is greater than 0-point-90. RMSEA, or the Root Mean Square Error of Approximation, quantifies the differences between the observed and expected data. RMSEA values are interpreted in the opposite direction as TLI values: smaller values are preferred. Values less than 0-point-05 can be said to indicate good fit.4. Finding the fit statistics
All the fit statistics discussed here are displayed in the model output. As you can see, when we run the multidimensional EFA on the bfi_EFA dataset with six factors, the chi-square value of 618-point-43 is significantly different from zero. This isn't ideal, but it's unsurprising given the sample size. You can also see the TLI value is point-916, which is above the cutoff, and the RMSEA is 0-point-045, which is below the cutoff. These are good values that indicate that the model adequately fits the data. You'll notice these values also contain the BIC value for this model, which is -576-point-87. However, since relative fit statistics don't have any value on their own, this doesn't mean much to us yet.5. Relative model fit
To use relative fit statistics, we need two different models to compare. If you remember, the theory behind the BFI dataset recommended five factors, while the eigenvalues recommended six factors. Let's set up those two models by changing up the nfactors argument. When looking at BICs, the lowest BIC is always preferred. You can see that for these two models, the BIC is lower for the bfi_eigen model, which was estimated with six factors.6. In sum: evaluating fit
To sum up, when you are in the process of model development, the first step is to make sure your model or models have adequate fit according to the absolute fit statistics. If you are comparing multiple models that all have good fit, you can use relative fit statistics to make an empirical determination about which model is mathematically preferred.7. Let's practice!
Now you know how to evaluate models' absolute and relative fit statistics! Let's apply these principles to your data.Create Your Free Account
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