rallel () is a function of the psych library that helps us to evaluate which is the most optimal solution in terms of number of factors, considering parsimony -where having fewer factors is better- and fitting with the data -where having more factors is better.
The graph gives more information than we really need, what matters is the FA line (factor analysis). The first factor manages to explain more variance on the scale than the second factor, which in turn manages to explain more variance on the scale than the third factor. Adding a third factor is certainly impractical, since two factors can explain most of the variance.
With this information, we can do an exploratory factor analysis with two factors, occupying the fa () function of the psych library.
The information provided in the first table tells us how much each item is related to each of the factors. This can be seen graphically with
Items 1 and 2 are strongly related to the first factor (MR1), and items 4 and 5 are strongly related to the second factor (MR2). Item 3 is more related to the first factor (.41) than to the second (-.09).
What does this mean? It means that the scale measures two things, which are in fact perfectly understandable when reading the items:
When it’s time to sleep, I want to watch TV, read or do something else (insom4)
I tend to have messy sleep schedules, nap, or spend excessive time in bed (insom5)
Obviously these two constructs are related, in fact they have a correlation of .39 according to the factor analysis. But they are not the same.
The alpha is .78. Item 3 could be removed, as we did before, but for now we are going to keep it.
What happens when we do a factor analysis for the anxiety items in the evaluation period? According to the scree plot,
Items 3, 4 and 5 load on one factor (MR2), and items 1 and 2 load on another (MR1). The MR2 factor can be more properly called anxiety in the evaluation period (irritable, pain and inability to disconnect), the second factor is the insomnia items during this period. When reviewing the reliability that these scales would have,
We see that it is usable, but it is certainly not good. What to do in this case? The answer is not in statistical analysis, but rather in a conceptual analysis and research objectives.