# How to handle variables with low correlation but high loadings in factor analysis

I am doing factor analysis to check the factorial validity of a 14-items scale with four subscales. Two items have low (less than 0.3) correlations with other items in the subscale to which they belong. However, they load considerably (greater than 0.32) on the factor (latent variable) to which they correspond. Under such condition, should the two variables be dropped from the scale on grounds of low correlations or be retained within the scale on grounds of the acceptable loadings?

Update: After going further through the analysis--removing one item on substantive ground and another item due to low loading (in the range of .2)--I found the correlation matrix depicted below.

The highlighted correlations indicate the correlations of items with other items in the same subscale. However, some items also correlate with items in other subscales considerably (>0.3). Yet, the four factors themselves are inter-correlated which I think is the reason why items also show non-negligible correlations with other items of a different factor. Below is the inter-correlation of factors.

Given these results, how should I go about interpreting my subscales? May I be justified to consider the sub-scales as being suited to measure the underlying constructs/factors of interest?

Do these two correlate highly with each other? If you add another factor to the solution, do they form a separate factor?

If so, then they may be another factor (but with only two variables that relate to it) and this factor may relate to the factor you discuss in your post.

Try different numbers of factors and try oblique rotations as well as orthogonal ones in order to further explore what is going on.

In the end, though, I think the determination should be made based on which solution makes substantive sense.

• The correlation between the two variables is weak (0.156). When two other factors are added to the solution, the two items load on two different factors (with loadings of 0.73 and 0.65). No considerable difference with orthogonal and oblique rotations. However, at the outset the two items were designed to be part of the four-factor solution. In the four-factor solution, they load onto the factors to which they belong with loadings of 0.57 and 0.89. Aug 28, 2014 at 13:23
• To me that sounds like your original solution was the right one. Aug 29, 2014 at 10:44
• In your opinion, does it seem reasonable (at least tentatively) to retain the two items regardless of their low correlation coefficients? Aug 29, 2014 at 14:27
• Now I have included updates to my initial post. Based on the updates, what would you suggest? Sep 9, 2014 at 12:25
• That solution looks reasonable to me. Sep 9, 2014 at 18:33