Let me recommend you first to read [this Q/A][1]. It is about rotations and can hint towards or partly answer your question.

A more specific answer from me about interpretation might be as follows. Theoretically, factor of Factor analysis is a univariate latent feature, or essence. It is not the same thing as a set or cluster of phenomena. Term "construct" in psychometry is generic and could be conceptualized as factor (essence) or cluster (prototype) or something else. Since factor is univariate essence it should be interpreted as the (relatively simple) meaning lying on (or "behind") the *intersection* of the meanings/contents of the variables loaded by the factor.

With oblique rotation, factors are not orthogonal; still, we usually prefer to interpret a factor as clean entity from the other factors. That is, ideally, factor X *label* would dissociate from a correlated factor Y label, to stress individuality of both factors, while assuming that "in outer reality" they correlate. Correlatedness thus gets to be an isolated characteristic of entities from the labels of the entities.

If it is this the strategy typically preferred then **pattern** matrix appears to be the main tool for interpretation. Coefficients of pattern matrix are the *unique* loads or investments of the given factor into variables. Because it is regression coefficients. [I insist that it is better to say "factor loads variable" than "variable loads factor".] **Structure** matrix contains (zero-order) correlations between factors and variables. The more two factors X and Y correlate with each other the greater *can* be the discrepancy between the pattern loadings and the structure loadings on some variable V. While V ought to correlate higher and higher with both factors, the regression coefficients can rise both *or* only one of the two. The latter case will mean that it is that part of X which is different from Y what loads V so much; and thence the V-X pattern coefficient is what is highly valuable in interpretation of X.

Weak side of pattern matrix is that it is less stable from sample to sample (as usually regression coefficients in comparison to correlation coefficients). Relying on pattern matrix in interpretation requires well planned study with sufficient sample size. For pilot study and tentative interpretation structure matrix might be better choice.

Structure matrix seems to me potentially better than pattern matrix in back interpretation of *variables* by factors, if such a task arises. And it can rise when we validate items in questionnaire construction, - that is, decide which variables to select and which to drop in the scale being created. Just remember that in psychometry common validity coefficient is correlation (and not regression) coefficient between construct/criterion and item. Usually I include an item in a scale this way: (1) look at maximal correlation (structure matrix) in the item's row; (2) if the value is above a threshold (say, .40), select the item *if* its situation in pattern matrix confirms the decision (i.e. the item is loaded by the factor - and desirably only by this one - which scale we're constructing). Also [factor scores coefficient matrix][2] is what is useful in addition to pattern and structure loadings in the job of selection items for a factor construct.

If you do not perceive a construct as univariate trait then using classic factor analysis would be questioned. Factor is thin and sleek, it is not like pangolin or armful of whatever. Variable loaded by it is its mask: factor in it shows through what appears to be completely *not* that factor in it.

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**Some geometry**. Loadings are coordinates of variables (as their vector endpoints) in the factor space. We use to encounter those on "loading plots" and "biplots". See [formulas][3].

[![enter image description here][4]][4]

Left. Without rotation or with orthogonal rotation, axes (factors) are geometrically orthogonal (as well as statistically uncorrelated) to each other. The only coordinates possible are square like what are shown. That is what is called "factor loading matrix" values.

Right. After oblique rotation factors are no longer orthogonal (and statistically they are correlated). Here two types of coordinates can be drawn: perpendicular (and that are structure values, correlations) and skew (or, to coin a word, "alloparallel": and that are pattern values, regression weights).

Of course, it is possible to plot pattern or structure coordinates while forcing the axes to be geometrically orthogonal on the plot - it is what when you take the table of the loadings (pattern or structure) and give to your software to build a standard scatterplot of those, - but then the angle between the variable vectors will appear widened. And so it will be a distorted loading plot, since the aforesaid original angle was the correlation coefficient between the variables.


  [1]: http://stats.stackexchange.com/q/151653/3277
  [2]: http://stats.stackexchange.com/q/126885/3277
  [3]: http://stats.stackexchange.com/q/52752/3277
  [4]: https://i.sstatic.net/cdO4K.png