Hi, PCA is used for reducing/summarizing many input variables to a few PCs. The factor loading is simply the correlation of the specific variable on the respective PC. It therefore can be positive or negative. The higher the number, the higher the correlation. With the information of factor loadings, you can interpret the "key variable" behind the PC.

31 input variable are (too)  many...there exist a rule of thumb: the sampling number number should be at least 3 times more than the number of input variables. In you case you would need about 95 sampling events to justify 31 input vars.

All the best

Michael

Hi Michael,

Thank you for your answer. Are you suggesting that I leave the item and include it in the same factor with other items that loaded positively?

My sample size is over 300. Thank you

As far as I know, you should delete items with negative factor loadings. This can happen because the item is wrong (for example, people have not understood the question) or the item is reversed while others in the same construct are not.

In any case, based on the recommendations of the SmarPLS manual (Hair et al., 2016), you should always delete item with factor loadings < 0.40.

Hair Jr, J. F., Hult, G. T. M., Ringle, C., & Sarstedt, M. (2016). A primer on partial least squares structural equation modeling (PLS-SEM). Sage Publications.

ISO 690

Regards

A negative loading, as such, is not a problem.  Often several items thought to form a scale (a factor or dimension) are intentionally worded in opposite directions, to minimize the impact of acquiescent response-set.  The "positively-valenced" items, like "I consider myself a happy person" will necessarily correlate negatively with the "reverse-valenced" items, like "I often feel sad."  In a PCA of these (and other) items, you would expect both of them to load highly on a single factor of "Subjective Well-Being" but they should load in opposite directions -- one positive, the other negative.

 If that kind of interpretation makes sense for the variables in your analysis, then the negative loading is a good thing, not a concern.  If it doesn't make sense, then check the coding of the variable with a negative loading.  Was it scored (say) from 1 to 5, where 1 means "strongly agree" whereas the other items were scored from 5 to 1, where 1 means "strongly disagree."  In that case, again, the negative loading is not a problem; it just alerts you that you need to interpret the variable that was scored backwards in the opposite sense from the others.  (or in that case, you can treat the negative loading as positive, which is what it would be if to 1 to 5 scoring of that variable were reversed and the whole analysis re-run.)  

If none of these re-interpretations of the negative loading makes sense substantively, then that variable (perhaps along with some of the others) is not measuring what you intended, and/or that factor does not mean what you think it means, and/or that factor is just picking up measurement error or sampling error.  That would imply you should delete that variable from the analysis, or drop the whole factor from the solution.

Thanks all.

PCA just identify the groups. forget about positive and negative but just consider those values which is 0.5 or above.

I will repost here my answer to this question addressed by another user, since the question is recurrent. Yes, the component values in PCA / FA (eigenvectors, 'loadings') may have both negative and positive values, in |0,1| interval. While the main indication for a variable to fit a component is the value of the corresponding loading (usually look for loadings > 0.3, but for other indications as well), for the sign keep in mind that the representation is of a linear vector, with zero as origin, pointing in one sense (+ or -). The loadings with the same sign contribute within the component in the same way, while those with opposite sign still contribute to the component but in an opposed way. I.e. think about a component which captures athletes performance in short distance running, with three significant eigenvectors: 1. number of hours of training/week (hrs) 2. amount of energy available to burn/hour (kJ/hr) 3. last race time recorded (seconds/100 m). Our intuition is that all this three variables may be related to "race performance", but while the 1st and the 2nd variable importance increases with larger values - the more training hours and energy available, the better -, for the 3rd variable the lower values are important, since performance in race is related to lower times /distance. C.

When the value is positive, then a higher score is correlated with a higher component score, whereas when the value is negative, then a higher component score implies a lower component score.