I used PCA method to consider 6 values as one. Considering that all the values were positive, PCA gave a score with a negative sign (for example -1.49), what this mean ?
** I'd read in a forum that negative loading just means that the variable in question correlates negatively with the axis. But still I can not undrestand the meaning.
PCA is a statistical technique used to transfer a data space of high dimension into a
feature space of lower dimension having the most significant features. PCA rigidly rotates the axes of the p-dimension space to new position (principle axes) such that principle axis 1 has the highest variance, axis 2 has the next highest
variance and so on.
Many of the feature have high correlation with
each other. So PCA is used to transfer raw feature to variables
that are not correlated to each other when the original
data are feature, called a new principal
component variables domain metrics.
Interpretation of the principal components is based on finding which variables are most strongly correlated with each component, i.e., which of these numbers are large in magnitude, the farthest from zero in either positive or negative direction.
Elahe, we need more information: How many variables are in your analysis, how large is the sample size, which rotation method did you use and do you observe such a large and negative value also in the unrotated solution? How many principal components were selected using which method?
Why did you choose PCA instead of exploratory factor analysis?
Regards, Karin
PCA is an orthogonal transformation of a set of correlated variables into one or more hypothetical dimensions. The factor loading could be positive measuring the positive side of the dimension or negative measuring the negative side of the dimension
Nobody seems to have noticed the large value of the component loading. If the components were orthogonally rotated, then the sum of the squared component loadings should be 1.0. Therefore, a loading larger than one, either positive or negative, seems to point to an estimation problem. That is why I asked for more information.
Regards, Karin
Dear Karin
For illustrating ICT development, there are six different indicators. For example with counting "individuals who have access o internet ", one indicator is been measured. therefore, all the values here are positive values, which normally is the counted number. I have six of this indicators, for each country.
What I want to do is to consider these six indicators as one, so that I can say for example ICT generally changed during these years like this or that.
By using PCA to turn these six indicators into one, the results from 2007 to 2014 are like :
2007: -1.49
2008: -0.93
2009: -0.58
2010:-0.18
2011: 0.12
2012: 0.61
2013: 1.70
2014: 1.39
What I an not undrestand is that why there is a negative sign involved.
If I understand you correctly, you performed a PCA without rotation and received the values listed above. Is this correct?
Then, the results show that this component contrasts the first four indicators against the last four indicators. Large (either positive or negative) loadings indicate that a variable has a strong effect on that principal component. Subjects (or objects) scoring high on the variables with positive loadings will tend to have higher component scores on this particular component, while subjects scoring low on these variables tend to have lower component scores. Subjects scoring high on the variables with negative loadings will tend to have lower component scores. The trouble is, that components to not need to have a meaning, they are just the sum of the indicators loading onto this component.
The component loadings do not seem to be standardized, therefore higher values than one occur in your results. If the metric is not important, you may wish to standardize your variables.
Does this help?
Regards, Karin
Check Q residuals and T2 statistic,to be shure that sample with negative score is vell describes by the PCA model. Very often meancentering is made before PCA, if so negative scores is normal.
dear Karin, your answer definitely helped. Thank you so much for your help.
Thanks to other dear friends who answered my question.
I have collected data on 9 yield related traits in tomato. While doing PCA using correlation matrix, I am getting very small contribution (28%) for PC1 followed by 17.5% for PC2. The PCA using covariance matrix is giving very high contribution (83.2%) for PC1. Which one should be considered for interpretation?
@ Hem Raj Bhandari It is generally a good idea to use correlated matrix PCA when you have variables with different units. If all your original variables are the same units then you can use covariance matrix.
Dear Karin Schermelleh-Engel I have similar problem to the issues raised by Elahe Meydani I used PCA to construct an index using 4variables from 1980 to 2015 for more than 100 countries; the 4 variables were normalised before running the PCA in Stata. The Principal component loadings I got from Stata are as follow:
Components| Comp1 Comp2 Comp3 Comp4
Variable 1| .4446 .6024 .5618 .3518
Variable 2| .5058 .4407 -.5987 -.4377
Variable 3| .5086 -.4913 .4604 -.5366
Variable 4| .5365 -.4489 -.3376 .6298
I adopted the first component which has no negative eigenvector.
However, when I used the predict command (predict PCA4b_Index1, PCA4b_Index2, PCA4b_Index3, and PCA4b_Index4) to get the index, many of the observations particularly for developing countries were negative up to year 2000 and 2006. Sub-Saharan African countries (region) also improve but it was negative up to 2015.
This seems logical in real sense but it is I cannot explain based on how PCA works; the index (observations) is supposed to be sum of the 4 variables based on their weight in Component 1 and outcome logically should therefore not have been negative?
I would appreciate it if you can help with the explanation of why some of my observations are negative?
Thank you
Did you rotate your components? A rotation may help to interpret the results.
Kind regards, Karin
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