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When to use the correlation matrix in PCA?
Using the correlation matrix is equivalent to standardizing each of the variables (to mean 0 and standard deviation 1). In general, PCA with and without standardizing will give different results. Especially when the scales are different. As an example, take a look at this R heptathlon data set.
How does collinearity affect the SDM model parameters?
One of those possible pitfalls − collinearity among environmental predictors − is assumed as an important source of model uncertainty, although it has not been subjected to a detailed evaluation in recent SDM studies. It is expected that collinearity will increase uncertainty in model parameters and decrease statistical power.
How are PCA-derived variables used to control collinearity?
We concluded that the use of PCA-derived variables is advised both to control the negative effects of collinearity and as a more objective solution for the problem of variable selection in studies dealing with large number of species with heterogeneous responses to environmental variables.
Which is more informative PCA or covariance?
PCA on correlation is much more informative and reveals some structure in the data and relationships between variables (but note that the explained variances drop to 64 % and 71 % ). Notice also that the outlying individuals (in this data set) are outliers regardless of whether the covariance or correlation matrix is used.
What do you mean by normalization before PCA?
By “normalize” I mean either standardization, linear scaling or some other techniques. You should normalize the data before doing PCA. For example, consider the following situation. I create a data set X with a known correlation matrix C:
How are the variances equal to one in PCA?
In the normalized PCA, the variances are equal to one; thus the squared cosines will be squared of the coordinates of the variables: In general, we have that: The contribution of each variable to the inertia of an axis is the part of the inertia accounted for the variable.