Principal components refer to a statistical method used to simplify complex data by identifying and focusing on the essential patterns or variables. It involves summarizing a large set of data points into fewer, more manageable components without losing crucial information. These components represent the major sources of variation in the data, making them useful for understanding and analyzing the data more effectively.
Full definition
Third, it used the exploratory technique of
principal components analysis combined with a obscure weighting formula, producing hockey sticks from random data.
Maybe we need to
use principal component analysis to tease it out, but we do need to simplify the broad parts of the strategy for testing.
Principal component series can include negative weights, which result in showing a contrast between different series — picture a series with positive weights for finance stocks and negative weights for tech stocks.
We made the narrower point that, using correct
principal components calculations on their data, they could not conclude that the 1990s were the warmest decade and 1998 the warmest year.
The basic idea behind
principal component regression is to replace the predictors (i.e., individual proxies) with a smaller number of objectively determined variables that are linear combinations of the original proxies.
In general, one should judge the set of
principal components taken together as a group because they are used together to form a reconstruction.
We used a variant of
principal components analysis to generate marital quality profiles, based on one's endorsement of positive and negative marital characteristics.
In principal components discussions, the weights have forbidding names like eigenvectors or empirical orthogonal functions, but, at the end of the day, these are just weights.
These SST and SLP patterns around the North America also appear in the regression maps derived from the leading
principal components of total water storage (Fig. 6e, f).
, Malcolm Baker, Johnathan Wang and Jeffrey Wurgler investigate returns for different types of stocks in the context of broad investor sentiment index derived
from principal component analysis of six indicators: trading volume as measured by NYSE turnover; the dividend premium; the closed - end fund discount; the number of, and first - day returns on, Initial Public Offerings; and the equity share in new issues.
They also compare DR - CAPM to optimal models based
on principal component analysis within and across asset classes.
A pool of 25 items was chosen to capture the two dimensions (Anxiety and Avoidance), which were obtained
through principal components analysis in a sample of 477 adults.
It failed to mention an extremely important inaccuracy in MBH98 description of methods (the significance of which we had discussed at length in our submission): their failure to describe the subtraction of the 1902 - 1980 mean prior to tree
ring principal components calculation.
To tease out whether these correlations were due to a small sample size or chance, the researchers used a more sophisticated statistical technique
called principal components analysis, testing the actual results against 10,000 randomly generated simulations.
The factor structures of the GHQ - 12 and GHQ - 28 extracted
by principal component analysis were compared in participating centres.
Linear metrics (cerebral lobe dimensions and sulcal lengths) and
principal component scores of cortical shape variation in 206 chimpanzees and 218 human brains.
MAnnian principal components on the North American tree ring network; then Partial Least Squares regression of NH temperature against the PC1 and other proxies; then re-scaling done a smidge differently.
In particular, their paper indicates that they
did principal components on the correlation matrix of short - centered data, whereas MBH98 did singular value decomposition (SVD) on the short - centered data matrix itself.
Mann obviously objected at the time (and subsequently) to reconstructions without bristlecones, with the objections couched in language of
retained principal components — that sort of thing.
2) I claimed an argument wasn't new, «the hockey stick was an artifact of the conventions used in
applying principal component analysis (PCA).»
I think that many non-academic people, who would be put off by technical questions like the validity of
principal components algorithms, may very well be interested in what I have learned about these processes as they apply to modern climate studies.