pcdfs
(Package: pAnalysis) :
R2 values with corresponding probability density and cumulative density functions.
This function builds a data frame of all possible R2 values over its range of 0 to 1, with corresponding values of probability (pdf) and cumulative probability (cdf) for a given number of degrees of freedom. R2 is divided uniformly over its range into bins whose width is determined by the number of decimal places chosen (default=3). The number of samples is determined by order (10^order). Values of the cumulative density function (cdf) are used to calculate the baseline noise level, R2p.
● Data Source:
CranContrib
● Keywords: cdf, cumulative probability, noise distribution, pcdfs, pdf, probability
● Alias: pcdfs
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plotR2p
(Package: pAnalysis) :
Plot several noise baselines (R2p)
Plots R2 values at several baseline noise levels (pct). Measured R2 values above the baseline can be distinguished from noise while those R2 values below the baseline can not.
R2p
(Package: pAnalysis) :
Calculation of baseline noise level (R2p) at a single value of degrees of freedom (dof)
This function determines the value of R2, called R2p here, below which a certain percentile level of noise is present. Any models with R2 values below this baseline R2 value are therefore indistingushable from noise.
R-sqaured (R2), as a function of n datapoints of x and y, is a standard goodness-of-fit measure that has the unfortunate behavior of becoming more sensitive to noise as the number of degrees of freedom (n) decreases. The mean of R2 measuring just noise is 1/(n-1). However, the distributions of R2 values measuring just noise varies greatly for each n: they are neither uniform nor consistent in shape, especially at low n. At the next-to-lowest value of n, where n=3, the mean R2 value is 0.5 but the distribution of possible R2 values is symmetric about that point - rising from the mean (0.5) toward the extremes of both 0 and 1 - and every other possible value of R2 is more likely than the mean. When n=3, R2 values of 0 or 1 (the extremes) are more than 30 times more likely than the value of 0.5 (P(R2>0.999 or R2<0.001)=0.020; P(R2>0.499 and R2<0.501)=0.00069). For n=4 and higher, the distributions of R2 are not symmetric about the mean and high values of R2 are not as likely as they are at n=3 but there are still significant probabilities of achieving high R2 values. As n increases, the probability of obtaining high R2 values with just noise decreases sharply. We invite the reader to run the plotpdf() function for 3, 4 and 5 degrees of freedom. See plotpdf() examples for syntax.
R2pTable
(Package: pAnalysis) :
Creates a table R2p values for combinations of degrees of freedom and percentiles
R2pTable builds a table (a data frame) of baseline noise levels (R2p values) for each combination of degree of freedom and percentile. A matrix is created with the number of rows equal to the length of doflist and the number of columns equal to the length of pctlist. The elements of this matrix are the results of calls to the R2p function with arguments of each of combination of the elements of doflist and pctlist. Additional arguments desired for R2p can be passed along through these calls. The resulting matrix is converted to a data frame. Although it takes a few seconds longer, we recommend using order=5 for sufficient accuracy. (order=4 is the default to meet the CRAN recommendation that default functions should take no more than a few seconds.)
● Data Source:
CranContrib
● Keywords: degrees of freedom, dof, percentile
● Alias: R2pTable
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plotR2k
(Package: pAnalysis) :
Plot R2k for a single measured R2 and a single noise percentile across a range of degrees of freedom
This function plots R2k values presuming that the same R2 value was obtained using varying numbers of degrees of freedom. Provide the R2 value of interest and the desired noise baseline level (pct).
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