quantV: Quantitative Validation Methods

In qualV: Qualitative Validation Methods

Quantitative Validation Methods

Description

Different methods for calculating the difference between two vectors.

Usage

generalME(o, p,
          ignore   = c("raw", "centered", "scaled", "ordered"),
          geometry = c("real", "logarithmic", "geometric", "ordinal"),
          measure  = c("mad", "var", "sd"),
          type     = c("dissimilarity", "normalized", "similarity",
                       "reference", "formula", "name", "function"),
                       method = NULL)
   MAE(o, p, type = "dissimilarity")
  MAPE(o, p, type = "dissimilarity")
   MSE(o, p, type = "dissimilarity")

  RMSE(o, p, type = "dissimilarity")
  CMAE(o, p, type = "dissimilarity")
  CMSE(o, p, type = "dissimilarity")
 RCMSE(o, p, type = "dissimilarity")
  SMAE(o, p, type = "dissimilarity")
  SMSE(o, p, type = "dissimilarity")
 RSMSE(o, p, type = "dissimilarity")
  MALE(o, p, type = "dissimilarity")
  MAGE(o, p, type = "dissimilarity")
 RMSLE(o, p, type = "dissimilarity")
 RMSGE(o, p, type = "dissimilarity")

 SMALE(o, p, type = "dissimilarity")
 SMAGE(o, p, type = "dissimilarity")
 SMSLE(o, p, type = "dissimilarity")

RSMSLE(o, p, type = "dissimilarity")
RSMSGE(o, p, type = "dissimilarity")

  MAOE(o, p, type = "dissimilarity")
  MSOE(o, p, type = "dissimilarity")
 RMSOE(o, p, type = "dissimilarity")

Arguments

o	vector of observed values
p	vector of corresponding predicted values
type	one of "dissimilarity", "normalized", "similarity", "reference", "formula", for the dissimilarity measure, the normalized dissimilarity measure, the similarity measure, or the formula for the normalized measure. For generalME it is additionally possible to specify "function" for getting the corresponding function and "name" for getting the name of the function.
ignore	specifies which aspects should be ignored: "raw" compares original values, "centered" removes differences in mean, "scaled" ignores scaling, "ordered" indicates the use of the ordinal geometry only.
geometry	indicating the geometry to be used for the data and the output, "real" corresponds to arithmetic differences and means, "logarithmic" to handling relative data on a logarithmic scale, "geometric" to geometric means and differences and "ordinal" to a pure ordinal treatment.
measure	indicates how distances should be measured: as mean absolute distances like in MAD, as squared distances like in a variance, or as the root of mean squared distances like in sd.
method	optionally the function to be used can specified directly as a function or as a string.

Details

These comparison criteria are designed for a semiquantitative comparison of observed values o with predicted values p to validate the performance of the prediction.
The general naming convention follows the grammar scheme
[R][C|S]M[S|A][L|G|O]E
corresponding to [Root] [Centered | Scaled] Mean [Squared | Absolute]
[Logarithmic, Geometric, Ordinal] Error

Root

is used together with squared errors to indicate, that a root is applied to the mean.

Centered

indicates that an additive constant is allowed.

Scaled

indicates that a scaling of the predictive sequence is allowed. Scaled implies centered for real scale.

Squared

indicates that squared error is used.

Absolute

indicates that absolute error is used.

Logarithmic

indicates that the error is calculated based on the logarithms of the values. This is useful for data on a relative scale.

Geometric

indicates that the result is to be understood as a factor, similar to a geometric mean.

Ordinal

indicates that only the order of the observations is taken into account by analyzing the data by ranks scaled to the interval [0, 1].

The mean errors for squared error measures are based on the number of degrees of freedom of the residuals.

Value

generalME	selects the best deviance measure according to the description given in the parameters. It has the two additional possibilities of name and function in the type parameter.
MAE	mean absolute error \frac1n
MAPE	mean absolute percentage error
MSE	mean squared error
RMSE	root mean squared error
CMAE	centered mean absolute error
CMSE	centered mean squared error
RCMSE	root centered mean squared error
SMAE	scaled mean absolute error
SMSE	scaled mean squared error
RSMSE	root scaled mean squared error
MALE	mean absolute logarithmic error
MAGE	mean absolute geometric error
MSLE	mean squared logarithmic error
MSGE	mean squared geometric error
RMSLE	root mean squared logarithmic error
SMALE	scaled mean absolute logarithmic error
SMAGE	scaled mean absolute relative error
SMSLE	scaled mean squared logarithmic error
RSMSLE	root scaled mean squared logarithmic error
RSMSGE	root scaled mean squared geometric error
MAOE	mean absolute ordinal error
MSOE	mean squared ordinal error
RMSOE	root mean squared ordinal error

References

Mayer, D. G. and Butler, D. G. (1993) Statistical Validation. Ecological Modelling, 68, 21-32.

Jachner, S., van den Boogaart, K.G. and Petzoldt, T. (2007) Statistical methods for the qualitative assessment of dynamic models with time delay (R package qualV), Journal of Statistical Software, 22(8), 1–30. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v022.i08")}.

See Also

EF, GRI, compareME

Examples

data(phyto)
obsb <- na.omit(obs[match(sim$t, obs$t), ])
simb <- sim[na.omit(match(obs$t, sim$t)), ]
o <- obsb$y
p <- simb$y

generalME(o, p, ignore = "raw", geometry = "real")

   MAE(o, p)
  MAPE(o, p)
   MSE(o, p)
  RMSE(o, p)
  CMAE(o, p)
  CMSE(o, p)
 RCMSE(o, p)
  SMAE(o, p)
  SMSE(o, p)
 RSMSE(o, p)
  MALE(o, p)
  MAGE(o, p)
 RMSLE(o, p)
 RMSGE(o, p)

 SMALE(o, p)
 SMAGE(o, p)
 SMSLE(o, p)

RSMSLE(o, p)
RSMSGE(o, p)

  MAOE(o, p)
  MSOE(o, p)
 RMSOE(o, p)
   MAE(o, p)
  MAPE(o, p)


   MSE(o, p, type = "s")
  RMSE(o, p, type = "s")
  CMAE(o, p, type = "s")
  CMSE(o, p, type = "s")
 RCMSE(o, p, type = "s")
  SMAE(o, p, type = "s")
  SMSE(o, p, type = "s")
 RSMSE(o, p, type = "s")
  MALE(o, p, type = "s")
  MAGE(o, p, type = "s")
 RMSLE(o, p, type = "s")
 RMSGE(o, p, type = "s")

 SMALE(o, p, type = "s")
 SMAGE(o, p, type = "s")
 SMSLE(o, p, type = "s")

RSMSLE(o, p, type = "s")
RSMSGE(o, p, type = "s")

  MAOE(o, p, type = "s")
  MSOE(o, p, type = "s")
 RMSOE(o, p, type = "s")

qualV documentation built on July 9, 2023, 6:09 p.m.