quantV {qualV}

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. 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")