R: Quantitative Validation Methods

quantV {qualV} | R Documentation

## 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 1/n
`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. URL http://dx.doi.org/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")

[Package qualV version 0.3-3 Index]