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These functions are appropriate for cases where the model outcome is a numeric. The ratio of performance to deviation (rpd()) and the ratio of performance to inter-quartile (rpiq()) are both measures of consistency/correlation between observed and predicted values (and not of accuracy).


rpd(data, ...)

# S3 method for data.frame
rpd(data, truth, estimate, na_rm = TRUE, case_weights = NULL, ...)

rpd_vec(truth, estimate, na_rm = TRUE, case_weights = NULL, ...)



A data.frame containing the columns specified by the truth and estimate arguments.


Not currently used.


The column identifier for the true results (that is numeric). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For _vec() functions, a numeric vector.


The column identifier for the predicted results (that is also numeric). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For _vec() functions, a numeric vector.


A logical value indicating whether NA values should be stripped before the computation proceeds.


The optional column identifier for case weights. This should be an unquoted column name that evaluates to a numeric column in data. For _vec() functions, a numeric vector, hardhat::importance_weights(), or hardhat::frequency_weights().


A tibble with columns .metric, .estimator, and .estimate and 1 row of values.

For grouped data frames, the number of rows returned will be the same as the number of groups.

For rpd_vec(), a single numeric value (or NA).


In the field of spectroscopy in particular, the ratio of performance to deviation (RPD) has been used as the standard way to report the quality of a model. It is the ratio between the standard deviation of a variable and the standard error of prediction of that variable by a given model. However, its systematic use has been criticized by several authors, since using the standard deviation to represent the spread of a variable can be misleading on skewed dataset. The ratio of performance to inter-quartile has been introduced by Bellon-Maurel et al. (2010) to address some of these issues, and generalise the RPD to non-normally distributed variables.


Williams, P.C. (1987) Variables affecting near-infrared reflectance spectroscopic analysis. In: Near Infrared Technology in the Agriculture and Food Industries. 1st Ed. P.Williams and K.Norris, Eds. Am. Cereal Assoc. Cereal Chem., St. Paul, MN.

Bellon-Maurel, V., Fernandez-Ahumada, E., Palagos, B., Roger, J.M. and McBratney, A., (2010). Critical review of chemometric indicators commonly used for assessing the quality of the prediction of soil attributes by NIR spectroscopy. TrAC Trends in Analytical Chemistry, 29(9), pp.1073-1081.

See also

The closely related inter-quartile metric: rpiq()

Other numeric metrics: ccc(), huber_loss_pseudo(), huber_loss(), iic(), mae(), mape(), mase(), mpe(), msd(), poisson_log_loss(), rmse(), rpiq(), rsq_trad(), rsq(), smape()

Other consistency metrics: ccc(), rpiq(), rsq_trad(), rsq()


Pierre Roudier


# Supply truth and predictions as bare column names
rpd(solubility_test, solubility, prediction)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 rpd     standard        2.88


size <- 100
times <- 10

# create 10 resamples
solubility_resampled <- bind_rows(
    n = times,
    expr = sample_n(solubility_test, size, replace = TRUE),
    simplify = FALSE
  .id = "resample"

# Compute the metric by group
metric_results <- solubility_resampled %>%
  group_by(resample) %>%
  rpd(solubility, prediction)

#> # A tibble: 10 × 4
#>    resample .metric .estimator .estimate
#>    <chr>    <chr>   <chr>          <dbl>
#>  1 1        rpd     standard        2.78
#>  2 10       rpd     standard        2.87
#>  3 2        rpd     standard        3.04
#>  4 3        rpd     standard        3.41
#>  5 4        rpd     standard        3.02
#>  6 5        rpd     standard        2.66
#>  7 6        rpd     standard        2.81
#>  8 7        rpd     standard        2.61
#>  9 8        rpd     standard        3.45
#> 10 9        rpd     standard        2.93

# Resampled mean estimate
metric_results %>%
  summarise(avg_estimate = mean(.estimate))
#> # A tibble: 1 × 1
#>   avg_estimate
#>          <dbl>
#> 1         2.96