Root mean square error (RMSE)

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Description

This function computes the root mean square error (RMSE).

Usage

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rmse(predicted, observed, na.rm = FALSE)

Arguments

predicted

numeric vector that contains the predicted data points (1st parameter)

observed

numeric vector that contains the observed data points (2nd parameter)

na.rm

logical vector that determines whether the missing values should be removed or not.

Details

RMSE is expressed as

√{n^{-1} ∑ \limits_{i=1}^n{ ≤ft| P_i - O_i \right|^2}}

n

the number of observations

P

the "model estimates or predictions"

O

the "thought-to-be reliable and pairwise matched observations"

RMSE is fully discussed in the Willmott reference, including a comparison to mean-absolute error (MAE).

Value

mean absolute percent error (RMSE) as a numeric vector. The default choice is that any NA values will be kept (na.rm = FALSE). This can be changed by specifying na.rm = TRUE, such as rmse(pre, obs, na.rm = TRUE).

Source

r - Better error message for stopifnot? - Stack Overflow answered by Andrie on Dec 1 2011. See http://stackoverflow.com/questions/8343509/better-error-message-for-stopifnot.

References

Cort J. Willmott and Kenji Matsuura, "Advantages of the mean-absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance", Climate Research, Vol. 30: 79-82, 2005, http://climate.geog.udel.edu/~climate/publication_html/Pdf/WM_CR_05.pdf.

See Also

mape for mean absolute percent error (MAPE), mae for mean-absolute error (MAE), madstat for mean-absolute deviation (MAD), dr for "index of agreement (dr)", and vnse for Nash-Sutcliffe model efficiency (NSE).

Examples

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library(ie2misc)
obs <- 1:10 # observed
pre <- 2:11 # predicted
rmse(pre, obs)


require(stats)
set.seed(100) # makes the example reproducible
obs1 <- rnorm(100) # observed
pre1 <- rnorm(100) # predicted


# using the vectors pre1 and obs1
rmse(pre1, obs1)


# using a matrix of the numeric vectors pre1 and obs1
mat1 <- matrix(data = c(obs1, pre1), nrow = length(pre1), ncol = 2,
  byrow = FALSE, dimnames = list(c(rep("", length(pre1))),
  c("Predicted", "Observed")))
rmse(mat1[, 2], mat1[, 1])

# mat1[, 1] # observed values from column 1 of mat1
# mat1[, 2] # predicted values from column 2 of mat1


# using a data.frame of the numeric vectors pre1 and obs1
df1 <- data.frame(obs1, pre1)
rmse(df1[, 2], df1[, 1])

# df1[, 1] # observed values from column 1 of df1
# df1[, 2] # predicted values from column 2 of df1


# using a data.table of the numeric vectors pre1 and obs1
df2 <- data.table(obs1, pre1)
rmse(df2[, 2, with = FALSE][[1]], df2[, 1, with = FALSE][[1]])

# df2[, 1, with = FALSE][[1]] # observed values from column 1 of df2
# df2[, 2, with = FALSE][[1]] # predicted values from column 2 of df2