rmse: Root mean square error (RMSE)
In iembry-USGS/ie2misc: Irucka Embry's Miscellaneous USGS Functions

Description Usage Arguments Details Value Source References See Also Examples

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

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

`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.

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).

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).

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.

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.

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).

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