dr: Index of agreement (dr)
In iembry-USGS/ie2misc: Irucka Embry's Miscellaneous USGS Functions

Description Usage Arguments Details Value Source References See Also Examples

This function computes the "index of agreement (dr)".

1	dr(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.

dr is expressed as

d_{r} = 1 - \frac{∑ \limits_{i=1}^n{≤ft|P_i - O_i\right|}}{c ∑ \limits_{i=1}^n{≤ft|O_i - \bar{O}\right|}}, \: when \: ∑ \limits_{i=1}^n{≤ft|P_i - O_i\right|} ≤q c \: ∑ \limits_{i=1}^n{≤ft|O_i - \bar{O}\right|}

d_{r} = \frac{{c ∑ \limits_{i=1}^n{≤ft|O_i - \bar{O}\right|}}}{∑ \limits_{i=1}^n{≤ft|P_i - O_i\right|}} - 1, \: when \: ∑ \limits_{i=1}^n{≤ft|P_i - O_i\right|} > c \: ∑ \limits_{i=1}^n{≤ft|O_i - \bar{O}\right|}

d_r: the "index of agreement (dr)"
n: the number of observations
P: the "model estimates or predictions"
O: the "pairwise-matched observations that are judged to be reliable"
\bar{O}: the "true" mean of the observations

Note: Both P and O should have the same units.

The "index of agreement (dr)" is fully discussed in the Willmott reference.

"index of agreement (dr)" 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 dr(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, Scott M. Robeson, and Kenji Matsuura, "A refined index of model performance", International Journal of Climatology, Volume 32, Issue 13, pages 2088-2094, 15 November 2012, http://onlinelibrary.wiley.com/doi/10.1002/joc.2419/pdf.

mape for mean absolute percent error (MAPE), mae for mean-absolute error (MAE), madstat for mean-absolute deviation (MAD), vnse for Nash-Sutcliffe model efficiency (NSE), and rmse for root mean square error (RMSE).

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