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R/accuracy.r
In rcompanion: Functions to Support Extension Education Program Evaluation
#' @title Minimum maximum accuracy, mean absolute percent error,
#' median absolute error,
#' root mean square error, coefficient of variation,
#' and Efron's pseudo r-squared
#'
#' @description Produces a table of fit statistics for multiple models.
#'
#' @param fits A series of model object names.
#' Must be a list of model objects or a single model object.
#' @param plotit If \code{TRUE}, produces plots of the predicted values
#' vs. the actual values for each model.
#' @param digits The number of significant digits in the output.
#' @param ... Other arguments passed to \code{plot}.
#'
#' @details Produces a table of fit statistics for multiple models:
#' minimum maximum accuracy, mean absolute percentage error,
#' median absolute error,
#' root mean square error, normalized root mean square error,
#' Efron's pseudo r-squared, and coefficient of variation.
#'
#' For minimum maximum accuracy, larger indicates
#' a better fit,
#' and a perfect fit is equal to 1.
#'
#' For mean absolute error (MAE), smaller
#' indicates a better fit,
#' and a perfect fit is equal to 0.
#' It has the same units as the dependent variable.
#' Note that here, MAE is simply the mean of the absolute
#' values of the differences of predicted values and the
#' observed values
#' (\code{MAE = mean(abs(predy - actual))}).
#' There are other definitions of MAE and similar-sounding
#' terms.
#'
#' Median absolute error (MedAE) is similar, except employing
#' the median rather than the mean.
#'
#' For mean absolute percent error (MAPE), smaller
#' indicates a better fit,
#' and a perfect fit is equal to 0. The result is reported
#' as a fraction. That is, a result of 0.1 is equal to 10 percent.
#'
#' Root mean square error (RMSE) has the same units as the predicted
#' values.
#'
#' Normalized root mean square error (NRMSE) is RMSE divided by
#' the mean or the median of the values of the dependent variable.
#'
#' Efron's pseudo r-squared is calculated as 1 minus the residual sum
#' of squares divided by the total sum of squares. For linear models
#' (\code{lm} model objects), Efron's pseudo r-squared will be equal
#' to r-squared. For other models, it should not be interpreted
#' as r-squared, but can still be useful as a relative measure.
#'
#' \code{CV.prcnt} is the coefficient of variation for the model.
#' Here it is expressed as a percent. That is, a result of 10 =
#' 10 percent.
#'
#' Model objects currently supported: lm, glm, nls, betareg, gls,
#' lme, lmer, lmerTest, glmmTMB,
#' rq, loess, gam, glm.nb, glmRob, mblm, and rlm.
#'
#'
#' @author Salvatore Mangiafico, \email{mangiafico@njaes.rutgers.edu}
#'
#' @references \url{https://rcompanion.org/handbook/G_14.html}
#'
#' @seealso \code{\link{compareLM}},
#' \code{\link{compareGLM}},
#' \code{\link{nagelkerke}}
#'
#' @concept accuracy
#' @concept r squared
#' @concept pseudo r squared
#' @concept RMSE
#' @concept MAPE
#' @concept coefficient of variation
#' @concept CV
#' @concept MAE
#'
#' @return A list of two objects: The series of model calls, and a data
#' frame of statistics for each model.
#'
#' @examples
#' data(BrendonSmall)
#' BrendonSmall$Calories = as.numeric(BrendonSmall$Calories)
#' BrendonSmall$Calories2 = BrendonSmall$Calories ^ 2
#' model.1 = lm(Sodium ~ Calories, data = BrendonSmall)
#'
#' accuracy(model.1, plotit=FALSE)
#'
#' model.2 = lm(Sodium ~ Calories + Calories2, data = BrendonSmall)
#' model.3 = glm(Sodium ~ Calories, data = BrendonSmall, family="Gamma")
#' quadplat = function(x, a, b, clx) {
#' ifelse(x < clx, a + b * x + (-0.5*b/clx) * x * x,
#' a + b * clx + (-0.5*b/clx) * clx * clx)}
#' model.4 = nls(Sodium ~ quadplat(Calories, a, b, clx),
#' data = BrendonSmall,
#' start = list(a=519, b=0.359, clx = 2300))
#'
#' accuracy(list(model.1, model.2, model.3, model.4), plotit=FALSE)
#'
#' ### Perfect and poor model fits
#' X = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
#' Y = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
#' Z = c(1, 12, 13, 6, 10, 13, 4, 3, 5, 6, 10, 14)
#' perfect = lm(Y ~ X)
#' poor = lm(Z ~ X)
#' accuracy(list(perfect, poor), plotit=FALSE)
#'
#' @importFrom graphics plot
#' @importFrom stats predict residuals
#'
#' @export
accuracy =
function (fits, plotit=FALSE, digits=3, ...)
{
if(class(fits)[1]!="list"){fits=list(fits)}
n = length(fits)
Y = matrix(rep(NA,n),
ncol=1)
colnames(Y) = c("Call")
rownames(Y) = seq(1,n)
Z = data.frame(Min.max.accuracy=rep(NA,n),
MAE=rep(NA,n),
MedAE=rep(NA,n),
MAPE=rep(NA,n),
MSE=rep(NA,n),
RMSE=rep(NA,n),
NRMSE.mean=rep(NA,n),
NRMSE.median=rep(NA,n),
Efron.r.squared=rep(NA,n),
CV.prcnt=rep(NA,n),
stringsAsFactors=FALSE)
for(i in 1:n)
{
TOGGLE=FALSE
predy = 1
actual = 1
if(class(fits[[i]])[1]=="lm"){predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="glm"){predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="nls"){predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="betareg"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="gls"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="lme"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="lmerMod"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]@call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="lmerModLmerTest"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]@call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="rq"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="loess"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="gam"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="negbin"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="glmRob"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="rlm"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="glmmTMB"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="mblm"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
Y[i,] = "Not supported"
if(TOGGLE==TRUE){Y[i,] = deparse(call)[1]}
actual = unname(actual)
predy = unname(predy)
data = data.frame(cbind(actual=actual, predy=predy))
mma = mean(apply(data, 1, min) / apply(data, 1, max))
mae = mean(abs(predy - actual))
medae = median(abs(predy - actual))
mape = mean(abs((predy - actual)/actual))
mse = mean((actual - predy)^2)
rmse = sqrt(mse)
nrmse_mean = rmse/mean(actual)
cv_prcnt = nrmse_mean*100
nrmse_median = rmse/median(actual)
Var = sum((actual - mean(actual))^2)
RSS = sum((actual - predy)^2)
var_r_squared = 1 - RSS / Var
Z[i,]=rep(NA,10)
if(TOGGLE==TRUE){
Z[i,]=c(signif(mma, digits=digits),
signif(mae, digits=digits),
signif(medae, digits=digits),
signif(mape, digits=digits),
signif(mse, digits=digits),
signif(rmse, digits=digits),
signif(nrmse_mean, digits=digits),
signif(nrmse_median, digits=digits),
signif(var_r_squared, digits=digits),
signif(cv_prcnt, digits=digits))
if(plotit){plot(data$actual, data$predy,
main=paste0("Model ", i),
xlab="Actual", ylab="Predicted",
...)}
}
}
W = list(Y, Z)
names(W) = c("Models",
"Fit.criteria")
return(W)
}
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#' @title Minimum maximum accuracy, mean absolute percent error,
#' median absolute error,
#' root mean square error, coefficient of variation,
#' and Efron's pseudo r-squared
#'
#' @description Produces a table of fit statistics for multiple models.
#'
#' @param fits A series of model object names.
#' Must be a list of model objects or a single model object.
#' @param plotit If \code{TRUE}, produces plots of the predicted values
#' vs. the actual values for each model.
#' @param digits The number of significant digits in the output.
#' @param ... Other arguments passed to \code{plot}.
#'
#' @details Produces a table of fit statistics for multiple models:
#' minimum maximum accuracy, mean absolute percentage error,
#' median absolute error,
#' root mean square error, normalized root mean square error,
#' Efron's pseudo r-squared, and coefficient of variation.
#'
#' For minimum maximum accuracy, larger indicates
#' a better fit,
#' and a perfect fit is equal to 1.
#'
#' For mean absolute error (MAE), smaller
#' indicates a better fit,
#' and a perfect fit is equal to 0.
#' It has the same units as the dependent variable.
#' Note that here, MAE is simply the mean of the absolute
#' values of the differences of predicted values and the
#' observed values
#' (\code{MAE = mean(abs(predy - actual))}).
#' There are other definitions of MAE and similar-sounding
#' terms.
#'
#' Median absolute error (MedAE) is similar, except employing
#' the median rather than the mean.
#'
#' For mean absolute percent error (MAPE), smaller
#' indicates a better fit,
#' and a perfect fit is equal to 0. The result is reported
#' as a fraction. That is, a result of 0.1 is equal to 10 percent.
#'
#' Root mean square error (RMSE) has the same units as the predicted
#' values.
#'
#' Normalized root mean square error (NRMSE) is RMSE divided by
#' the mean or the median of the values of the dependent variable.
#'
#' Efron's pseudo r-squared is calculated as 1 minus the residual sum
#' of squares divided by the total sum of squares. For linear models
#' (\code{lm} model objects), Efron's pseudo r-squared will be equal
#' to r-squared. For other models, it should not be interpreted
#' as r-squared, but can still be useful as a relative measure.
#'
#' \code{CV.prcnt} is the coefficient of variation for the model.
#' Here it is expressed as a percent. That is, a result of 10 =
#' 10 percent.
#'
#' Model objects currently supported: lm, glm, nls, betareg, gls,
#' lme, lmer, lmerTest, glmmTMB,
#' rq, loess, gam, glm.nb, glmRob, mblm, and rlm.
#'
#'
#' @author Salvatore Mangiafico, \email{mangiafico@njaes.rutgers.edu}
#'
#' @references \url{https://rcompanion.org/handbook/G_14.html}
#'
#' @seealso \code{\link{compareLM}},
#' \code{\link{compareGLM}},
#' \code{\link{nagelkerke}}
#'
#' @concept accuracy
#' @concept r squared
#' @concept pseudo r squared
#' @concept RMSE
#' @concept MAPE
#' @concept coefficient of variation
#' @concept CV
#' @concept MAE
#'
#' @return A list of two objects: The series of model calls, and a data
#' frame of statistics for each model.
#'
#' @examples
#' data(BrendonSmall)
#' BrendonSmall$Calories = as.numeric(BrendonSmall$Calories)
#' BrendonSmall$Calories2 = BrendonSmall$Calories ^ 2
#' model.1 = lm(Sodium ~ Calories, data = BrendonSmall)
#'
#' accuracy(model.1, plotit=FALSE)
#'
#' model.2 = lm(Sodium ~ Calories + Calories2, data = BrendonSmall)
#' model.3 = glm(Sodium ~ Calories, data = BrendonSmall, family="Gamma")
#' quadplat = function(x, a, b, clx) {
#' ifelse(x < clx, a + b * x + (-0.5*b/clx) * x * x,
#' a + b * clx + (-0.5*b/clx) * clx * clx)}
#' model.4 = nls(Sodium ~ quadplat(Calories, a, b, clx),
#' data = BrendonSmall,
#' start = list(a=519, b=0.359, clx = 2300))
#'
#' accuracy(list(model.1, model.2, model.3, model.4), plotit=FALSE)
#'
#' ### Perfect and poor model fits
#' X = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
#' Y = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
#' Z = c(1, 12, 13, 6, 10, 13, 4, 3, 5, 6, 10, 14)
#' perfect = lm(Y ~ X)
#' poor = lm(Z ~ X)
#' accuracy(list(perfect, poor), plotit=FALSE)
#'
#' @importFrom graphics plot
#' @importFrom stats predict residuals
#'
#' @export
accuracy =
function (fits, plotit=FALSE, digits=3, ...)
{
if(class(fits)[1]!="list"){fits=list(fits)}
n = length(fits)
Y = matrix(rep(NA,n),
ncol=1)
colnames(Y) = c("Call")
rownames(Y) = seq(1,n)
Z = data.frame(Min.max.accuracy=rep(NA,n),
MAE=rep(NA,n),
MedAE=rep(NA,n),
MAPE=rep(NA,n),
MSE=rep(NA,n),
RMSE=rep(NA,n),
NRMSE.mean=rep(NA,n),
NRMSE.median=rep(NA,n),
Efron.r.squared=rep(NA,n),
CV.prcnt=rep(NA,n),
stringsAsFactors=FALSE)
for(i in 1:n)
{
TOGGLE=FALSE
predy = 1
actual = 1
if(class(fits[[i]])[1]=="lm"){predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="glm"){predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="nls"){predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="betareg"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="gls"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="lme"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="lmerMod"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]@call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="lmerModLmerTest"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]@call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="rq"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="loess"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="gam"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="negbin"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="glmRob"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="rlm"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="glmmTMB"){
predy = predict(fits[[i]], type="response")
actual = predict(fits[[i]], type="response") +
residuals(fits[[i]], type="response")
call = fits[[i]]$call
TOGGLE = TRUE}
if(class(fits[[i]])[1]=="mblm"){
predy = predict(fits[[i]])
actual = predict(fits[[i]]) +
residuals(fits[[i]])
call = fits[[i]]$call
TOGGLE = TRUE}
Y[i,] = "Not supported"
if(TOGGLE==TRUE){Y[i,] = deparse(call)[1]}
actual = unname(actual)
predy = unname(predy)
data = data.frame(cbind(actual=actual, predy=predy))
mma = mean(apply(data, 1, min) / apply(data, 1, max))
mae = mean(abs(predy - actual))
medae = median(abs(predy - actual))
mape = mean(abs((predy - actual)/actual))
mse = mean((actual - predy)^2)
rmse = sqrt(mse)
nrmse_mean = rmse/mean(actual)
cv_prcnt = nrmse_mean*100
nrmse_median = rmse/median(actual)
Var = sum((actual - mean(actual))^2)
RSS = sum((actual - predy)^2)
var_r_squared = 1 - RSS / Var
Z[i,]=rep(NA,10)
if(TOGGLE==TRUE){
Z[i,]=c(signif(mma, digits=digits),
signif(mae, digits=digits),
signif(medae, digits=digits),
signif(mape, digits=digits),
signif(mse, digits=digits),
signif(rmse, digits=digits),
signif(nrmse_mean, digits=digits),
signif(nrmse_median, digits=digits),
signif(var_r_squared, digits=digits),
signif(cv_prcnt, digits=digits))
if(plotit){plot(data$actual, data$predy,
main=paste0("Model ", i),
xlab="Actual", ylab="Predicted",
...)}
}
}
W = list(Y, Z)
names(W) = c("Models",
"Fit.criteria")
return(W)
}
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