Calculate Comparative Fit Measures for Regression Models

Calculates goodness-of-fit metrics based on Kvalseth (1985), including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Squared Error (MSE). This function provides a unified output for comparing different model specifications.

Usage

comp_fit(model, type = c("auto", "linear", "power"))

RMSE(model, type = c("auto", "linear", "power"))

MAE(model, type = c("auto", "linear", "power"))

MSE(model, type = c("auto", "linear", "power"))

Arguments

model: A linear model or power regression model of the lm.
type: Character string. Selects the model type: "linear", "power", or "auto" (default). In "auto", the function detects if the dependent variable is log-transformed.

Value

For comp_fit(): An object of class comp_kvr2, which is a list containing the calculated RMSE, MAE, and MSE values.
For individual functions (RMSE(), MAE(), MSE()): A named numeric value of the specific metric.

Details

The metrics are calculated according to the formulas in Kvalseth (1985):

RMSE: Root Mean Squared Residual or Error $$RMSE = \sqrt{\frac{\sum (y - \hat{y})^2}{n}}$$
MAE: Mean Absolute Residual or Error $$MAE = \frac{\sum |y - \hat{y}|}{n}$$
MSE: Mean Squared Residual or Error (Adjusted for degrees of freedom) $$MSE = \frac{\sum (y - \hat{y})^2}{n - p}$$

where $n$ is the sample size and $p$ is the number of model parameters (including the intercept).

Note on MSE: In many modern contexts, "MSE" refers to the mean squared error without degree-of-freedom adjustment (denominator $n$). However, this function follows Kvalseth's definition, which uses $n - p$ as the denominator.

Note

The power regression model must be based on a logarithmic transformation.

When type = "auto", the choice between linear and power regression is determined by analyzing the model formula. It identifies a power regression if the dependent variable is a function call to log() (e.g., lm(log(y) ~ x)).

Note that simple variable names containing the string "log" (e.g., lm(log_value ~ x)) are correctly treated as linear regression. To override this automatic detection, manually specify type = "linear" or type = "power".

References

Tarald O. Kvalseth (1985) Cautionary Note about R 2 , The American Statistician, 39:4, 279-285, doi: 10.1080/00031305.1985.10479448

Examples

# example data set 1. Kvålseth (1985).
df1 <- data.frame(x = c(1:6),
                 y = c(15,37,52,59,83,92))
model_intercept <- lm(y ~ x, df1)
model_without <- lm(y ~ x - 1, df1)
model_power <- lm(log(y) ~ log(x), df1)
comp_fit(model_intercept)
#> RMSE :  3.6165 
#> MAE :  3.5238 
#> MSE :  19.6190 
#> ---------------------------------
#> (Type: linear, with intercept, n: 6, k: 2)
comp_fit(model_without)
#> RMSE :  3.9008 
#> MAE :  3.6520 
#> MSE :  18.2593 
#> ---------------------------------
#> (Type: linear, without intercept, n: 6, k: 1)
comp_fit(model_power)
#> RMSE :  3.8982 
#> MAE :  3.6334 
#> MSE :  22.7938 
#> ---------------------------------
#> (Type: power, with intercept, n: 6, k: 2)