kvr2 (version 0.2.0)

comp_fit: Calculate Comparative Fit Measures for Regression Models

Description

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"))

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.

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.

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.

References

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

See Also

print.comp_kvr2()

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)
comp_fit(model_without)
comp_fit(model_power)