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Goodness-of-fit, non-linear regression

Source: R/nls_indicators.R
goodness_of_fit.Rd

Function that returns the following goodness-of-fit statistics for non-linear regression: AIC, AICc, BIC, RMSE and reduced Chi-squared.

Usage

goodness_of_fit(fit)

Arguments

fit

a nls, lm or ord_res object

Value

It returns a table with the values of AIC, AICc, BIC, RSME and reduced Chi squared. Single goodness-of-fit measures can be obtained as follows:

  1. call standard R functions stats::AIC(), stats::BIC(), stats::sigma() for AIC, BIC and RMSE, respectively;

  2. call chemdeg functions AICC() and chiquad_red() for AICc and reduced chi-squared, respectively.

Details

The function returns the values of AIC, AICC, BIC, RMSE and reduced chi-squared (\(\chi^2_{red}\)) for nls objects. If a linear model object is passed, the function returns its summary.

Given an ord_res object (output of the function det_order()), the function returns one of the results above depending on the model chosen to explain the data.

Because the chiquad_red() function returns the value only with weighted data, the \(\chi^2_{red}\) will be returned only with weighted regressions.

See also

stats::AIC(), AICC(), stats::BIC(), stats::sigma(), chiquad_red()

Examples

x <- c(1, 2, 3, 4, 5)
y <- c(1.2, 3.9, 8.6, 17.4, 26)
er <- c(0.5, 0.8, 0.5, 1.9, 1.2)
fit1 <- nls(y ~ k * x^2,
  data = list(x = x, y = y), start = list(k = 1),
  weights = 1 / er^2
)
goodness_of_fit(fit1)
#>                  Value
#> AIC:        11.9141544
#> AICc:       13.2474878
#> BIC:        11.1330303
#> RMSE:        0.6984450
#> Chi-sq_red:  0.9896681