Reduced chi-squared

Function that returns the reduced chi-squared (\(\chi^2_{red}=\chi^2/df\), where \(df\) are the degrees of freedom) value for a non-linear regression model (nls object). Reduced-chi squared is a goodness-of-fit measure. Values close to 1 indicates a good fit, while values \(>>1\) indicate poor fit and values \(<1\) indicate over-fitting. The function is calculated only with non-linear regression weighted on experimental error.

Usage

chiquad_red(fit)

Arguments

fit

nls object with weighted fit

Value

Returns the reduced chi-squared value

References

Philip R. Bevington, D. Keith Robinson, J. Morris Blair, A. John Mallinckrodt, Susan McKay (1993). Data Reduction and Error Analysis for the Physical Sciences

See also

stats::dchisq() for chi-squared distribution; stats::AIC(), stats::BIC(), stats::sigma() (for RMSE), AICC() for other goodness-of-fit indicators. goodness_of_fit()

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
)
chiquad_red(fit1)
#> [1] 0.9896681

fit2 <- nls(y ~ k * x^3,
  data = list(x = x, y = y),
  start = list(k = 1),
  weights = 1 / er^2
)
chiquad_red(fit2)
#> [1] 22.55793