bfsl calculates the best-fit straight line to independent points with
(possibly correlated) normally distributed errors in both coordinates.
bfsl(...)# S3 method for default
bfsl(x, y = NULL, sd_x = 0, sd_y = 1, r = 0, control = bfsl_control(), ...)
# S3 method for formula
bfsl(
formula,
data = parent.frame(),
sd_x,
sd_y,
r = 0,
control = bfsl_control(),
...
)
Further arguments passed to or from other methods.
A vector of x observations or a data frame (or an
object coercible by as.data.frame to a data frame) containing
the named vectors x, y, and optionally sd_x,
sd_y and r. If weights w_x and w_y are given,
then sd_x and sd_y are calculated from sd_x = 1/sqrt(w_x)
and sd_y = 1/sqrt(w_y). Specifying y, sd_x, sd_y
or r directly as function arguments overwrites these variables in the
data structure.
A vector of y observations.
A vector of x measurement error standard deviations. If it is of length one, all data points are assumed to have the same x standard deviation.
A vector of y measurement error standard deviations. If it is of length one, all data points are assumed to have the same y standard deviation.
A vector of correlation coefficients between errors in x and y. If it is of length one, all data points are assumed to have the same correlation coefficient.
A list of control settings. See bfsl_control
for the names of the settable control values and their effect.
A formula specifying the bivariate model (as in lm,
but here only y ~ x makes sense).
A data.frame containing the variables of the model.
An object of class "bfsl", which is a list containing
the following components:
A 2x2 matrix with columns of the fitted coefficients
(intercept and slope) and their standard errors.
The goodness of fit (see Details).
The fitted mean values.
The residuals, that is y observations minus fitted values.
The residual degrees of freedom.
The covariance of the slope and intercept.
The control list used, see the control argument.
A list with convergence information.
The matched call.
A list containing x, y, sd_x, sd_y
and r.
bfsl provides the general least-squares estimation solution to the
problem of fitting a straight line to independent data with (possibly
correlated) normally distributed errors in both x and y.
With sd_x = 0 the (weighted) ordinary least squares solution is
obtained. The calculated standard errors of the slope and intercept
multiplied with sqrt(chisq) correspond to the ordinary least squares
standard errors.
With sd_x = c, sd_y = d, where c and d are
positive numbers, and r = 0 the Deming regression solution is obtained.
If additionally c = d, the orthogonal distance regression solution,
also known as major axis regression, is obtained.
Setting sd_x = sd(x), sd_y = sd(y) and r = 0 leads to
the geometric mean regression solution, also known as reduced major
axis regression or standardised major axis regression.
The goodness of fit metric chisq is a weighted reduced chi-squared
statistic. It compares the deviations of the points from the fit line to the
assigned measurement error standard deviations. If x and y are
indeed related by a straight line, and if the assigned measurement errors
are correct (and normally distributed), then chisq will equal 1. A
chisq > 1 indicates underfitting: the fit does not fully capture the
data or the measurement errors have been underestimated. A chisq < 1
indicates overfitting: either the model is improperly fitting noise, or the
measurement errors have been overestimated.
York, D. (1968). Least squares fitting of a straight line with correlated errors. Earth and Planetary Science Letters, 5, 320<U+2013>324, https://doi.org/10.1016/S0012-821X(68)80059-7
# NOT RUN {
x = pearson_york_data$x
y = pearson_york_data$y
sd_x = 1/sqrt(pearson_york_data$w_x)
sd_y = 1/sqrt(pearson_york_data$w_y)
bfsl(x, y, sd_x, sd_y)
bfsl(y~x, pearson_york_data, sd_x, sd_y)
fit = bfsl(pearson_york_data)
plot(fit)
# }
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