Fit Gradient Models to Data

This function fits three gradient models (exponential, power, and modified power) to given data by linear regression of log(Y) and returns the parameters, R-squared values (on the log scale) and diagnostic plots for each model. The models are not ranked; compare them using the R-squared values and the residual patterns in the plots.

Usage

fit_gradients(data, C = 1)

Arguments

data

A dataframe containing the data, with columns "x" representing distances and "Y" representing the corresponding measurements or counts.

C

A constant to be used in the modified power model. Defaults to 1.

Value

A list containing:

data

The input data, which will include an additional column 'mod_x'.

results_table

A data frame with one row per model: intercept a, slope b, their standard errors and significance symbols ("*" p < 0.05, "**" p < 0.01), the back-transformed intercept a_back = exp(a) and R2. Values are rounded to three decimals; the fitted curves in the plots use unrounded estimates.

plot_exponential

Diagnostic plot for the exponential model.

plot_power

Diagnostic plot for the power model.

plot_modified_power

Diagnostic plot for the modified power model.

plot_exponential_original

Plot of the original data with the exponential model fit.

plot_power_original

Plot of the original data with the power model fit.

plot_modified_power_original

Plot of the original data with the modified power model fit.

See also

Other Spatial analysis: AFSD(), BPL(), count_subareas(), count_subareas_random(), join_count(), oruns_test(), oruns_test_boustrophedon(), oruns_test_byrowcol(), plot_AFSD()

Examples

x <- c(0.8, 1.6, 2.4, 3.2, 4, 7.2, 12, 15.2, 21.6, 28.8)
Y <- c(184.9, 113.3, 113.3, 64.1, 25, 8, 4.3, 2.5, 1, 0.8)
grad1 <- data.frame(x = x, Y = Y)
library(ggplot2)
#> Warning: package ‘ggplot2’ was built under R version 4.5.3
mg <- fit_gradients(grad1, C = 0.4)
mg$plot_power_original +
  labs(title = "", x = "Distance from focus (m)", y = "Count of lesions")