ct_chi2_select: Select best detection function model by Chi-squared...

In ct: Camera Trap Data Management and Multi-Method Ecological Analysis

Select best detection function model by Chi-squared Goodness-of-fit

Description

Compares detection function models with different key functions using the ratio of the chi-squared statistic to its degrees of freedom. This method selects the best model among different key functions after the best adjustment term model is chosen for each key function.

Usage

ct_chi2_select(models)

Arguments

models

A list of fitted detection function models (objects returned by Distance::ds() or ct_fit_ds()).

Details

If only one model is supplied, the function returns the chi-squared goodness-of-fit ratio for that model and issues a warning that model selection cannot be performed. For multiple models, each must have a unique key function. This step is designed to be applied after selecting the best model within each key function family using QAIC (see ct_QAIC()). The model with the smallest chi-squared/df ratio is typically preferred.

Value

A tibble with one row per model containing:

• key: The key function of the model.

• model: The model name.

• criteria: The chi-squared goodness-of-fit statistic divided by its degrees of freedom, i.e. \chi^2/\mathrm{df}. Lower values indicate better fit.

References

Howe, E. J., Buckland, S. T., Després-Einspenner, M., & Kühl, H. S. (2019). Model selection with overdispersed distance sampling data. Methods in Ecology and Evolution, 10(1), 38-47. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/2041-210X.13082")}

Examples

library(Distance)
library(dplyr)

data("duiker")
duiker_data <- duikers$DaytimeDistances %>%
  dplyr::slice_sample(prop = .3) # sample 30% of rows
truncation <- list(left = 2, right = 15) # Keep only distance between 2-15 m

# fit hazard-rate key models
w3_hr0 <- ds(duiker_data, transect = "point", key = "hr", adjustment = NULL,
             truncation = truncation)
w3_hr1 <- ds(duiker_data, transect = "point", key = "hr", adjustment = "cos",
             order = 2, truncation = truncation)
w3_hr2 <- ds(duiker_data, transect = "point", key = "hr", adjustment = "cos",
             order = c(2, 4), truncation = truncation)
# fit half-normal key models
w3_hn0 <- ds(duiker_data, transect = "point", key = "hn", adjustment = NULL,
             truncation = truncation)
w3_hn1 <- ds(duiker_data, transect = "point", key = "hn", adjustment = "cos",
             order = 2, truncation = truncation)
w3_hn2 <- ds(duiker_data, transect = "point", key = "hn", adjustment = "cos",
             order = c(2, 4), truncation = truncation)
# fit uniform key models
w3_u0 <- ds(duiker_data, transect = "point", key = "unif", adjustment = NULL,
            truncation = truncation)
w3_u1 <- ds(duiker_data, transect = "point", key = "unif", adjustment = "cos",
            order = 2, truncation = truncation)
w3_u2 <- ds(duiker_data, transect = "point", key = "unif", adjustment = "cos",
            order = c(2, 4), truncation = truncation)

# Create model list
model_list <- list(w3_hn0, w3_hn1, w3_hn2,
                   w3_hr0, w3_hr1, w3_hr2,
                   w3_u0, w3_u1, w3_u2)

# Compute model QAICs
ct_QAIC(list(w3_hr0, w3_hr1, w3_hr2)) # All key functions must be the same
ct_QAIC(list(w3_hn0, w3_hn1, w3_hn2)) # All key functions must be the same

# Compute Chi-squared Goodness-of-fit
ct_chi2_select(list(w3_hn0, w3_hr0, w3_u0)) # All key functions must be different
ct_chi2_select(list(w3_hn2, w3_hr1, w3_u0)) # All key functions must be different

# Two-step model selection
ct_select_model(model_list)

ct documentation built on Oct. 22, 2026, 1:07 a.m.