ct_QAIC: Compute QAIC for a set of detection function models

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

Compute QAIC for a set of detection function models

Description

Calculates the quasi-Akaike Information Criterion (QAIC) for one or more detection function models within the same key function family. If multiple models are provided, all must have the same key function. This function is typically used as the first step of a two-step model selection approach (Howe et al., 2019).

Usage

ct_QAIC(models, chat = NULL, k = 2)

Arguments

models	A list of fitted detection function models (objects returned by Distance::ds() or ct_fit_ds()).
chat	Optional numeric value of overdispersion (\hat{c}). If not provided, it is estimated from the most parameterised model in each key function set.
k	Numeric. The penalty term used in QAIC (default is 2).

Details

If only one model is supplied and chat is not provided, the function estimates \hat{c} using the provided model and issues a warning that model selection cannot be performed. For multiple models, All models must use the same key function.

QAIC is calculated as:

QAIC = -2 \times \log(L) / \hat{c} + 2k

where L is the likelihood, \hat{c} is the estimated overdispersion, and k is the number of parameters.

Value

A tibble with one row per model containing:

• model: The model name

• df: The degrees of freedom for the model.

• QAIC: The computed QAIC value.

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.