我的数据集可以在这里找到：https://raw.githubusercontent.com/yuliaUU/test/main/test.csv

library(gamlss)
library(tidyverse)
data_final<- read_csv("https://raw.githubusercontent.com/yuliaUU/test/main/test.csv")

# Normal model with log transformation 
model_1 <-  gamlss(log(Abundance) ~ salinity*avrg_dep, data = data_final, family = NO())
# log normal model 
model_2 <- gamlss(Abundance ~  salinity*avrg_dep, data = data_final,  family = LOGNO())
#  Model with inverse gaussian distribution
model_3 <- gamlss(Abundance ~ salinity*avrg_dep, data = data_final,  family = IG())
# Gamma model
model_4 <- gamlss(Abundance ~ salinity*avrg_dep,  data = data_final, family = GA())

我想用GAIC来比较模型之间的差异，但第一个模型的GAIC值与其他模型相差甚远
我读到：
为确保具有转换响应的线性模型的GAIC相当，使用转换对数似然乘以雅可比矩阵，并手动重新计算GAIC。
我试着用下面的方法来做：

Jacobian <- 1/abs(data_final$Abundance)
# Calculate fitted values (on the log scale)
fitted_values_log <- predict(model_1)

# Calculate residuals manually (on the log scale)
residuals_transformed <- log(data_final$Abundance) - fitted_values_log

# Calculate standard deviation of the residuals
sd_residuals_transformed <- sd(residuals_transformed)

# Transformed log-likelihood calculation
log_likelihood_transformed <- sum(dnorm(log(data_final$Abundance), mean=fitted_values_log, sd=sd_residuals_transformed, log=TRUE) * Jacobian)

# Calculate degrees of freedom: number of parameters in the model
df <- length(coef(model_1))

# Manually calculate GAIC
GAIC_transformed <- -2 * log_likelihood_transformed + 2 * df
GAIC_transformed

但是产生的价值太低了，所以我想我在某个地方犯了一个错误