在mgcv多项GAM中使用权重：鱼类洄游阶段比例建模问询

Hey there! Great question—using mgcv to fit multinomial GAMs with proportional weights is totally feasible, and I’ll break down exactly how to set this up correctly for your fry/parr/smolt stage data.

First, Let’s Clarify the Data Structure #

Unlike nnet::multinom which often works with wide-format data (one column per stage), mgcv’s multinomial GAM expects long-format data. That means each row should represent a single stage observation for a given day, with columns for:

• Your predictor variables (e.g., water temperature, day of year, river flow)
• A factor variable for the stage (fry, parr, smolt)
• A weight column tied to the observed proportion for that stage on the day (typically the count of individuals in that stage, or the total daily count—more on this below)

Step 1: Prepare Your Data #

Let’s use a simulated example to mirror your scenario. Suppose you have daily counts for each stage and some covariates:

library(mgcv)
set.seed(123) # For reproducibility

# Simulate 100 days of data
n_days <- 100
days <- 1:n_days
temp <- rnorm(n_days, mean = 12, sd = 2) # Water temperature covariate

# Generate true proportional probabilities for each stage
p_fry <- plogis(0.08*days - 0.15*temp)
p_parr <- plogis(-0.05*days + 0.1*temp)
p_smolt <- 1 - p_fry - p_parr

# Total daily observations (varying per day)
total_daily <- sample(60:200, n_days, replace = TRUE)

# Simulate counts for each stage
fry_counts <- rbinom(n_days, size = total_daily, prob = p_fry)
parr_counts <- rbinom(n_days, size = total_daily - fry_counts, prob = p_parr/(p_parr + p_smolt))
smolt_counts <- total_daily - fry_counts - parr_counts

# Reshape to long format
dat_long <- data.frame(
  day = rep(days, 3),
  temp = rep(temp, 3),
  stage = factor(rep(c("fry", "parr", "smolt"), each = n_days)),
  count = c(fry_counts, parr_counts, smolt_counts),
  total_daily = rep(total_daily, 3) # Optional: total daily counts for weighting
)

Step 2: Fit the Weighted Multinomial GAM #

The key here is using the weights argument in mgcv::gam() alongside the multinom() family. The weights should reflect the reliability of each stage’s proportion on a given day:

• If you want to weight by the number of individuals observed in the stage, use the count column (this gives more weight to days where you have more observations for that stage)
• If you want to weight by the total daily observations (giving equal weight to each day, regardless of stage-specific counts), use the total_daily column

Here’s how to fit the model with stage-specific counts as weights:

# Fit the multinomial GAM with splines for day and temperature
mod <- gam(
  formula = stage ~ s(day) + s(temp),
  data = dat_long,
  family = multinom(),
  weights = count, # This is where your regression weights go!
  method = "REML" # Recommended for smoothness selection
)

# Check model summary
summary(mod)

# Run diagnostic checks
gam.check(mod)

Key Notes to Avoid Pitfalls #

• Reference Category: By default, multinom() uses the first level of your stage factor as the reference. To change this (e.g., set smolt as reference), use dat_long$stage <- relevel(dat_long$stage, ref = "smolt") before fitting.
• Weight Interpretation: The weights in this context act like case weights—they scale the contribution of each observation to the log-likelihood. Using stage counts makes sense because days with more individuals in a stage have more reliable proportion estimates.
• Predictions: To get predicted probabilities for each stage, use predict(mod, newdata = your_new_data, type = "response"). This will return a matrix where each column is the predicted probability for a stage.

Quick Comparison to nnet::multinom #

The main difference is that mgcv lets you easily add smooth spline terms (like s(day)) to model non-linear relationships between covariates and stage proportions, whereas nnet::multinom is limited to linear terms. The weighting setup is analogous, but the data format switch (wide → long) is critical for mgcv.

内容的提问来源于stack exchange，提问作者Hugh Sturrock