使用nlme估计Logistic参数及随机效应时的一致性问题求助

Hey, let's break down this problem step by step—nonlinear mixed models for growth curves can be tricky, especially when you're dealing with inconsistent parameters and convergence issues. I've run into this exact scenario with fish growth data before, so here's what I'd recommend:

First: The Core Issue You're Facing #

That "either consistent coefficients or consistent variance estimates" problem almost always boils down to bad initial values or insufficient optimization iterations for the nonlinear mixed model. Nonlinear models are super sensitive to starting points—if you throw random initial values at nlme, it often converges to a local optimum where either the random effect variance gets squeezed to 0 (giving you stable fixed coefficients but useless variance estimates) or the variance estimates look reasonable but fixed coefficients drift.

Step 1: Fix Your Simulation & Initial Value Pipeline #

First, let's make sure your simulated data matches the structure you'd expect from real fish growth, then build up to the mixed model with solid starting values:

1.1 Simulate Realistic Logistic Growth Data with Random Effects #

Let's create data that mirrors your 3 groups, 129 individuals setup, with meaningful random variation in growth parameters:

set.seed(100)
n_ind <- 129
n_groups <- 3

# Group-level fixed parameters (asymptotic length L_inf, growth rate K, t0)
group_fixed <- data.frame(
  group = factor(1:n_groups),
  L_inf = c(50, 60, 70),
  K = c(0.1, 0.12, 0.08),
  t0 = c(0, 0.5, -0.3)
)

# Individual-level random effects (correlated for L_inf and K, realistic covariance)
rand_eff <- MASS::mvrnorm(n_ind, mu = c(0,0), Sigma = matrix(c(2, 0.005, 0.005, 0.001), ncol=2))

# Assign individuals to groups, generate time points per fish
ind_group <- sample(1:n_groups, n_ind, replace = TRUE)
n_obs_per_ind <- sample(5:10, n_ind, replace = TRUE) # Ensure each fish has enough observations

dat <- data.frame(
  id = rep(1:n_ind, n_obs_per_ind),
  group = rep(factor(ind_group), n_obs_per_ind),
  t = unlist(lapply(n_obs_per_ind, function(x) sort(runif(x, 0, 10))))
)

# Merge parameters and calculate observed length (with noise)
dat <- merge(dat, group_fixed, by = "group")
dat$rand_L <- rand_eff[dat$id, 1]
dat$rand_K <- rand_eff[dat$id, 2]
dat$L <- with(dat, (L_inf + rand_L)/(1 + exp(-(K + rand_K)*(t - t0)))) + rnorm(nrow(dat), 0, 1)

1.2 Fit with nlme Using Stable Initial Values #

Never start a mixed nonlinear model from scratch—first fit a fixed-effects only model to get reliable starting parameters, then feed those into the mixed model:

library(nlme)

# First: Fixed-effects only model to get initial values
fixed_model <- nls(L ~ L_inf/(1 + exp(-K*(t - t0))), 
                   data = dat,
                   start = list(L_inf = 60, K = 0.1, t0 = 0))
fixed_start <- coef(fixed_model)

# Now: Mixed-effects model with group-level fixed effects and individual random effects
mixed_model <- nlme(L ~ L_inf/(1 + exp(-K*(t - t0))),
                    data = dat,
                    fixed = L_inf + K + t0 ~ group,  # Group-specific fixed parameters
                    random = L_inf + K ~ 1 | id,     # Individual variation in L_inf and K
                    start = fixed_start,
                    control = nlmeControl(
                      maxIter = 1000,    # More iterations to avoid premature convergence
                      pnlsMaxIter = 500,
                      tolerance = 1e-6,  # Tighter tolerance for better convergence
                      msMaxIter = 1000
                    ))

summary(mixed_model)

This should give you both stable fixed coefficients (matching your simulated group parameters) and reasonable random effect variance estimates.

Step 2: Troubleshoot Your Real Data Model Crashes #

For your actual 129-fish dataset, the crashes are likely from one or more of these issues:

• Too few observations per individual: If some fish only have 1-2 time points, the model can't estimate random effects for them—filter these out.
• Outliers: Plot each individual's growth curve and remove points that clearly don't follow a Logistic trend (or use robust weighting in nlme with weights = varIdent() or weights = varPower()).
• Extreme group variation: If your 3 groups have wildly different asymptotic lengths/growth rates, try fitting separate fixed-effects models for each group first to confirm the Logistic model is appropriate for all groups.
• Overcomplicating random effects: Start with only random variation in L_inf (the most variable parameter in fish growth) before adding random effects to K or t0.

Alternative: Try nlmer from lme4 #

If nlme still gives you grief, lme4's nlmer uses a different optimization algorithm (L-BFGS-B) that sometimes handles tricky nonlinear mixed models better:

library(lme4)

nlmer_model <- nlmer(L ~ L_inf/(1 + exp(-K*(t - t0))) ~ (L_inf + K | id) + (L_inf + K | group),
                     data = dat,
                     start = fixed_start,
                     control = nlmerControl(optCtrl = list(maxfun = 20000)))

summary(nlmer_model)

Final Takeaway #

The key fix here is building up your model incrementally—start with fixed effects, validate the model structure, then add random effects with solid initial values. Don't jump straight to the most complex model; that's how you end up with convergence failures or inconsistent estimates.

内容的提问来源于stack exchange，提问作者Max13