Model Initialization and Parameter Constraints

Description

Guidance on supplying starting values through argument start in gamlss2 and on fixing distribution parameters via fixed in gamlss2_control.

Details

The start argument can be used to initialize estimation in several ways. Supported inputs include:

  • a named numeric vector or list giving one starting value per distribution parameter, such as mu, sigma, nu, or tau;

  • a data frame or matrix with one column per distribution parameter and one row per observation, providing starting values for the full additive predictors on the link scale;

  • a fitted “gamlss2” object, in which case fitted() values are used as starting values for all distribution parameters;

  • a coef.gamlss2 object, allowing coefficient-wise initialization of linear and smooth terms.

Parameters can be fixed during estimation using the fixed control argument. This is useful, for example, when shape parameters should remain constant while the remaining parameters are estimated.

Starting values from a previous fit can reduce optimizer iterations. For coefficient-wise initialization, coef(object, full = TRUE) includes smooth coefficients; lambdas = TRUE also includes smoothing parameters. Compare iteration counts using the same model, observations, and controls.

See Also

gamlss2, gamlss2_control, RS

Examples

library("gamlss2")


## hold the smoothing parameter fixed for comparable refits
f <- Ozone ~ s(Wind, sp = 1) | 1
ctrl <- gamlss2_control(maxit = 100, eps = 1e-7)

## scalar starting values for the distribution parameters
m1 <- gamlss2(f, data = air, family = GA,
  start = c(mu = 200, sigma = 0.1), control = ctrl)

## reuse fitted additive predictors on the link scale
m2 <- gamlss2(f, data = air, family = GA,
  start = fitted(m1, type = "link"), control = ctrl)

## coef() without full = TRUE initializes only the linear coefficients
m3 <- gamlss2(f, data = air, family = GA,
  start = coef(m1), control = ctrl)

## reuse all linear and smooth coefficients from the previous fit
m4 <- gamlss2(f, data = air, family = GA,
  start = coef(m1, full = TRUE, lambdas = TRUE, dropall = FALSE),
  control = ctrl)

## full coefficient starts reduce iterations in this example
## check convergence and compare the final log-likelihoods as well
fits <- list(scalar = m1, predictors = m2, linear = m3, full = m4)
data.frame(
  iterations = sapply(fits, function(m) m$iterations),
  converged = sapply(fits, function(m) m$converged),
  logLik = sapply(fits, function(m) as.numeric(logLik(m)))
)

## fix BCT shape parameters at their supplied starting values
m5 <- gamlss2(Ozone ~ s(Wind, sp = 1) | 1 | 1 | 1,
  data = air, family = BCT,
  start = c(mu = 200, sigma = 0.1, nu = 1, tau = 10),
  fixed = c(nu = TRUE, tau = TRUE), maxit = 100)

## fixed flags must also be supplied when reusing coefficients
m6 <- gamlss2(Ozone ~ s(Wind, sp = 1) | 1 | 1 | 1,
  data = air, family = BCT,
  start = coef(m5, full = TRUE, dropall = FALSE),
  fixed = c(nu = TRUE, tau = TRUE), maxit = 100)
unique(fitted(m6, parameter = c("nu", "tau")))