Gaussian examples

Use family = "gaussian" for continuous responses. This page shows TDMM workflows for both repeated observations (random_intercept = TRUE) and independent observations (random_intercept = FALSE). Coefficient functions are on the response scale. Because the examples are simulated, the true coefficient functions are known.

Repeated observations

This repeated-observation example uses irregular observation times, unequal visit counts, one baseline covariate, and one covariate measured at each visit.

set.seed(27181)
truth <- function(t) cbind(beta0 = sin(2*pi*t),
                           beta1 = cos(2*pi*t),
                           beta2 = 1.5*(t-0.5))
dat <- do.call(rbind, lapply(seq_len(40), function(i) {
  n <- sample(5:8, 1)
  time <- sort(runif(n))
  baseline <- rnorm(1)
  changing <- rnorm(n)
  b <- rnorm(1, sd=sqrt(0.5))
  beta <- truth(time)
  y <- rnorm(n, beta[,1] + baseline*beta[,2] + changing*beta[,3] + b,
             sd=sqrt(0.1))
  data.frame(id=paste0("person-",i), time=time, y=y,
             baseline=baseline, changing=changing)
}))

library(TDMM)
fit <- tdmm(dat, family="gaussian", subject.var="id",
            time.var="time", y.var="y",
            x.var=c("baseline","changing"), n_basis=8,
            random_intercept=TRUE,
            control=tdmm_control(chains=3, iterations=4000,
              burn_in=1500, thin=2, adapt=2000, seed=77181),
            priors=tdmm.priors("gaussian"))
summary(fit)
plot(fit)
plot.trace.tdmm(fit,c("sigma.b","sigma2.e","tau.alpha[1]"))

Compare the reconstructed curves with truth() and examine the pointwise credible bands. The Getting Started guide explains the scales and diagnostics and illustrates recovery from a larger repeated-observation Gaussian dataset.

Independent observations

The Gaussian simulation helper can also generate one observation per subject. In an independent-observation study, time may represent age, time since an event, or time relative to an event.

independent_data <- data.gen.tdmm.gauss(random_intercept = FALSE, seed = 27181)
fit_independent <- tdmm(independent_data, family = "gaussian",
                        x.var = c("x1", "x2"),
                        random_intercept = FALSE,
                        control = tdmm_control(seed = 77181))
summary(fit_independent)
plot(fit_independent)