The metagam package offers a way to visualize the heterogeneity of the estimated smooth functions over the range of explanatory variables. This will be illustrated here.
Simulation
We start by simulating 5 datasets using the gamSim()
function from mgcv. We use the response
and the explanatory variable
,
but add an additional shift
where
differs between datasets, yielding heterogeneous data.
library("mgcv")
#> Loading required package: nlme
#> This is mgcv 1.9-3. For overview type 'help("mgcv-package")'.
set.seed(1233)
shifts <- c(0, .5, 1, 0, -1)
datasets <- lapply(shifts, function(x) {
## Simulate data
dat <- gamSim(scale = .1, verbose = FALSE)
## Add a shift
dat$y <- dat$y + x * dat$x2^2
## Return data
dat
})Fit GAMs
Next, we analyze all datasets, and strip individual participant data.
models <- lapply(datasets, function(dat){
b <- gam(y ~ s(x2, bs = "cr"), data = dat)
strip_rawdata(b)
})Meta-Analysis
Next, we meta-analyze the models. Since we only have a single smooth
term, we use type = "response" to get the response
function. This is equivalent to using type = "iterms" and
intercept = TRUE.
meta_analysis <- metagam(models, type = "response")Next, we plot the separate estimates together with the meta-analytic fit. We see that dataset 3, which had a positive shift , lies above the others for close to 1, and opposite for dataset 5.
plot(meta_analysis, legend = TRUE)
We can investigate this further using a heterogeneity plot, which visualizes Cochran’s Q-test (Cochran (1954)) as a function of . By default, the test statistic (Q), with 95 % confidence bands, is plotted. We can see that the confidence band for Q is above 0 for larger than about 0.7.
plot_heterogeneity(meta_analysis)
We can also plot the -value of Cochran’s Q-test. The dashed line shows the value . The -value plot is in full agreement with the Q-statistic plot above: There is evidence that the underlying functions from each dataset are different for values from about 0.7 and above.
plot_heterogeneity(meta_analysis, type = "p")