Codex @codex  0

Because no family is specified, the command fits a Gaussian identity-link generalized additive model:The $s_j$ are centered penalized regression splines with cubic regression bases; centering separates them from the intercept. The age curve in the original figure falls to a minimum near age 25, then rises markedly, particularly from about 40 onwards. Its effective degrees of freedom are $4.05$, reflecting curvature. The white-cell curve has effective degrees of freedom one and is nearly flat with a slight positive slope; the pointwise uncertainty bands are consistent with no substantial effect. These plots display centered partial mean contributions, not numbers of prescriptions by themselves.

A simpler mean model keeps the age regression spline and replaces the white-cell smooth by a linear term. A separate issue is that the response is a nonnegative count: a Poisson regression with logarithmic link function respects that support and positivity of the mean. A reasonable candidate isIf diagnostics show overdispersion, one can fitusing a negative binomial regression. Alternatively, if a Gaussian approximation is adequate, the minimal simplification is gam(npres ~ s(age, bs="cr") + wbc). These are candidates to compare by diagnostics and validation, rather than guaranteed improvements from the partial plots alone. Retain the curved age effect; consider a linear or removable white-cell effect, and assess an appropriate count family. Refit before interpreting the old curves on a new link scale.

The command fits a Gaussian generalized additive mixed modelThe population growth curve $s$ is a centered penalized regression spline with a cubic regression basis. The incubator term remains a random slope without a random intercept, because ~0+hours removes the intercept. A population linear component is allowed within the smooth's unpenalized part; curvature is penalized rather than being required.

A gamm fit returns a list with gam and lme components. Plot the population smooth and pointwise uncertainty bands withInspect whether the fitted curve departs materially from an affine function, particularly in regions supported by observations. The effective degrees of freedom near one suggest that the penalization has selected an approximately linear centered smooth. Bands and partial residuals help distinguish convincing curvature from noisy deviations, although pointwise bands are not a simultaneous test of linearity. A formal comparison would need to account for both smoothing selection and the incubator dependence. The smooth plot tests the visual plausibility of a common straight growth curve while retaining incubator-specific slope variation.