which is called a spline function. The final approximate to an

function is defined as below, where ݂ଵሺݔሻ, ݂ଶሺݔሻ and ݂ଷሺݔሻ are

roximate functions for three segments,

ݏሺݔሻൌቐ

݂ଵሺݔሻ

ݔ∈ሾݔ௦௧௔௥௧, ݔଵሿ

݂ଶሺݔሻ

ݔ∈ሾݔଵ,

ݔଶሿ

݂ଷሺݔሻ

ݔ∈ሾݔଶ, ݔ௘௡ௗሿ



multivariate regression problem, a GAM model can be re-written

, where K is the number of independent variables, ݔ௜ is the i^th

ent variable and ߚ௜ is its spline coefficient,

ݕൌߚ଴൅෍ߚ௜ݏሺݔ௜ሻ

௄

௜ୀଵ

൅ߝ



has also been applied to biological/medical research. For

it has been applied to examine how the heat stress impact on

ws [Benni, et al., 2020] and used in a haemorrhagic fever research

t al., 2019].

is an R package called gam for using GAM to analyse data. The

n is also named as gam in that package and its format is shown

here df is the degrees of freedom for a spline function

gam(y~s(x,df),⋯)

eate the confidence bands for a GAM model, the predict

should be called, in which a constructed GAM model (model) is

he first input.

predict(model,type='link',se.fit=TRUE)

employs the Akaike information criterion (AIC) [Akaike, 1981]

l optimisation, i.e., selecting the order (degrees of freedom) of

mployed in a model. Figure 4.15 shows an example of using this

for a nonlinear regression problem with three different degrees of

(being 3, 5 and 7), where the confidence bands and AIC values