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CPS1965 Chin Tsung R. et al.

More specifically, an m-knot model can be expressed as

where (, ), , 0, ( = 0,1,2), ( = 0,1, … , ), 0, ( = 0,1,2) and
,
( = 0,1, … , ) are the parameters to be estimated. The functions (),
,
() ( = 1,2) and () ( = 0,1, … , ) are defined in equations (6), (7)
0

and (8) depending on the restriction above the last knot, . Depending on

application of linear or quadratic restrictions below the first knot, we set
() = () = 0 () = 0 respectively.
0
02
0

3. Results and Discussion
The modified LC model was applied to the Malaysian mortality data (1991-
2015) obtained from the Department of Statistics Malaysia. We used the
middle point of the age period to represent the age group since the data is
only available in intervals. To select a suitable model, we will select the model
from a selection of candidate models with the lowest residual deviance. For
ease of computation, we added 1 to as it is undefined at 0. The number of
knots available in the data is small due to the lack of granularity of the age
groups. As such, 3 sets of knots(see Figure 1 for shape of curve) were selected
i.e. {7,12,17,22,27}, {12, 22, 27,32} and {17,22,27}. The models listed in Table 1
are based on gender, additive function, restriction on the tail, number of
parameters and the residual deviance for each model. We used the ‘glm’ and
‘logit’ link in R to fit the logistic regressions.
In general, it is observed (Figure 1) that the mortality rate decreases from
birth (age group 0) until age group 12 and increases thereafter. It also appears
that the change in death rates for younger age groups is more significant than
the change in mortality rates for older ages. Compared to the female mortality
rate, male mortality is generally higher for all age groups. Additionally, it is
observed that there is a significant increase in mortality rate between age
groups 17 and 22 for male mortality data compared to female mortality data.
We considered Male 1 and Female 1 to be the best models for each
gender. The parameters and their corresponding p-values are listed in
Table 2. From Table 2, it is observed all the parameters of Male 1 and Female
1 are significant.

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