Page 75 - IJPS-8-2
P. 75
International Journal of
Population Studies Projecting sex ratio at birth in Pakistan
new g b g new g new g After generating the simulated values, we calculate
new
t t t results as described for the out-of-sample validation
(Appendix C.1.1).
g
g
Where the simulated new , new and
t t Appendix D. Validation and simulation results
new g refer to a “new” province without data. This Table D.1 summarizes the results of the left-out SRB
simulation follows the model specifications of these observations in the out-of-sample validation exercise and
parameters without considering any province-specific one-province simulation. The median errors are nearly zero
g
data. In particular, new is simulated as: in the left-out observations. Although the median absolute
t errors are slightly higher than the median errors, the average
( ) 2 coefficient of variance of the absolute errors for left-out
( ) g
σ
( ) ) observations (calculated as absolute errors divided by the
( ) g
log Φ (new t ∼ 0, 2 , if t = 1980, left-out observation values) is only 5.6%. The coverage of
( )
−ρ ( ) g 1 the 95% and 80% prediction intervals is more conservative
than expected. The wider-than-expected prediction interval
( ) ) ( ) g ( ) )
( ) g
( ) g
log Φ (new t = ρ log Φ (new t −1 in the left-out observations can be primarily attributed to
larger uncertainty in more recent observations.
+ t ( ) g , if t ∈ {1981, ,2020}, Table D.2 compares the model estimates obtained
from the full dataset and the training set in the out-of-
2
g
,
ε t g ii d.. . N 0 ε . sample validation exercise. Here, we examined the model
estimates of the true SRB Θ and the inflation process with
p,t
province-specific probability δ α . The median errors and
(g)
δ (new) is simulated as: the median absolute errors are close to zero.
p p,t
g
g
logit g , g 2 , new g ,
In summary, the validation results indicate reasonably
g
new is simulated as: good calibrations and prediction power of the inflation
model with conservative credible intervals.
t
Table D.1. Validation and simulation results for left‑out SRB
g 0060 006., . 2 , g ., . 2 observations
11 01 1 ,
0, 1 , 0
2 g , 0 ., . 2 3 g 0 ,inf ., . 2 Validation out Simulation
76 08 ,
16 11 6 ,
of sample
t 0 g 1970 2050, # Province in test dataset 6 8
,
Median error 0.020 0.003
( ) g
α (new ) ( ξ = ( ) g / λ ( ) g )( t −t ( ) g ) , if t ( ) g <<t t ( ) g , Median absolute error 0.047 0.071
t 1 0 0 1 Below 95% prediction interval (%) 0.0 0.2
α (new ) ( ) g = ξ ( ) g , if t ( ) g <<t t ( ) g Above 95% prediction interval (%) 0.0 3.2
Expected (%)
2.5
2.5
t 1 2
α (new ) ( ) g = ξ ( ) g ( ξ − ( ) g / λ ( ) g )( t −t ( ) g ) , if t ( ) g <<t t ( ) g Below 80% prediction interval (%) 0.0 7.6
9.2
8.0
Above 80% prediction interval (%)
t p 3 2 2 3
Expected (%) 10 10
α ( ) ( ) g =new 0, if t < ( ) g ort t ( ) g Note: Error is defined as the difference between a left-out SRB observation
> t
t 0 3
and the posterior median of its predictive distribution. SRB observations
Where, with data collection years since 2018 are left out. Numbers in the parentheses
after the proportions indicate the average number of left-out observations
g
g
g
t 1 g t 0 g , t 2 g t 1 g , t 3 g t 2 g . that fall below or above their respective 95% and 80% prediction intervals.
2
1
3
Volume 8 Issue 2 (2022) 69 https://doi.org/10.36922/ijps.v8i2.332
