Page 128 - IJPS-11-1

International Journal of
Population Studies Analysis of age-specific fertility in India

study the pattern of ASFRs. Modeling fertility behavior The general form of inverse k degree polynomial
th
is also beneficial for estimating fertility and facilitating model can be written as:
population projections. In this study, both types of
k
modeling techniques, that is, deterministic and non- fx a a x  (III)
i
deterministic, were explored, and a comparative study was 0 i1 i
also undertaken.
where ∈ is an error term follows (0,σ ), and here the
2
This paper is organized into five important sections. In aim is to choose a suitable value for k, which minimizes the
the first section, the background of the study is discussed. error sum of square (Gupta & Kapoor, 1997).
The second section deals with the information on the data
source and a detailed description of the methodologies From Equations II and III, we can obtain zero-degree
used in this study. The results of this study are given in the (constant), first-degree (linear), second-degree (quadratic),
third section. The discussion and conclusion are narrated third-degree (cubic), fourth-degree (bi-quadratic)
in the fourth and fifth sections, respectively. polynomial regression models and their reciprocal form
by putting the value of “k” as 0, 1, 2, 3, 4, −1, −2, −3, and
2. Data source and methodology −4, respectively.

2.1. Data source Age is a monotonic increasing function but probability
of bearing children in the later ages is lower than the
For this study, secondary data were collected from SRS- probability of childbearing for females in the younger
2020. SRS provides estimates of various demographic, ages. Therefore, we considered inverse of female age in
fertility, and mortality indicators based on the data the polynomial to examine notable changes (if any) in the
collected through annual sample surveys for both state predicted values of ASFR. The inverse of age of mother was
and national levels under the Ministry of Home Affairs, used as a variable in the polynomial model as it captures
Government of India. In this study, we considered ASFRs the declining trend of the fertility rate with increasing
for different age groups, viz. 15 – 19, 20 – 24, 25 – 29, 30 age (Pandey & Kour, 2019). Therefore, the inverse of
– 34, 35 – 39, 40 – 44, and 45 – 49, among total, rural, and age is a better predictor of fertility than only age. Using
urban women in India and considered TFRs of some bigger the inverse of age in polynomial models can improve the
states of India for the year 2020. To validate the proposed accuracy of these models and make them more useful for
best-fitted model, an additional data set on ASFR was understanding and forecasting fertility trends.
collected from the recent National Family Health Survey
(NFHS-5) 2019 – 2021, which is the fifth survey in a row 2.3. Model validation techniques
conducted by the International Institute for Population
Sciences (IIPS), Mumbai under the Ministry of Health and The model validation for the deterministic model can be
Family Welfare (MoHFW), Government of India. Here obtained using various measures such as cross-validation
ASFR is interpreted as the number of children born per prediction power (CVPP), shrinkage, F-test, velocity, and
1000 women in the respective age groups, and TFR refers elasticity curve. These techniques are discussed below in
to the total number of children born by a woman during detail.
her reproductive span. 2.3.1. Cross-validation prediction power
2.2. Polynomial regression model Here, we use CVPP to check the stability of the proposed
A polynomial relationship between age (x) and ASFR polynomial models, which is defined as (Stevens, 1996):
(y) of degree “k” is defined as (Van Der Waerdem, 1948; n 2 n 1
2
Spiegel, 1992): cvpp nn k 1 n k 2 1 R (IV)
1
2
2

3
f x
y a ax ax 2 2 ax ax k (I) where n is the total number of classes, k is the number
k
3
0
1
of regressors in the model, and R is the square of the
2
where a (≠0) is a constant, a (>0) is the coefficient of
i
0
x (i=1,2,3,…,k) correlation between observed and predicted values of the
i
dependent variable (i.e., ASFR) obtained from the fitting of
The above functional relationship can also be rewritten the different polynomial regression model.
as k degree polynomial model as:
th
2.3.2. Shrinkage
k
i
fx a a x  (II) In general, the higher the value of the coefficient of
i
0
2
i1 determination (R ), the better the model fits the data. To
Volume 11 Issue 1 (2025) 122 https://doi.org/10.36922/ijps.1338