Page 43 - Contributed Paper Session (CPS) - Volume 6

CPS1484 Neela A Gulanikar et al.
2.2 Test Procedure
Suppose we have n distinct education levels. Hence, the total population
TF of females and total population TM of males can be partitioned into n
disjoint groups each. Suppose the respective population sizes be denoted
by M1,M2,...,Mn and F1,F2,...,Fn. From the definition, it is clear that

, and .
Further, suppose ψij denotes the number of marriages between a female
th
th
from i level and a male from j level and ρij denotes the rate of marriages
th
between females from i level and males from j level in a given year. Our
th
aim is to examine if the values of ρij remain constant over the years. ψ and
ρ denote the m × m matrices of ψij and ρij respectively.
Given the data on number of marriages across each educational level, i.e.,
ψ, we first try to estimate ρ. For estimating ρ, any of the following three
formulae can be used.
 HMF: ̂ = ( + )

2
 GMF: ̂ =

√
 MF: ̂ = { , }

To determine which of the three estimates works well, we can compute
the fitted values of ψij by substituting ̂ the marriage functions given in the

above subsection.
̂
Once the best estimation method is chosen, we use those ℎij computed
from two different years to determine whether the difference between the
marriage rates across different subgroups is significant. To determine the
significance of the test statistic, we use cutoffs based on parametric bootstrap.
The procedure is described below.
Suppose ̂ be the estimate of marriage rate matrix for the first year. Using
1
the best marriage function chosen above, we simulate the matrices and
using this estimate of marriage rate matrix for both the years. We then
estimate the marriage rate matrices corresponding to these bootstrapped
matrices for number of marriages. Suppose the two estimates are denoted by
and . We then compute the mean of squared relative differences for these
two matrices. We repeat this procedure B(= say,5000) times and hence obtain
B values of the mean of squared relative differences. This constitutes a sample
of B mean of squared relative differences under the null hypothesis (as we
have used only the estimate of ρˆ1). The 95 percentile of this difference can
th
be used as the cutoff. If the actual value of the mean of squared relative
differences between ρˆ1 and ρˆ2 is greater than the above cutoff, we reject the
null hypothesis and conclude that there is a significant change in the marriage
rates between the two time points under study.

32 | I S I W S C 2 0 1 9