Page 331 - Special Topic Session (STS) - Volume 3

STS547 Maarten C. et al.
total is Māori. For the Census the estimated number is 721,971. For the MOH
it is 640,711.
3.2 Four registers
We now add the other two registers, DIA and MOE, to the analysis. Now
the maximal model is [ABCd][ABDc] [ACDb][BCDa] [ABcd][ACbd] [ADbc][BCad]
[BDac][CDab] [Abcd][Bacd] [Cabd] [Dabc][abcd]. Notice that, as for the two
registers, a capital variable label cannot be in the same interaction term as a
lower case variable label, as these interactions cannot be estimated from the
data. Notice that the assumptions become less and less demanding as more
registers are involved. The number of unique individuals in the four linked
registers is 4,401,282, and the estimated number missed by all registers is
25,939, giving an estimated population size of 4,427,221.
The estimated numbers of Maori are displayed in Table 2. To arrive at a
final estimate of the number of non-Māori and Māori we describe two
approaches, both using the concept of measurement error. Consider the
margins of the ethnicity variables a; b; c and d of the four registers. A statistical
approach to measurement error is to make use of a latent class model
(McCutcheon, 1987). See Table 3. In this latent class model, the first latent class
is to be interpreted as the class for non-Māori, and the estimated probability
of falling in this class is 0.826. The probability for the Māori class corresponds
to an estimated Māori population size of about 770,000. Estimated conditional
probabilities of being Māori for each latent class are also shown in Table 3;
they are consistently low for the non-Māori latent class and high for the Māori
latent class.
Panel 1: Observed counts
C = 1 C = 0 Totals
c = 0 c = 1 c = - c = x
A = 1 a = 0 3,004,329 31,998 150,855 38,640 3,225,822
a = 1 108,192 435,468 12,402 4,377 530,439
a = - 16,512 2,769 894 435 20,160
A = 0 a = x 398,838 146,985 24,642 - 570465
Totals 3,527,871 617,220 188,793 43,452 4,377,336
Panel 2: Fitted values under [Ac][ac][Ca]
C = 1 C = 0 Totals
c = 0 c = 1 c = 0 c = 1

A = 1 a = 0 3,170,298.4 33,791.2 38,619.1 411.6 3,243,120.3
a = 1 111,244.8 448,084.6 879.3 3,541.9 563,750.6
A = 0 a = 0 402,713.4 10,772.5 4,905.7 131.2 418,522.8
a = 1 14,131.1 142,848.3 111.7 1,129.2 158,220.3
Totals 3,698,387.7 635,496.6 44,515.8 5,213.9 4,383,613.7

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