Abstract

This paper demonstrates the estimation of the parameters in the Coale model for marital fertility by the maximum likelihood method, under the assumption of a simple Poisson process model. The necessary calculations are easily performed in the statistical computer program package GLIM, and the necessary commands are noted. Without access to GLIM, or any equivalent, it is still possible to fit the model approximately by the use of any weighted finear regression program. In both cases, goodness of fit tests are available.

References

Borgan, Ø. 1984. Maximum likelihood estimation in parametric counting process models, with applications to censored failure time data. Scandinavian Journal of Statistics 1–16.
Broström, G. (
1983
).
Estimation in a model for marital fertility
.
Sweden
:
Institute of Mathematical Statistics, University of Umeå
.
Coale, A. J. (
1971
).
Age patterns of marriage
.
Populations Studies
,
25
,
193
214
. 10.2307/2173210
Coale, A. J., & Trussell, T. J. (
1978
).
Technical note: Finding the two parameters that specify a model schedule for marital fertility
.
Population Index
,
44
,
203
213
. 10.2307/2735537
Haberman, S. J. (
1978
).
Analysis of Qualitative Data
.
New York
:
Academic Press
.
Kalbfleisch, J. D., & Prentice, R. L. (
1980
).
The Statistical Analysis of Failure Time Data
.
New York
:
John Wiley and Sons
.
Knodel, J. (
1977
).
Family limitation and the fertility transition: Evidence from the age patterns of fertility in Europe and Asia
.
Population Studies
,
31
,
219
249
. 10.2307/2173916
Knodel, J. (
1978
).
Natural fertility in pre-industrial Germany
.
Population Studies
,
32
,
481
510
. 10.2307/2173723
Lockridge, K., & Broström, G. (
1983
).
Coale and Trussell’s “m” visits Sweden, or, why do we get such lousy fits?
. In Lockridge, K. (Ed.),
The Fertility Transition in Sweden; A Preliminary Look at Smaller Geographic Units, 1855–1890
.
Sweden
:
The Demographic Data Base, University of Umeå
.
McCullagh, P., & Neider, J. A. (
1983
).
Generalized Linear Models
.
London
:
Chapman and Hall
.