Date of Award


Degree Type


Degree Name

Doctor of Philosophy


This thesis examines various mathematical models suitable for the analysis of event histories. The models discussed include Coale-McNeil model, Cox's model, and parametric failure time models. All these models are applied to data on age at first marriage and first birth, obtained from the Canadian Fertility Survey of 1984. The extended Coale-McNeil model to incorporate covariates has been examined. The covariates considered are place of residence, education, work, first birth status, and religion. The results of the model indicate that fewer young Canadian women are expected to marry compared to the older ones. The application of the Coale-McNeil model to first birth got limited support. Higher education, urban residence, working, and having the first birth in marriage are the covariates associated with later age at first marriage and first birth.;The Cox's proportional hazard model has been applied to the study of age at first marriage and first birth. The parametric failure time models examined include exponential, weibull, loglogistic and lognormal. The regression models are formulated by specifying the parameters as a function of covariates. All four models considered are fitted, first without covariates, and later with the five covariates, for each birth cohort of women. The full model consisting of the covariates, was found to be significantly better than the null model with the exception of the exponential for certain cohorts. The estimated survival probabilities from the parametric models were examined in relation to the Kaplan-Meier estimates. The lognormal and loglogistic models provide consistent estimates compared to the weibull model. Though these models provide good estimates up to the age at which data are available, they perform poorly beyond that point. The results from all the models indicate similar trends and patterns across birth cohorts. Some of the available computer software for estimation of parameters in various models is reviewed.;The log likelihood statistic across cohorts and among models within cohorts are examined. The loglogistic and the lognormal emerge as preferred models among the parametric models, which provide reasonable fit across birth cohorts. The thesis ends by calling for more research on heterogeneity, and an examination of the parametric failure time models.



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