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61 MATHEMATICAL POPULATION STUDIES, 1999, Vol. 7, N° 2
00.61.1 - MARTCHEVA, Maia; MILNER, Fabio A.
A two-sex age-structured population model: Well posedness.
In this paper we consider a two-sex population model proposed by Hoppenstead. We do not assume any special form of the mating function. We address the problem of existence and uniqueness of continuous and classical solutions. We give sufficient conditions for continuous solutions to exist globally and we show that they have in fact a directional derivative in the direction of the characteristic lines and satisfy the equations of the model with the directional derivative replacing the partial derivatives. The existence of classical solutions is established with mild assumptions on the vital rates.
English - pp. 111-129.
F. A. Milner, Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, U.S.A.
MILNER@Math.Purdue.edu.
(MATHEMATICAL DEMOGRAPHY, DEMOGRAPHIC MODELS, MATHEMATICAL MODELS.)
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00.61.2 - HENZ, Ursula; HUININK, Johannes.
Problems concerning the parametric analysis of the age at first birth.
The application of parametric split models to analyse the birth of the first child is discussed by applying the model of Coale and McNeil and the log-logistic model. We show that serious problems of estimating the final survival probability may occur when the empirical age distribution of the analysed event is not fully known and the model deviates considerably from the empirical distribution. We suggest strategies to handle these problems in a pragmatic way.
English - pp. 131-145.
U. Henz, Demography Unit, Stockholm University, 10691 Stockholm, Sweden.
ursula.henz@suda.su.se.
(MATHEMATICAL DEMOGRAPHY, DEMOGRAPHIC MODELS, EVENT HISTORY ANALYSIS, FIRST BIRTH, MATERNAL AGE.)
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00.61.3 - DENTON, Frank T.; SPENCER, Byron G.
How old is old? Revising the definition based on life table criteria.
Sixty-five has long been thought of as the point of entry into "old age." We propose a number of life table criteria for answering the following questions: If 65 was considered appropriate four decades ago, what is the corresponding age today? If 65 was (implicitly) a male-oriented definition four decades ago, as we believe it was, what would have been the appropriate definition for women at that time, and what is it today? We address these questions by applying our criteria to Canada, using 1951 and 1991 life tables, but the criteria could be applied equally well to other countries. For other developed countries we would expect broadly similar results.
English - pp. 147-159.
F. T. Denton and B. G. Spencer, Department of Economics, McMaster University, Hamilton, Ontario L8S 4M4, Canada.
dentonf@mcmaster.ca.
(CANADA, MATHEMATICAL DEMOGRAPHY, AGEING, AGE AT RETIREMENT, LIFE TABLES.)
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00.61.4 - SHAVELLE, Robert; STRAUSS, David.
A long period multistate life table using micro data.
The multistate life table (MLT) has been widely used by demographers for the past twenty years. However, the pivotal Markov condition upon which the entire methodology rests is rarely satisfied in practice. We lessen reliance upon the assumption by computing transition probabilities for longer periods of time than was previously practical. An extended Kaplan-Meier estimator accomplishes this task, simultaneously addressing the issue of censoring. This allows for the construction of a long period MLT. We provide an illustrative example of a 10-year period MLT, with comparison to a 1-year period MLT.
English - pp. 161-177.
R. Shavelle and D. Strauss, Department of Statistics, University of California, Riverside, CA 92521, U.S.A.
shavelle@citrus.ucr.edu.
(MATHEMATICAL DEMOGRAPHY, DECREMENT TABLES.)
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61 MATHEMATICAL POPULATION STUDIES, 1999, Vol. 7, N° 3
"The Indirect Estimation of Migration" Editor: Andrei Rogers
00.61.5 - ROGERS, Andrei; RAYMER, James.
Estimating the regional migration patterns of the foreign-born population in the Unites States: 1950-1990.
The regional distribution of the foreign-born population is determined by two principal migration processes: internal and external migration, modified, of course, by the impacts of mortality. (Since the fertility of the U.S. foreign-borns increases only the population of native-borns, it only needs to be included in studies of the regional distribution of the U.S. native-born population). In this paper, we apply model schedules to graduate data on the internal and external regional migration patterns of the foreign-born population for the 1950-1990 period. Prior to the graduation we "cleanse" the observed foreignborn data of obvious inconsistencies and errors arising from a small sample size. No observed data are available for emigration, forcing us to draw on methods of indirect estimation to obtain it. To find estimates of the unrecorded migration flows in-between the four census-defined periods in our study (that is, for 1950-1955, 1960-1965, 1970-1975, and 1980-1985) we interpolate between the data of adjacent census time periods. Finally, we combine the estimated migration data with the corresponding mortality data to calculate and analyze the multiregional life tables and projections associated with each five-year time interval.
English - pp. 181-216.
A. Rogers and J. Raymer, Population Program, Institute of Behavioral Science, University of Colorado, Boulder, Colorado 80309-0484, U.S.A.
(UNITED STATES, FOREIGNERS, INTERNAL MIGRATION, INTERNATIONAL MIGRATION, ESTIMATES, MODELS.)
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Assessing structural change in U.S. migration patterns: A log-rate modeling approach.
A set of log-rate models is proposed to transform Rogers and Wilson's accounting-based migration models into statistics-oriented migration models. This study demonstrates not only how log-rate models can be used to replicate results generated from Rogers-Wilson's cohort and multi-region mobility models, but also how log-rate models can be used to make statistical inferences and to derive more parsimonious models. Estimation issues and model fit are discussed, and case studies with U.S. mobility and interregional migration data are provided. The flexibility of log-rate models is emphasized, and possible uses for such models, such as the testing of various hypotheses and migration projection, are explored. Potential applications and limitations of log-rate models are also discussed.
English - pp. 217-237.
G. Lin, Department of Geography and Center on Aging, P.O. box 3050, University of Victoria, Victoria, BC V8W 3P5, Canada.
(UNITED STATES, INTERNAL MIGRATION, MODELS, METHODOLOGY.)
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Modeling approaches to the indirect estimation of migration flows: From entropy to EM.
The paper presents probability models to recover information on migration flows from incomplete data. Models are used to predict migration and to combine data from different sources. The parameters of the model are estimated from the data by the maximum likelihood method. If data are incomplete, an extension of the maximum likelihood method, the EM algorithm, may be applied. Two models are considered: the binomial (multinomial) model, which underlies the logit model and the logistic regression, and the Poisson model, which underlies the loglinear model, the log-rate model and the Poisson regression. The binomial model is viewed in relation to the Poisson model. By way of illustration, the probabilistic approach and the EM algorithm are applied to two different missing data problems. The first problem is the prediction of migration flows using spatial interaction models. The probabilistic approach is compared to conventional methods, such as the gravity model and entropy maximization. In fact, spatial interaction models are particular variants of log-linear models. The second problem is one of unobserved heterogeneity. A mixture model is applied to determine the relative sizes of different migrant categories.
English - pp. 239-278.
F. Willekens, Population Research Centre, University of Groningen, Netherlands.
(METHODOLOGY, MODELS, MIGRATION FLOW, ESTIMATES, COMPARATIVE ANALYSIS.)
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Model-based incomplete data analysis with an application to occupational mobility and migration accounts.
In many planning and policy research settings available secondary data sources may be incapable of answering pertinent research questions because certain variable combinations are unavailable. One solution to this constraint is to try to construct the desired data using information from multiple data sources and prior information. Current methods for accomplishing this task tend to focus predominantly on updating transaction matrices (input-output tables, transportation flows, or interregional migration accounts) and emphasize an algorithmic approach to the problem. This paper attempts to broaden the applications and generalize the solution by extending the model-based approach to incomplete data analysis advocated by Willekens (1982). The log-linear model is presented here as a flexible platform for incomplete data analysis and a path diagram describes several alternative modeling approaches; different paths are determined by the level of available information. The paper concludes with an application to incomplete occupational migration and mobility tables.
English - pp. 279-305.
S. H. Sweeney, University of California at Santa Barbara, U.S.A.
(METHODOLOGY, MODELS, DEFECTIVE DATA, MIGRATION, OCCUPATIONAL MOBILITY.)
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