Carl P Schmertmann
Biographic Data
| ID | 3594644 |
|---|---|
| NAME | Carl P Schmertmann |
| GIVEN NAMES | Carl P |
| FAMILY NAME | Schmertmann |
| SIGNATURE | SCHMERTMANN C P |
| AFFILIATIONS | Florida State University |
| ORCID | 0000-0001-6066-2418 |
| VERIFIED | Yes |
| TOTAL WORKS | 26 |
| TOTAL CITATIONS | 155 |
| AUTHOR COUNT | 26 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1992 |
| LATEST PUBLICATION YEAR | 2024 |
| H-INDEX | 8 |
Commentary on van Raalte et al.’s “The Dangers of Drawing Cohort Profiles From Period Data: A Research Note”
van Raalte et al. (2023) alerted demographers to the potential dangers of calculating cohort measures from the “diagonals” of gridded age–period (AP) data. In the case of cohort fertility, however, a minor change to the estimation procedure can mitigate the trend and cohort size biases that the authors identify. With an appropriate algorithm, researchers can estimate cohort fertility indices from AP data quite well
Data errors in mortality estimation: Formal demographic analysis of under-registration, under-enumeration, and age misreporting
BACKGROUNDOmissions and misreported ages in both death and exposure data cause bias in mortality and life expectancy estimates.Most discussions of data errors have focused on a single type of error only, and most rely on empirical examples rather than formal analysis. OBJECTIVEWe wish to analyze data errors and their interactions in a single, coherent framework in which all three of the major data problems -death under-registration, census undere…
D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties
High-dimensional parametric models with penalized likelihood functions strike a good balance between bias and variance for estimating continuous age schedules from large samples. The penalized spline (P-spline) approach is particularly useful for these pur
Population Pyramids Yield Accurate Estimates of Total Fertility Rates
The primary fertility index for a population, the total fertility rate (TFR), cannot be calculated for many areas and periods because it requires disaggregation of births by mother’s age. Here we discuss a flexible framework for estimating TFR using inputs as minimal as a population pyramid. We develop five variants, each with increasing complexity and data requirements. We test accuracy across a diverse set of data sources that comprise more tha…
Revivorship and life lost to mortality
Some formal demographic models describe mortality improvement in terms of averted deaths. In such models individuals who would have died in an earlier regime are instead revived and returned to the population to face the same age-speciï¬ c mortality risks as
Bayesian Estimation of Age-Specific Mortality and Life Expectancy for Small Areas With Defective Vital Records
High sampling variability complicates estimation of demographic rates in small areas. In addition, many countries have imperfect vital registration systems, with coverage quality that varies significantly between regions. We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with…
Estimating age- and sex-specific mortality rates for small areas with Topals regression: An application to Brazil in 2010
High variability in recorded vital events creates serious problems for small-area mortality estimation by age and sex. Many existing approaches to fitting local mortality schedules, including those most often used in Brazil, estimate rates by making rigid mathematical assumptions about local age patterns. Such methods assume that all areas within a larger area (for example, microregions within a mesoregion) have identically-shaped log mortality s…
Calibrated spline estimation of detailed fertility schedules from abridged data1
I develop and explain a new method for interpolating detailed fertility schedules from age-group data. The method allows estimation of fertility rates over any fine grid of ages, from either standard or non-standard age groups. The new method, called the calibrated spline (CS) estimator, expands an abridged fertility schedule by finding the smooth curve that minimizes a squared error penalty. The penalty is based both on fit to the available age-…
Changes in Service Delivery Patterns After Introduction of Telemedicine Provision of Medical Abortion in Iowa
Objectives. We assessed the effect of a telemedicine model providing medical abortion on service delivery in a clinic system in Iowa. Methods. We reviewed Iowa vital statistic data and billing data from the clinic system for all abortion encounters during the 2 years prior to and after the introduction of telemedicine in June 2008 (n = 17 956 encounters). We calculated the distance from the patient’s residential zip code to the clinic and to the …
Bayes plus Brass: Estimating total fertility for many small areas from sparse census data
Estimates of fertility in small areas are valuable for analysing demographic change, and important for local planning and population projection. In countries lacking complete vital registration, however, small-area estimates are possible only from sparse survey or census data that are potentially unreliable. In these circumstances estimation requires new methods for old problems: procedures must be automated if thousands of estimates are required…
Stationary populations with below-replacement fertility
A population with sustained below-replacement fertility and constant immigration eventually becomes stationary. Stationary-through-immigration (SI) populations have unusual age structures that depend on the distribution of immigrants' arrival ages
Knox meets Cox: Adapting epidemiological space-time statistics to demographic studies
Many important questions and theories in demography focus on changes over time, and on how those changes differ over geographic and social space. Space-time analysis has always been important in studying fertility transitions, for example. However, demographers have seldom used formal statistical methods to describe and analyze time series of maps. One formal method, used widely in epidemiology, criminology, and public health, is Knox’s space-tim…
Mapping the Timing, Pace, and Scale of the Fertility Transition in Brazil
Between 1960 and 2000, fertility fell sharply in Brazil, but this transition was unevenly distributed in space and time. Using Bayesian spatial statistical methods and microdata from five censuses, we develop and apply a procedure for fitting logistic curves to the fertility transitions in more than 500 small regions of Brazil over this 40-year period. Doing so enables us to map the main features of the Brazilian fertility transition in considera…
Exploratory Analysis of Spatial Patterns in Brazil’s Fertility Transition
Empirical bayes estimation of demographic schedules for small areas
In this article, we analyze empirical Bayes (EB) methods for estimating small-area rate schedules. We develop EB methods that treat schedules as vectors and use adaptive neighborhoods to keep estimates appropriately local. This method estimates demographic rates for local subpopulations by borrowing strength not only from similar individuals elsewhere but also from other groups in the same area and from regularities in schedules across locations.…
Quadratic spline fits by nonlinear least squares
This web program fits a Quadratic Spline model, as described in Schmertmann (2003; Demographic Research Volume 9, Article 5), to any empirical fertility schedule supplied by the user. The fit minimizes the sum of squared differences between the empiri
A system of model fertility schedules with graphically intuitive parameters
I propose and examine a new family of models for age-specific fertility schedules, in which three index ages determine the schedule's shape. The new system is based on constrained quadratic splines. It has easily interpretable parameters, is flexible e
A Simple Method for Estimating Age-Specific Rates from Sequential Cross Sections
I develop and demonstrate a simple formula for estimating age-specific event rates for a period from "before" and "after" cross sections. The general approach applies to a wide range of estimation problems in demography, the social sciences, and epidemiology. The method arises from the formal mathematics of unstable populations and is similar in spirit to "variable-r" methods. Unlike those methods, however, the new technique does not require spec…
A Simple method for estimating age-specific rates from sequential cross sections
I develop and demonstrate a simple formula for estimating age-specific event rates for a period from “before” and “after” cross sections. The general approach applies to a wide range of estimation problems in demography, the social sciences, and epidemiology. The method arises from the formal mathematics of unstable populations and is similar in spirit to “variable-r” methods. Unlike those methods, however, the new technique does not require spec…
Fertility and development: Evidence from Brazil
Using microdata from the Brazilian demographic censuses of 1960, 1970, 1980, and 1991, aggregated into 518 consistently defined spatial units called microregions, we estimated fertility and mortality and constructed indicators of development and living conditions in the rural and urban areas of the microregions in each census. We then estimated cross-sectional and fixed-effects models to answer questions about the degree to which changes in these…
Fertility estimation from open birth-interval data
Censuses and surveys frequently collect information on period fertility through questions on the timing of last births. The standard approach to estimating fertility with open-interval data uses the proportion of women giving birth in the year before the interview. I propose a more efficient, maximum likelihood method for estimating fertility from open-interval data. I illustrate a mathematical derivation of the new method, perform sensitivity an…
Estimating Parametric Fertility Models with Open Birth Interval Data
In the past thirty years, more than 100 censuses gathered fertility data through questions on women's date of last birth. The standard "births last year" (BLY) approach for such data truncates timing information, using binary indicators for births in t
Three strikes and you're out: Demographic analysis of mandatory prison sentencing
Much of the debate about the costs and benefits of “three-strikes” laws for repeat felony offenders is implicitly demographic, relying on unexamined assumptions about prison population dynamics. However, even state-of-the-art analysis has omitted important demographic details. We construct a multistate life-table model of population flows to and from prisons, incorporating age-specific transition rates estimated from administrative data from Flor…
An introduction to nonparametric regression in demographic research
Immigrants’ ages and the structure of stationary populations with below-replacement fertility
A sustained regime of low fertility plus immigration yields an unusual kind of stationary population. The author demonstrates that all stationary populations have a common structure, and that the familiar replacement-level fertility population is the youngest among the many stationary populations corresponding to a particular life table. This finding has important consequences for policy because although fertility increase and immigration are equ…
Fertility and development: Evidence from Brazil
Using microdata from the Brazilian demographic censuses of 1960, 1970, 1980, and 1991, aggregated into 518 consistently defined spatial units called microregions, we estimated fertility and mortality and constructed indicators of development and living conditions in the rural and urban areas of the microregions in each census. We then estimated cross-sectional and fixed-effects models to answer questions about the degree to which changes in these…
Mapping the Timing, Pace, and Scale of the Fertility Transition in Brazil
Between 1960 and 2000, fertility fell sharply in Brazil, but this transition was unevenly distributed in space and time. Using Bayesian spatial statistical methods and microdata from five censuses, we develop and apply a procedure for fitting logistic curves to the fertility transitions in more than 500 small regions of Brazil over this 40-year period. Doing so enables us to map the main features of the Brazilian fertility transition in considera…
Empirical bayes estimation of demographic schedules for small areas
In this article, we analyze empirical Bayes (EB) methods for estimating small-area rate schedules. We develop EB methods that treat schedules as vectors and use adaptive neighborhoods to keep estimates appropriately local. This method estimates demographic rates for local subpopulations by borrowing strength not only from similar individuals elsewhere but also from other groups in the same area and from regularities in schedules across locations.…
Bayesian Estimation of Age-Specific Mortality and Life Expectancy for Small Areas With Defective Vital Records
High sampling variability complicates estimation of demographic rates in small areas. In addition, many countries have imperfect vital registration systems, with coverage quality that varies significantly between regions. We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with…
Immigrants’ ages and the structure of stationary populations with below-replacement fertility
A sustained regime of low fertility plus immigration yields an unusual kind of stationary population. The author demonstrates that all stationary populations have a common structure, and that the familiar replacement-level fertility population is the youngest among the many stationary populations corresponding to a particular life table. This finding has important consequences for policy because although fertility increase and immigration are equ…
Changes in Service Delivery Patterns After Introduction of Telemedicine Provision of Medical Abortion in Iowa
Objectives. We assessed the effect of a telemedicine model providing medical abortion on service delivery in a clinic system in Iowa. Methods. We reviewed Iowa vital statistic data and billing data from the clinic system for all abortion encounters during the 2 years prior to and after the introduction of telemedicine in June 2008 (n = 17 956 encounters). We calculated the distance from the patient’s residential zip code to the clinic and to the …
A system of model fertility schedules with graphically intuitive parameters
I propose and examine a new family of models for age-specific fertility schedules, in which three index ages determine the schedule's shape. The new system is based on constrained quadratic splines. It has easily interpretable parameters, is flexible e
Estimating age- and sex-specific mortality rates for small areas with Topals regression: An application to Brazil in 2010
High variability in recorded vital events creates serious problems for small-area mortality estimation by age and sex. Many existing approaches to fitting local mortality schedules, including those most often used in Brazil, estimate rates by making rigid mathematical assumptions about local age patterns. Such methods assume that all areas within a larger area (for example, microregions within a mesoregion) have identically-shaped log mortality s…
Knox meets Cox: Adapting epidemiological space-time statistics to demographic studies
Many important questions and theories in demography focus on changes over time, and on how those changes differ over geographic and social space. Space-time analysis has always been important in studying fertility transitions, for example. However, demographers have seldom used formal statistical methods to describe and analyze time series of maps. One formal method, used widely in epidemiology, criminology, and public health, is Knox’s space-tim…
Calibrated spline estimation of detailed fertility schedules from abridged data1
I develop and explain a new method for interpolating detailed fertility schedules from age-group data. The method allows estimation of fertility rates over any fine grid of ages, from either standard or non-standard age groups. The new method, called the calibrated spline (CS) estimator, expands an abridged fertility schedule by finding the smooth curve that minimizes a squared error penalty. The penalty is based both on fit to the available age-…
Bayes plus Brass: Estimating total fertility for many small areas from sparse census data
Estimates of fertility in small areas are valuable for analysing demographic change, and important for local planning and population projection. In countries lacking complete vital registration, however, small-area estimates are possible only from sparse survey or census data that are potentially unreliable. In these circumstances estimation requires new methods for old problems: procedures must be automated if thousands of estimates are required…
Exploratory Analysis of Spatial Patterns in Brazil’s Fertility Transition
Three strikes and you're out: Demographic analysis of mandatory prison sentencing
Much of the debate about the costs and benefits of “three-strikes” laws for repeat felony offenders is implicitly demographic, relying on unexamined assumptions about prison population dynamics. However, even state-of-the-art analysis has omitted important demographic details. We construct a multistate life-table model of population flows to and from prisons, incorporating age-specific transition rates estimated from administrative data from Flor…
A Simple method for estimating age-specific rates from sequential cross sections
I develop and demonstrate a simple formula for estimating age-specific event rates for a period from “before” and “after” cross sections. The general approach applies to a wide range of estimation problems in demography, the social sciences, and epidemiology. The method arises from the formal mathematics of unstable populations and is similar in spirit to “variable-r” methods. Unlike those methods, however, the new technique does not require spec…
Population Pyramids Yield Accurate Estimates of Total Fertility Rates
The primary fertility index for a population, the total fertility rate (TFR), cannot be calculated for many areas and periods because it requires disaggregation of births by mother’s age. Here we discuss a flexible framework for estimating TFR using inputs as minimal as a population pyramid. We develop five variants, each with increasing complexity and data requirements. We test accuracy across a diverse set of data sources that comprise more tha…
Stationary populations with below-replacement fertility
A population with sustained below-replacement fertility and constant immigration eventually becomes stationary. Stationary-through-immigration (SI) populations have unusual age structures that depend on the distribution of immigrants' arrival ages
Quadratic spline fits by nonlinear least squares
This web program fits a Quadratic Spline model, as described in Schmertmann (2003; Demographic Research Volume 9, Article 5), to any empirical fertility schedule supplied by the user. The fit minimizes the sum of squared differences between the empiri
Estimation of Historical Migration Rates from a Single Census: Interregional Migration in Brazil 1900-1980
The author proposes an indirect method for estimating trends in historical migration rates, based on data commonly available from a single census. The method exploits the logical relationship between cohorts' lifetime and single-period transition probabilities, by comparing observed lifetime migration probabilities with those expected under various parametric time trends in period migration rates. In tests with figures from Brazil's Census of 198…
Data errors in mortality estimation: Formal demographic analysis of under-registration, under-enumeration, and age misreporting
BACKGROUNDOmissions and misreported ages in both death and exposure data cause bias in mortality and life expectancy estimates.Most discussions of data errors have focused on a single type of error only, and most rely on empirical examples rather than formal analysis. OBJECTIVEWe wish to analyze data errors and their interactions in a single, coherent framework in which all three of the major data problems -death under-registration, census undere…
D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties
High-dimensional parametric models with penalized likelihood functions strike a good balance between bias and variance for estimating continuous age schedules from large samples. The penalized spline (P-spline) approach is particularly useful for these pur
Revivorship and life lost to mortality
Some formal demographic models describe mortality improvement in terms of averted deaths. In such models individuals who would have died in an earlier regime are instead revived and returned to the population to face the same age-speciï¬ c mortality risks as
Fertility estimation from open birth-interval data
Censuses and surveys frequently collect information on period fertility through questions on the timing of last births. The standard approach to estimating fertility with open-interval data uses the proportion of women giving birth in the year before the interview. I propose a more efficient, maximum likelihood method for estimating fertility from open-interval data. I illustrate a mathematical derivation of the new method, perform sensitivity an…
An introduction to nonparametric regression in demographic research
Immigrants’ ages and the structure of stationary populations with below-replacement fertility
A sustained regime of low fertility plus immigration yields an unusual kind of stationary population. The author demonstrates that all stationary populations have a common structure, and that the familiar replacement-level fertility population is the youngest among the many stationary populations corresponding to a particular life table. This finding has important consequences for policy because although fertility increase and immigration are equ…
Estimation of Historical Migration Rates from a Single Census: Interregional Migration in Brazil 1900-1980
The author proposes an indirect method for estimating trends in historical migration rates, based on data commonly available from a single census. The method exploits the logical relationship between cohorts' lifetime and single-period transition probabilities, by comparing observed lifetime migration probabilities with those expected under various parametric time trends in period migration rates. In tests with figures from Brazil's Census of 198…
An introduction to nonparametric regression in demographic research
Three strikes and you're out: Demographic analysis of mandatory prison sentencing
Much of the debate about the costs and benefits of “three-strikes” laws for repeat felony offenders is implicitly demographic, relying on unexamined assumptions about prison population dynamics. However, even state-of-the-art analysis has omitted important demographic details. We construct a multistate life-table model of population flows to and from prisons, incorporating age-specific transition rates estimated from administrative data from Flor…
Fertility estimation from open birth-interval data
Censuses and surveys frequently collect information on period fertility through questions on the timing of last births. The standard approach to estimating fertility with open-interval data uses the proportion of women giving birth in the year before the interview. I propose a more efficient, maximum likelihood method for estimating fertility from open-interval data. I illustrate a mathematical derivation of the new method, perform sensitivity an…
Estimating Parametric Fertility Models with Open Birth Interval Data
In the past thirty years, more than 100 censuses gathered fertility data through questions on women's date of last birth. The standard "births last year" (BLY) approach for such data truncates timing information, using binary indicators for births in t
A Simple Method for Estimating Age-Specific Rates from Sequential Cross Sections
I develop and demonstrate a simple formula for estimating age-specific event rates for a period from "before" and "after" cross sections. The general approach applies to a wide range of estimation problems in demography, the social sciences, and epidemiology. The method arises from the formal mathematics of unstable populations and is similar in spirit to "variable-r" methods. Unlike those methods, however, the new technique does not require spec…
A Simple method for estimating age-specific rates from sequential cross sections
I develop and demonstrate a simple formula for estimating age-specific event rates for a period from “before” and “after” cross sections. The general approach applies to a wide range of estimation problems in demography, the social sciences, and epidemiology. The method arises from the formal mathematics of unstable populations and is similar in spirit to “variable-r” methods. Unlike those methods, however, the new technique does not require spec…
Fertility and development: Evidence from Brazil
Using microdata from the Brazilian demographic censuses of 1960, 1970, 1980, and 1991, aggregated into 518 consistently defined spatial units called microregions, we estimated fertility and mortality and constructed indicators of development and living conditions in the rural and urban areas of the microregions in each census. We then estimated cross-sectional and fixed-effects models to answer questions about the degree to which changes in these…
A system of model fertility schedules with graphically intuitive parameters
I propose and examine a new family of models for age-specific fertility schedules, in which three index ages determine the schedule's shape. The new system is based on constrained quadratic splines. It has easily interpretable parameters, is flexible e
Empirical bayes estimation of demographic schedules for small areas
In this article, we analyze empirical Bayes (EB) methods for estimating small-area rate schedules. We develop EB methods that treat schedules as vectors and use adaptive neighborhoods to keep estimates appropriately local. This method estimates demographic rates for local subpopulations by borrowing strength not only from similar individuals elsewhere but also from other groups in the same area and from regularities in schedules across locations.…
Quadratic spline fits by nonlinear least squares
This web program fits a Quadratic Spline model, as described in Schmertmann (2003; Demographic Research Volume 9, Article 5), to any empirical fertility schedule supplied by the user. The fit minimizes the sum of squared differences between the empiri
Exploratory Analysis of Spatial Patterns in Brazil’s Fertility Transition
Knox meets Cox: Adapting epidemiological space-time statistics to demographic studies
Many important questions and theories in demography focus on changes over time, and on how those changes differ over geographic and social space. Space-time analysis has always been important in studying fertility transitions, for example. However, demographers have seldom used formal statistical methods to describe and analyze time series of maps. One formal method, used widely in epidemiology, criminology, and public health, is Knox’s space-tim…
Mapping the Timing, Pace, and Scale of the Fertility Transition in Brazil
Between 1960 and 2000, fertility fell sharply in Brazil, but this transition was unevenly distributed in space and time. Using Bayesian spatial statistical methods and microdata from five censuses, we develop and apply a procedure for fitting logistic curves to the fertility transitions in more than 500 small regions of Brazil over this 40-year period. Doing so enables us to map the main features of the Brazilian fertility transition in considera…
Stationary populations with below-replacement fertility
A population with sustained below-replacement fertility and constant immigration eventually becomes stationary. Stationary-through-immigration (SI) populations have unusual age structures that depend on the distribution of immigrants' arrival ages
Changes in Service Delivery Patterns After Introduction of Telemedicine Provision of Medical Abortion in Iowa
Objectives. We assessed the effect of a telemedicine model providing medical abortion on service delivery in a clinic system in Iowa. Methods. We reviewed Iowa vital statistic data and billing data from the clinic system for all abortion encounters during the 2 years prior to and after the introduction of telemedicine in June 2008 (n = 17 956 encounters). We calculated the distance from the patient’s residential zip code to the clinic and to the …
Bayes plus Brass: Estimating total fertility for many small areas from sparse census data
Estimates of fertility in small areas are valuable for analysing demographic change, and important for local planning and population projection. In countries lacking complete vital registration, however, small-area estimates are possible only from sparse survey or census data that are potentially unreliable. In these circumstances estimation requires new methods for old problems: procedures must be automated if thousands of estimates are required…
Calibrated spline estimation of detailed fertility schedules from abridged data1
I develop and explain a new method for interpolating detailed fertility schedules from age-group data. The method allows estimation of fertility rates over any fine grid of ages, from either standard or non-standard age groups. The new method, called the calibrated spline (CS) estimator, expands an abridged fertility schedule by finding the smooth curve that minimizes a squared error penalty. The penalty is based both on fit to the available age-…
Estimating age- and sex-specific mortality rates for small areas with Topals regression: An application to Brazil in 2010
High variability in recorded vital events creates serious problems for small-area mortality estimation by age and sex. Many existing approaches to fitting local mortality schedules, including those most often used in Brazil, estimate rates by making rigid mathematical assumptions about local age patterns. Such methods assume that all areas within a larger area (for example, microregions within a mesoregion) have identically-shaped log mortality s…
Bayesian Estimation of Age-Specific Mortality and Life Expectancy for Small Areas With Defective Vital Records
High sampling variability complicates estimation of demographic rates in small areas. In addition, many countries have imperfect vital registration systems, with coverage quality that varies significantly between regions. We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with…
Population Pyramids Yield Accurate Estimates of Total Fertility Rates
The primary fertility index for a population, the total fertility rate (TFR), cannot be calculated for many areas and periods because it requires disaggregation of births by mother’s age. Here we discuss a flexible framework for estimating TFR using inputs as minimal as a population pyramid. We develop five variants, each with increasing complexity and data requirements. We test accuracy across a diverse set of data sources that comprise more tha…
Revivorship and life lost to mortality
Some formal demographic models describe mortality improvement in terms of averted deaths. In such models individuals who would have died in an earlier regime are instead revived and returned to the population to face the same age-speciï¬ c mortality risks as
D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties
High-dimensional parametric models with penalized likelihood functions strike a good balance between bias and variance for estimating continuous age schedules from large samples. The penalized spline (P-spline) approach is particularly useful for these pur
Commentary on van Raalte et al.’s “The Dangers of Drawing Cohort Profiles From Period Data: A Research Note”
van Raalte et al. (2023) alerted demographers to the potential dangers of calculating cohort measures from the “diagonals” of gridded age–period (AP) data. In the case of cohort fertility, however, a minor change to the estimation procedure can mitigate the trend and cohort size biases that the authors identify. With an appropriate algorithm, researchers can estimate cohort fertility indices from AP data quite well
Demography (18 works) · Mathematics (17 works) · Population (17 works) · Statistics (17 works) · Econometrics (16 works) · Insurance, Mortality, Demography, Risk Management (16 works) · Sociology (15 works) · Economics (14 works) · Geography (13 works) · Fertility (12 works)