| Type: | Package |
| Title: | Fertility Models |
| Version: | 1.4 |
| Date: | 2024-11-29 |
| Author: | Michail Tsagris [aut, cre] |
| Maintainer: | Michail Tsagris <mtsagris@uoc.gr> |
| Depends: | R (≥ 4.0) |
| Imports: | quadprog, stats |
| Suggests: | Rfast, Rfast2 |
| Description: | Four fertility models are fitted using non-linear least squares. These are the Hadwiger, the Gamma, the Model1 and Model2, following the terminology of the following paper: Peristera P. and Kostaki A. (2007). "Modeling fertility in modern populations". Demographic Research, 16(6): 141–194. <doi:10.4054/DemRes.2007.16.6>. Model based averaging is also supported. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2024-11-29 14:28:39 UTC; mtsag |
| Repository: | CRAN |
| Date/Publication: | 2024-11-29 15:00:02 UTC |
This is an R package that fits 4 fertility models.
Description
Four fertility models are fitted using non-linear least squares. These are the Hadwiger, the Gamma, the Model1 and Model2, following the terminology of the following paper: Peristera P. and Kostaki A. (2007). Modeling fertility in modern populations. Demographic Research, 16(6): 141–194. <doi:10.4054/DemRes.2007.16.6>.
Details
| Package: | nlgmcr Type: | Package |
| Version: | 1.4 | |
| Date: | 2024-11-29 | |
| License: | GPL-2 | |
Maintainers
Michail Tsagris mtsagris@uoc.gr.
Note
Acknowledgments: This package is dedicated to Sanaa who introduced me to these models and whom I may never see again.
Author(s)
Michail Tsagris mtsagris@uoc.gr.
References
Peristera P. and Kostaki A. (2007). Modeling fertility in modern populations. Demographic Research, 16(6), 141–194. <doi:10.4054/DemRes.2007.16.6>.
Fertility models
Description
Fertility models.
Usage
Hadwiger(rate, age)
Gama(rate, age)
Model1(rate, age)
Model2(rate, age)
Arguments
rate |
A vector with the age-specific fertility rates. |
age |
A vector with the age of the women. |
Details
The following fertility models are fitted: Hadwiger:
f(x)=\frac{ab}{c}(\frac{c}{x})^{3/2}\exp[-b^2(\frac{c}{x}+\frac{x}{c}-2)],
where x is the age of the mother at birth, a is associated with total fertility, the parameter b determines the height of the curve and the parameter c is related to the mean age of motherhood.
Gama:
f(x)=R\frac{1}{\Gamma(b)c^b}(x-d)^{b-1}\exp(-\frac{x-d}{c}),
where d represents the lower age at childbearing, while the parameter R determines the
level of fertility.
Model1:
f(x)=c_1\exp[-\frac{(x-\mu)^2}{\sigma^2(x)}],
where \sigma(x)=\sigma_{11} if x \leq \mu and \sigma(x)=\sigma_{12} if x>\mu. The parameter c_1 describes the base level of the fertility curve and is associated with the total fertility rate, \mu reflects the location of the distribution, i.e. the modal age and \sigma_{11} and \sigma_{12} reflect the spread of the distribution before and after its peak, respectively.
Model2:
f(x)=c_1\exp[-\frac{(x-\mu_1)^2}{\sigma_1^2}] + c_2\exp[-\frac{(x-\mu_2)^2}{\sigma_2^2}],
where the parameters c_1 and c_2 express the severity i.e. the total fertility rates of the first
and the second hump respectively, \mu_1 and \mu_2 are related to the mean ages of the two
subpopulations the one with earlier fertility and the other with fertility at later ages, while \sigma_1 and \sigma_2 reflect the variances of the two humps.
Value
A list including:
param |
The vector of the estimated parameters. |
sse |
The sum of squars of the errors |
fx |
The fitted values, the fitted age-specific fertility rates |
res |
The residuals, |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
References
Peristera P. and Kostaki A. (2007). Modeling fertility in modern populations. Demographic Research, 16(6): 141–194.
See Also
Examples
rate <- c(0.0001, 0.0006, 0.0033, 0.0111, 0.0263, 0.0412, 0.0544, 0.0622,
0.0660, 0.0704,0.0723, 0.0753, 0.0814, 0.0873, 0.0924, 0.0962, 0.0989,
0.1006, 0.0990, 0.0933,0.0831, 0.0747, 0.0634, 0.0529, 0.0424, 0.0326,
0.0242, 0.0172, 0.0115, 0.0073, 0.0040, 0.0022, 0.0012, 0.0006, 0.0003,
0.0002, 0.0001)
age <- 13:49
mod1 <- Hadwiger(rate, age)
mod2 <- Gama(rate, age)
mod3 <- Model1(rate, age)
mod4 <- Model2(rate, age)
Model based average of the estimated values from two or more fertility models
Description
Model based average of the estimated values from two or more fertility models.
Usage
comb(models)
Arguments
models |
A list with possible models. |
Value
A list including:
weights |
The weights assigned to each model. |
fit |
The weighted fitted age-specific fertility rates |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
See Also
Examples
rate <- c(0.0001, 0.0006, 0.0033, 0.0111, 0.0263, 0.0412, 0.0544, 0.0622,
0.0660, 0.0704,0.0723, 0.0753, 0.0814, 0.0873, 0.0924, 0.0962, 0.0989,
0.1006, 0.0990, 0.0933,0.0831, 0.0747, 0.0634, 0.0529, 0.0424, 0.0326,
0.0242, 0.0172, 0.0115, 0.0073, 0.0040, 0.0022, 0.0012, 0.0006, 0.0003,
0.0002, 0.0001)
age <- 13:49
mod1 <- Hadwiger(rate, age)
mod2 <- Gama(rate, age)
mod3 <- Model1(rate, age)
mod4 <- Model2(rate, age)
a <- list(mod1 = mod1, mod2 = mod2, mod3 = mod3, mod4 = mod4)
comb(a)
Plot of the age-specific fertility rates and the estimated values from one or more fertility models
Description
Plot of the age-specific fertility rates and the estimated values from one or more fertility models.
Usage
fertil.plot(rate, age, fit = NULL, grid = FALSE, names = NULL)
Arguments
rate |
A vector with the age-specific fertility rates. |
age |
A vector with the age of the women. |
fit |
Here you can specify nothing (omly plot the fertility rates across the ages), or you can specify a vector or a matrix with fitted values from at least one model. |
grid |
Do you want a grid of vertical and horizontal lines? TRUE or FALSE. |
names |
If you provided fitted models from a model, you can specify the name(s) of the model(s) so that they appear as a legend. |
Value
A plot with the age-specific fertility rates across the mothers' age and perhaps the fitted values from at least one model.
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
See Also
Examples
rate <- c(0.0000, 0.0005, 0.0023, 0.0073, 0.0175, 0.0283,
0.0420, 0.0523, 0.0601, 0.0712, 0.0789, 0.0865, 0.0939,
0.0991, 0.1052, 0.1115, 0.1155, 0.1178, 0.1211, 0.1159,
0.1104, 0.1031, 0.0916, 0.0776, 0.0639, 0.0498, 0.0387,
0.0281, 0.0185, 0.0117, 0.0067, 0.0038, 0.0020, 0.0011,
0.0007, 0.0003, 0.0002)
age <- 13:49
mod1 <- Hadwiger(rate, age)
mod2 <- Gama(rate, age)
fertil.plot(rate, age)
fertil.plot(rate, age, cbind(mod1$fit, mod2$fit), grid = TRUE, names = c("Hadwiger", "Gama") )