Cohort Component Model for Projecting Population.

Usage

ccm(
  Mx.f,
  Mx.m = NULL,
  Fx,
  Ix.f = NULL,
  Ix.m = NULL,
  age.mx,
  age.fx,
  N0.f,
  N0.m = NULL,
  srb = 100/205,
  ...
)

Arguments

Mx.f: Matrix or dataframe with mx for females, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents age-specific mortality rate.
Mx.m: Optional. Matrix or dataframe with mx for males, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents age-specific mortality rate.
Fx: Matrix or dataframe with fx, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents age-specific fertility rate.
Ix.f: Optional. Matrix or dataframe with net number of female migrants, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents net number of migrants.
Ix.m: Optional. Matrix or dataframe with net number of male migrants, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents net number of migrants.
age.mx: Numeric vector. Age groups for Mx.f rows.
age.fx: Numeric vector. Age groups for Fx rows.
N0.f: Numeric vector. Female population in the initial period by age groups.
N0.m: Optional. Numeric vector. Male population in the initial period by age groups.
srb: Numeric. Sex ratio at birth for females. By default, it is 100/205.
...: Optional. Additional arguments for leslie() function.

Value

(List of) Matrices with projected population. Columns represent periods, rows represent age groups. The first column is N0 (initial period).

Details

The model is calculated in matrix form as $$\mathbf{N}_{t+h} = \mathbf{L}_t(\mathbf{N}_{t} + \mathbf{I}_{t}/2) + \mathbf{I}_{t}/2$$ where $\mathbf{N}_t$ is a column vector of population for time $t$ with $h$ as a step of projection (it is the length of age interval), $\mathbf{L}_t$ is Leslie matrix and $\mathbf{I}_{t}$ is a column vector of net migration.

Note that the model assumes that in $\mathbf{N}$ all age intervals are the same (i.e. $age = \{0-1, 1-4, 5-9, ...\}$ is not permitted). Fortunately (and thanks to me), the function handles such situations automatically by transforming all age groups into a unified standard.