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Cohort Component Model for Projecting Population.

Source: R/ccm.R
ccm.Rd

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

If Mx.m is NULL, a numeric matrix with projected female population, where rows are age groups and columns are periods 0:h. If male mortality is supplied, a list with matrices female, male, and all, each with the same row/column structure.

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.

Examples

age.mx <- seq(0, 80, 5)
age.fx <- seq(15, 45, 5)
Mx.f <- matrix(
  rep(seq(0.005, 0.12, length.out = length(age.mx)), 2),
  nrow = length(age.mx),
  ncol = 2
)
Fx <- matrix(
  rep(c(0.02, 0.08, 0.11, 0.09, 0.05, 0.02, 0.005), 2),
  nrow = length(age.fx),
  ncol = 2
)
N0.f <- round(100000 * exp(-0.04 * age.mx))
ccm(Mx.f = Mx.f, Fx = Fx, age.mx = age.mx, age.fx = age.fx, N0.f = N0.f)
#>         0         1
#> 0  100000 32304.435
#> 5   81873 94739.033
#> 10  67032 75711.087
#> 15  54881 59813.167
#> 20  44933 47249.885
#> 25  36788 37322.133
#> 30  30119 29476.495
#> 35  24660 23276.574
#> 40  20190 18378.378
#> 45  16530 14507.862
#> 50  13534 11449.598
#> 55  11080  9034.409
#> 60   9072  7125.721
#> 65   7427  5619.607
#> 70   6081  4429.560
#> 75   4979  3490.480
#> 80   4076  4932.932