Wrapper for cross-classified data that standardises rates across a pair of populations. Because these are (r+r')/2 * Q(a_i), this requires 1) doing the rate standardisation on each sub-population, 2) performing the standardisation on the cross classified structure variables, 3) multiplying and (optionally) aggregating up

Description

Wrapper for cross-classified data that standardises rates across a pair of populations. Because these are (r+r')/2 * Q(a_i), this requires 1) doing the rate standardisation on each sub-population, 2) performing the standardisation on the cross classified structure variables, 3) multiplying and (optionally) aggregating up

Usage

ccwrap(
  pw,
  pop,
  factors,
  id_vars,
  crossclassified,
  agg,
  ratefunction = NULL,
  quietly = TRUE
)

Arguments

Value

data.frame that includes K-a standardised rates for each population and each factor a, along with differences between standardised rates

Standardisation and decomposition of rates over K rate-factors and 2 populations. We suggest using dgnpop, which will internally call this function.

Description

Standardisation and decomposition of rates over K rate-factors and 2 populations. We suggest using dgnpop, which will internally call this function.

Usage

dg2pop(pw, pop, factors, id_vars, ratefunction = NULL, quietly = TRUE)

Arguments

Value

named list along set of K factors included in the standardisation. Each list element contains a data.frame that includes K-a standardised rates for each population, along with differences between standardised rates

Das Gupta equation 3.54. internal function called by dg2pop.

Description

Das Gupta equation 3.54. internal function called by dg2pop.

Usage

dg354(df2, i, pop, factors, id_vars, ratefunction, quietly = TRUE)

Arguments

Value

data.frame object including K-a standardised rates for each population for given factor a, along with differences between standardised rates

Das Gupta equation 6.11: Standardises rates across populations

Description

Das Gupta equation 6.11: Standardises rates across populations

Usage

dg611(srates, all_p, y, factor)

Arguments

Value

data.frame object including K-a standardised rates for each population for given factor a, across N populations

Das Gupta equation 6.12 for a differences between 2 populations when standardised across N populations.

Description

Das Gupta equation 6.12 for a differences between 2 populations when standardised across N populations.

Usage

dg612(srates, all_p, ps, factor)

Arguments

Value

data.frame object including K-a standardised-rate-differences for each population for given factor a, across N populations

Creates a plot of Das Gupta standardised rates across the set of populations

Description

Creates a plot of Das Gupta standardised rates across the set of populations

Usage

dg_plot(dgo, legend.position = "topright")

Arguments

Value

A plot of each of the set of K-a standardised rates across populations

Creates a small table of Das Gupta standardised rates. If no populations are specified, rates will be shown for all available populations. If only two populations (or if two particular populations are specified), then rate-differences and 'decomposition effects' are calculated and presented.

Description

Creates a small table of Das Gupta standardised rates. If no populations are specified, rates will be shown for all available populations. If only two populations (or if two particular populations are specified), then rate-differences and 'decomposition effects' are calculated and presented.

Usage

dg_table(dgo, pop1 = NULL, pop2 = NULL)

Arguments

Value

data.frame object with rows for each of the K-a standardised rates and the crude rates, and columns for each of the N populations. When only two populations are included, or if two populations are explicitly specified, standardised rate differences are provided, and are also expressed as a percentage of the crude rate differences (typically referred to as 'decomposition effects').

Das Gupta equation 5.36 across N populations: Decomposes cross-classified population structures into a set of symmetric proportions indicating contribution of individual structural variables.

Description

Das Gupta equation 5.36 across N populations: Decomposes cross-classified population structures into a set of symmetric proportions indicating contribution of individual structural variables.

Usage

dgcc(x, pop, id_vars, crossclassified)

Arguments

Value

inputted data.frame is returned with the addition of variables for each of the the cross-classified variables representing the contribution to the population size.

Prithwis Das Gupta's 1993 standardisation and decomposition of rates over K rate-factors and N populations.

Description

Prithwis Das Gupta's 1993 standardisation and decomposition of rates over K rate-factors and N populations.

Usage

dgnpop(
  x,
  pop,
  factors,
  id_vars = NULL,
  crossclassified = NULL,
  ratefunction = NULL,
  agg = TRUE,
  baseline = NULL,
  quietly = TRUE,
  diffs = FALSE
)

Arguments

Details

Population rates are often composed of various different compositional factors. Standardisation techniques calculate the rate were a set of factors to be held constant (either with a specific population as standard, or at the average of the populations). Decomposition methods quantify the amount of the difference between two population crude rate that is due to differences in population characteristics.

Das Gupta's general solution for the decomposition of two rates can be written as:

\Delta\text{crude-}r = \sum\limits_{\vec{\alpha} \in K}Q(\vec{\alpha}^p) - Q(\vec{\alpha}^{p'})

Where K is the set of factors \alpha, \beta, ..., \kappa, which may take the form of vectors over sub-populations i. Q(\vec{\alpha}^p) denotes the rate in population p holding all factors other than \alpha — K \setminus \alpha — equal (standardised across populations p and p'). The total crude rate difference is the sum of all standardised-rate differences, and the standardisation Q is expressed as:

Q(\vec{\alpha}^p) = \sum\limits_{j=1}^{\lfloor \frac{|K|}{2} \rfloor} \frac{ \sum\limits_{L \in {K \setminus \{\alpha\} \choose j-1}}f(\{L^p,(K\setminus L)^{p'},\vec{\alpha}^p\}) + f(\{L^{p'},(K\setminus L)^p,\vec{\alpha}^p\})} { |K| {|K| -1\choose j-1} }

Where f(K) is the function that defines the calculation of the rate

Value

data.frame containing K-a standardised rates (or differences) for each population.

• rate: standardised rate such that factor a is from population p and all other factors are averaged across populations, f(a^p,...)

• pop: population p for which factor a is taken from

• std.set: set of N populations (minus p) across which the standardisation has been performed

• factor: name of factor a that is being considered, such that for the set of factors K, the {K-a}-standardised rate is returned

Examples

## 2 populations, R=ab
eg2.1 <- data.frame(
  pop = c("black", "white"),
  avg_earnings = c(10930, 16591),
  earner_prop = c(.717892, .825974)
)

dgnpop(eg2.1, pop = "pop", factors = c("avg_earnings", "earner_prop")) |>
  dg_table()

## 2 populations, R=abc
eg2.2 <- data.frame(
  pop = c("austria", "chile"),
  birthsw1549 = c(51.78746, 84.90502),
  propw1549 = c(.45919, .75756),
  propw = c(.52638, .51065)
)

dgnpop(eg2.2, pop = "pop", factors = c("birthsw1549", "propw1549", "propw")) |>
  dg_table()

## 2 populations, R=abcd
eg2.3 <- data.frame(
  pop = c(1971, 1979),
  birth_preg = c(25.3, 32.7),
  preg_actw = c(.214, .290),
  actw_prop = c(.279, .473),
  w_prop = c(.949, .986)
)

dgnpop(eg2.3,
  pop = "pop",
  factors = c("birth_preg", "preg_actw", "actw_prop", "w_prop")
) |>
  dg_table()

## 2 populations, R=abcde
eg2.4 <- data.frame(
  pop = c(1970, 1980),
  prop_m = c(.58, .72),
  noncontr = c(.76, .97),
  abort = c(.84, .97),
  lact = c(.66, .56),
  fecund = c(16.573, 16.158)
)

dgnpop(eg2.4,
  pop = "pop",
  factors = c("prop_m", "noncontr", "abort", "lact", "fecund")
) |>
  dg_table()

## 2 populations, vector factors, R=sum(abc)
eg4.3 <- data.frame(
  agegroup = rep(1:7, 2),
  pop = rep(c(1970, 1960), e = 7),
  bm = c(
    488, 452, 338, 156, 63, 22, 3,
    393, 407, 369, 274, 184, 90, 16
  ),
  mw = c(
    .082, .527, .866, .941, .942, .923, .876,
    .122, .622, .903, .930, .916, .873, .800
  ),
  wp = c(
    .058, .038, .032, .030, .026, .023, .019,
    .043, .041, .036, .032, .026, .020, .018
  )
)

dgnpop(eg4.3,
  pop = "pop", factors = c("bm", "mw", "wp"),
  ratefunction = "sum(bm*mw*wp)"
) |>
  dg_table()

## 2 populations, R=f(ab)
eg3.1 <- data.frame(
  pop = c(1940, 1960),
  crude_birth = c(19.4, 23.7),
  crude_death = c(10.8, 9.5)
)
dgnpop(eg3.1,
  pop = "pop",
  factors = c("crude_birth", "crude_death"),
  ratefunction = "crude_birth-crude_death"
) |>
  dg_table()

## 2 populations, vector factors, R=f(abcd)
eg4.4 <- data.frame(
  pop = rep(c(1963, 1983), e = 6),
  agegroup = c("15-19", "20-24", "25-29", "30-34", "35-39", "40-44"),
  A = c(
    .200, .163, .146, .154, .168, .169,
    .169, .195, .190, .174, .150, .122
  ),
  B = c(
    .866, .325, .119, .099, .099, .121,
    .931, .563, .311, .216, .199, .191
  ),
  C = c(
    .007, .021, .023, .015, .008, .002,
    .018, .026, .023, .016, .008, .002
  ),
  D = c(
    .454, .326, .195, .107, .051, .015,
    .380, .201, .149, .079, .025, .006
  )
)

dgnpop(eg4.4,
  pop = "pop", factors = c("A", "B", "C", "D"),
  id_vars = "agegroup",
  ratefunction = "sum(A*B*C) / (sum(A*B*C) + sum(A*(1-B)*D))"
) |>
  dg_table()

### alternatively:
myratef <- function(a, b, c, d) {
  return(sum(a * b * c) / (sum(a * b * c) + sum(a * (1 - b) * d)))
}
dgnpop(eg4.4,
  pop = "pop", factors = c("A", "B", "C", "D"),
  id_vars = "agegroup",
  ratefunction = "myratef(A,B,C,D)"
) |>
  dg_table()

## using crossclassified for relative size:
eg5.1 <- data.frame(
  age_group = rep(c(
    "15-19", "20-24", "25-29", "30-34", "35-39",
    "40-44", "45-49", "50-54", "55-59", "60-64",
    "65-69", "70-74", "75+"
  ), 2),
  pop = rep(c(1970, 1985), e = 13),
  size = c(
    12.9, 10.9, 9.5, 8.0, 7.8, 8.4, 8.6, 7.8, 7.0, 5.9, 4.7, 3.6, 4.9,
    10.1, 11.2, 11.6, 10.9, 9.4, 7.7, 6.3, 6.0, 6.3, 5.9, 5.1, 4.0, 5.5
  ),
  rate = c(
    1.9, 25.8, 45.7, 49.6, 51.2, 51.6, 51.8, 54.9, 58.7, 60.4, 62.8, 66.6, 66.8,
    2.2, 24.3, 45.8, 52.5, 56.1, 55.6, 56.0, 57.4, 57.2, 61.2, 63.9, 68.6, 72.2
  )
)
dgnpop(eg5.1,
  pop = "pop", factors = c("rate"),
  id_vars = "age_group",
  crossclassified = "size"
) |>
  dg_table()

## 2 cross-classified variables, 2 populations, R=sum(w*r)
eg5.3 <- data.frame(
  race = rep(rep(1:2, e = 11), 2),
  age = rep(rep(1:11, 2), 2),
  pop = rep(c(1985, 1970), e = 22),
  size = c(
    3041, 11577, 27450, 32711, 35480, 27411, 19555, 19795, 15254, 8022, 2472,
    707, 2692, 6473, 6841, 6547, 4352, 3034, 2540, 1749, 804, 236,
    2968, 11484, 34614, 30992, 21983, 20314, 20928, 16897, 11339, 5720, 1315,
    535, 2162, 6120, 4781, 3096, 2718, 2363, 1767, 1149, 448, 117
  ),
  rate = c(
    9.163, 0.462, 0.248, 0.929, 1.084, 1.810, 4.715, 12.187, 27.728, 64.068, 157.570,
    17.208, 0.738, 0.328, 1.103, 2.045, 3.724, 8.052, 17.812, 34.128, 68.276, 125.161,
    18.469, 0.751, 0.391, 1.146, 1.287, 2.672, 6.636, 15.691, 34.723, 79.763, 176.837,
    36.993, 1.352, 0.541, 2.040, 3.523, 6.746, 12.967, 24.471, 45.091, 74.902, 123.205
  )
)

dgnpop(eg5.3,
  pop = "pop", factors = c("rate"),
  id_vars = c("race", "age"),
  crossclassified = "size"
) |>
  dg_table()


## 5 populations, R = f(abcd)
eg6.5 <- data.frame(
  pop = rep(c(1963, 1968, 1973, 1978, 1983), e = 6),
  agegroup = c("15-19", "20-24", "25-29", "30-34", "35-39", "40-44"),
  A = c(
    .200, .163, .146, .154, .168, .169,
    .215, .191, .156, .137, .144, .157,
    .218, .203, .175, .144, .127, .133,
    .205, .200, .181, .162, .134, .118,
    .169, .195, .190, .174, .150, .122
  ),
  B = c(
    .866, .325, .119, .099, .099, .121,
    .891, .373, .124, .100, .107, .127,
    .870, .396, .158, .125, .113, .129,
    .900, .484, .243, .176, .155, .168,
    .931, .563, .311, .216, .199, .191
  ),
  C = c(
    .007, .021, .023, .015, .008, .002,
    .010, .023, .023, .015, .008, .002,
    .011, .016, .017, .011, .006, .002,
    .014, .019, .015, .010, .005, .001,
    .018, .026, .023, .016, .008, .002
  ),
  D = c(
    .454, .326, .195, .107, .051, .015,
    .433, .249, .159, .079, .037, .011,
    .314, .181, .133, .063, .023, .006,
    .313, .191, .143, .069, .021, .004,
    .380, .201, .149, .079, .025, .006
  )
)

dgnpop(eg6.5,
  pop = "pop", factors = c("A", "B", "C", "D"),
  id_vars = "agegroup",
  ratefunction = "1000*sum(A*B*C) / (sum(A*B*C) + sum(A*(1-B)*D))"
) |>
  dg_table()

dgnpop(eg6.5,
  pop = "pop", factors = c("A", "B", "C", "D"),
  id_vars = "agegroup",
  ratefunction = "1000*sum(A*B*C) / (sum(A*B*C) + sum(A*(1-B)*D))"
) |>
  dg_plot()

Scottish Reconvictions data 2004-2016

Description

Scottish Reconvictions data 2004-2016

Usage

data(reconv)

Format

An object of class data.frame with 130 rows and 8 columns.

References

Scottish Government Reconviction data: (2016/17)

Examples

data(reconv)

Das Gupta equation 5.36 for a single population: Decomposes cross-classified population structures into a set of symmetric proportions indicating contribution of individual structural variables.

Description

Das Gupta equation 5.36 for a single population: Decomposes cross-classified population structures into a set of symmetric proportions indicating contribution of individual structural variables.

Usage

split_popstr(x, id_vars, nvar)

Arguments

Value

inputted data.frame is returned with the addition of variables for each of the the cross-classified variables representing the contribution to the population size.

US population data 1940-1990

Description

US population data 1940-1990

Usage

data(uspop)

Format

An object of class data.frame with 459 rows and 4 columns.

Examples

data(uspop)