The `fmat`

object is the internal dataset used by the `outcomerate`

package.
It holds all definitions for the outcome rates. With the exception of location
rates, these are taken from the AAPOR Standard Definitions (2016).

## Details

The data is a 3-dimensional binary array consisting of:

outcome: codes I, P, R, NC, O, UH, UO, eUH, eUO, NE

rate: the shorthand name for the rate (e.g. RR1)

side: numerator (NUM) and denominator (DEN)

Given these three dimensions, each outcome rate can be defined as a rational number (i.e. a fraction) consisting of a summation of frequencies of outcome codes (where the matrix entries are nonzero).

The input parameters given by the user are I, P, R, NC, O, UH, UO and the parameter 'e'. The parameter e is multiplied by UH, UO internally so as to produce eUH, eUO.

The reason for this implementation is:

a) It conforms to a DRY (don't repeat yourself) philosophy by holding all definitions in one place. These definitions can be used as upstream inputs to functions/test suites requiring them.

b) It makes it easier to use intermediate steps in the formula calculations. For instance, it may be of use to a researchers to want to obtain the numerator/denominators of calculations, instead of only the output.

c) it makes it easy to compare the output

d) It is easier to maintain

## Examples

```
fmat <- outcomerate:::fmat
# Print the dimensions
dimnames(fmat)
#> $outcome
#> [1] "I" "P" "R" "NC" "O" "UH" "UO" "NE" "eUH" "eUO"
#>
#> $rate
#> [1] "RR1" "RR2" "RR3" "RR4" "RR5" "RR6" "COOP1" "COOP2" "COOP3"
#> [10] "COOP4" "REF1" "REF2" "REF3" "CON1" "CON2" "CON3" "LOC1" "LOC2"
#>
#> $side
#> [1] "NUM" "DEN"
#>
# Say we want to know the defintion of Response Rate 2, RR2. We see
# below that the numerator (NUM) column is defined by the entries with a 1,
# or (I + P). Likewise, the denominator (DEN) is defined as
# (I + P + R + NC + O + UH + UO)
fmat[, "RR2", ]
#> side
#> outcome NUM DEN
#> I 1 1
#> P 1 1
#> R 0 1
#> NC 0 1
#> O 0 1
#> UH 0 1
#> UO 0 1
#> NE 0 0
#> eUH 0 0
#> eUO 0 0
# To use linear algebra, we define a zero-one numerator matrix 'N'
# and a zero-one denominator matrix 'D'. Our count of disposition codes
# is given here manually as 'x' (in the same order as N and D).
N = fmat[ , , 1]
D = fmat[ , , 2]
x <- c(I = 5, P = 2, R = 1, NC = 7, O = 3,
UH = 4, UO = 8, NE = 1, eUH = 3, eUO = 6)
# Return all rates
(x %*% N) / (x %*% D)
#> rate
#> RR1 RR2 RR3 RR4 RR5 RR6 COOP1
#> [1,] 0.1666667 0.2333333 0.1851852 0.2592593 0.2777778 0.3888889 0.4545455
#> rate
#> COOP2 COOP3 COOP4 REF1 REF2 REF3 CON1
#> [1,] 0.6363636 0.625 0.875 0.03333333 0.03703704 0.05555556 0.3666667
#> rate
#> CON2 CON3 LOC1 LOC2
#> [1,] 0.4074074 0.6111111 0.6 0.6666667
# The same thing can be achieved with the apply family of functions
numden <- apply(x * fmat, 2:3, sum)
numden[, 1] / numden[, 2]
#> RR1 RR2 RR3 RR4 RR5 RR6 COOP1
#> 0.16666667 0.23333333 0.18518519 0.25925926 0.27777778 0.38888889 0.45454545
#> COOP2 COOP3 COOP4 REF1 REF2 REF3 CON1
#> 0.63636364 0.62500000 0.87500000 0.03333333 0.03703704 0.05555556 0.36666667
#> CON2 CON3 LOC1 LOC2
#> 0.40740741 0.61111111 0.60000000 0.66666667
```