# kott.ratio: Estimation of ratios between totals In DiegoZardetto/EVER: Estimation of Variance by Efficient Replication

## Description

Calculates estimates, standard errors and confidence intervals for ratios between totals in subpopulations.

## Usage

 ```1 2 3``` ```kott.ratio(deskott, num, den, by = NULL, vartype = c("se", "cv", "cvpct", "var"), conf.int = FALSE, conf.lev = 0.95) ```

## Arguments

 `deskott` Object of class `kott.design` containing the replicated survey data. `num` Formula defining the numerator variables for the ratio estimator. `den` Formula defining the denominator variables for the ratio estimator. `by` Formula specifying the variables that define the "estimation domains". If `NULL` (the default option) estimates refer to the whole population. `vartype` `character` vector specifying the desired variability estimators. It is possible to choose one or more of: standard error (the default), coefficient of variation, percent coefficient of variation, or variance. `conf.int` Boolean (`logical`) value to request confidence intervals for the estimates: the default is `FALSE`. `conf.lev` Probability specifying the desired confidence level: the default value is `0.95`.

## Details

This function calculates weighted estimates for ratios between totals of quantitative variables using suitable weights depending on the class of `deskott`: calibrated weights for class `kott.cal.design` and direct weights otherwise. Standard errors are calculated using the extended DAGJK method [Kott 99-01].

The mandatory argument `num` (`den`) identifies the variables whose totals appear as the numerator (denominator) in the ratio estimator: the corresponding formula must be of the type
`num=~num1+...+numk` (`den=~den1+...+denl`). The function calculates estimates for ratios between homologous variables in `num` and `den`; if `num` and `den` contain a different number of variables the shortest argument will be tacitly recycled. The `deskott` variables referenced by `num` (`den`) must be `numeric` and must not contain any missing value (`NA`).

The optional argument `by` specifies the variables that define the "estimation domains", that is the subpopulations for which the estimates are to be calculated. If `by=NULL` (the default option), the estimates produced by `kottby` refer to the whole population. Estimation domains must be defined by a formula: for example the statement `by=~B1:B2` selects as estimation domains the subpopulations determined by crossing the modalities of variables `B1` and `B2`. The `deskott` variables referenced by `by` (if any) must be `factor` and must not contain any missing value (`NA`).

The `conf.int` argument allows to request the confidence intervals for the estimates. By default `conf.int=FALSE`, that is the confidence intervals are not provided.

Whenever confidence intervals are requested (i.e. `conf.int=TRUE`), the desired confidence level can be specified by means of the `conf.lev` argument. The `conf.lev` value must represent a probability (`0<=conf.lev<=1`) and its default is chosen to be `0.95`. Given an input `kott.design` object with `nrg` random groups, `kott.ratio` builds the confidence intervals making use of a t distribution with `nrg-1` degrees of freedom.

## Value

The return value depends on the value of the input parameters. In the most general case, the function returns an object of class `list` (typically a list made up of data frames).

## Warning

It is possible that, in certain subpopulations, the estimate of the total of some `den` variables turns out to be zero for the original sample in `deskott` and/or for some of its `nrg` replicates. In these cases, `kott.ratio` (i) returns `NaN` for the estimates and/or for the corresponding standard errors and (ii) prints a `warning` message.

Diego Zardetto

## References

Kott, Phillip S. (1999) "The Extended Delete-A-Group Jackknife". Bulletin of the International Statistical Instititute. 52nd Session. Contributed Papers. Book 2, pp. 167-168.

Kott, Phillip S. (2001) "The Delete-A-Group Jackknife". Journal of Official Statistics, Vol.17, No.4, pp. 521-526.

## See Also

`kottby` for estimating totals and means, `kott.quantile` for estimating quantiles, `kott.regcoef` for estimating regression coefficients and `kottby.user` for calculating estimates based on user-defined estimators.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```data(data.examples) # Creation of a kott.design object: kdes<-kottdesign(data=example,ids=~towcod+famcod,strata=~SUPERSTRATUM, weights=~weight,nrg=15) # Estimate of the ratios y1/x1, y2/x2 e y3/x3 by marstat: kott.ratio(kdes,~y1+y2+y3,~x1+x2+x3,by=~marstat) # Estimate of the ratios z/x1, z/x2 e z/x3 # for the whole population (notice the recycling rule): kott.ratio(kdes,~z,~x1+x2+x3,conf.int=TRUE) # Estimators of means can be thought as # ratio estimators: kottby(kdes,~income,estimator="mean") kott.ratio(kott.addvars(kdes,population=1),num=~income,den=~population) ```

DiegoZardetto/EVER documentation built on April 8, 2021, 1:05 p.m.