kott.regcoef: Estimation of linear regression coefficients
In DiegoZardetto/EVER: Estimation of Variance by Efficient Replication

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates estimates, standard errors and confidence intervals for regression coefficients in subpopulations.

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kott.regcoef(deskott, model, by = NULL, 
             vartype = c("se", "cv", "cvpct", "var"),
             conf.int = FALSE, conf.lev = 0.95)

`deskott`	Object of class `kott.design` containing the replicated survey data.
`model`	Formula giving a symbolic description of the linear model.
`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`.

This function calculates weighted estimates of linear regression coefficients 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 model specifies, by means of a symbolic formula, the linear regression model whose coefficients are to be estimated. model must have the form response ~ terms where response is the (numeric) response variable and terms represents a series of terms which specifies a linear predictor for response. Variables referenced by model 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 and a regression model with p predictors plus an intercept term, kott.regcoef builds the confidence intervals making use of a t distribution with nrg-p-1 degrees of freedom.

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).

Diego Zardetto

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.

kottby for estimating totals and means, kott.ratio for estimating ratios between totals, kott.quantile for estimating quantiles and kottby.user for calculating estimates based on user-defined estimators.

data(data.examples)

# Creation of a kott.design object:
kdes<-kottdesign(data=example,ids=~towcod+famcod,strata=~SUPERSTRATUM,
      weights=~weight,nrg=15)


# A model with one predictor and no intercept:
kott.regcoef(kdes,income~z-1)

# ...compare with ratio estimator:
kott.ratio(kott.addvars(kdes,income.mult.z=income*z,z2=z^2),~income.mult.z,~z2)


# A model with a factor term and no intercept:
kott.regcoef(kdes,income~age5c-1)

# ...compare with mean estimator in subpopulations:
kottby(kdes,~income,~age5c,estimator="mean")

# ...and with regression coefficients (for a different model)
# in subpopulations:
kott.regcoef(kdes,income~1,~age5c)


# An awkward model with many coefficients:
kott.regcoef(kdes,income~z:age5c+x3+marstat-1)