Package 'CovSel' reference manual

Title:	Model-Free Covariate Selection
Description:	Model-free selection of covariates under unconfoundedness for situations where the parameter of interest is an average causal effect. This package is based on model-free backward elimination algorithms proposed in de Luna, Waernbaum and Richardson (2011). Marginal co-ordinate hypothesis testing is used in situations where all covariates are continuous while kernel-based smoothing appropriate for mixed data is used otherwise.
Authors:	Jenny Häggström, Emma Persson,
Maintainer:	Jenny Häggström <[email protected]>
License:	GPL-3
Version:	1.2.1
Built:	2024-11-02 06:20:07 UTC
Source:	CRAN

Model-Free Selection of Covariate Sets

Description

Dimension reduction of the covariate vector under unconfoundedness using model-free backward elimination algorithms, based on either marginal co-ordinate hypothesis testing, (MCH), (continuous covariates only) or kernel-based smoothing, (KS).

Usage

cov.sel(T, Y, X, type=c("dr", "np"), alg = 3,scope = NULL, alpha = 0.1,
		thru=0.5,thro=0.25,thrc=100,...)
cov.sel(T, Y, X, type=c("dr", "np"), alg = 3,scope = NULL, alpha = 0.1,
		thru=0.5,thro=0.25,thrc=100,...)

Arguments

`T`	A vector, containing `0` and `1`, indicating the binary treatment variable.
`Y`	A vector of observed outcomes.
`X`	A matrix or data frame containing columns of covariates. The covariates may be a mix of continuous, unordered discrete (to be specified in the data frame using `factor`), and ordered discrete (to be specified in the data frame using `ordered`).
`type`	The type of method used. `"dr"` for MCH and `"np"` for KS. MCH is suitable in situations with only continuous covariates while KS can be used if discrete covariates are present.
`alg`	Specifying which algorithm to be use. `1` indicates Algorithm A, `2` indicates Algorithm B and `3` runs them both. See Details. `alg = 3` is default.
`scope`	A character string giving the name of one (or several) covariate(s) that must not be removed.
`alpha`	Stopping criterion for MCH: will stop removing covariates when the p-value for the next covariate to be removed is less then `alpha`. The default is `alpha = 0.1`.
`thru`	Bandwidth threshold used for unordered discrete covariates if `type="np"`. Values in $[0,1]$ are valid. `thru=0` removes all unordered discrete covariates and `thru=1` removes none of them. Default is `thru=0.5`. See Details.
`thro`	Bandwidth threshold used for ordered discrete covariates if `type="np"`. Values in $[0,1]$ are valid. `thro=0` removes all unordered discrete covariates and `thro=1` removes none of them. Default is `thro=0.25`. See Details.
`thrc`	Bandwidth threshold used for continuous covariates if `type="np"`. Non-negative values are valid. Default is `thr=100`. See Details.
`...`	Additional arguments passed on to `dr`, `dr.step` or `npregbw`. If `type="dr"`, `method`, can be set to `"sir"` or `"save"`, the first being default, `trace=0` supresses the output generated by `dr.step`. If `type="np"`, `regtype` can be set to `"lc"` or `"ll"`, the first being default and `bwtype` can be set to `"fixed"`, `"generalized_nn"` or `"adaptive_nn"`, defaults to `"fixed"`. See `dr` and `npregbw` for usage of `na.action`.

Details

Performs model-free selection of covariates for situations where the parameter of interest is an average causal effect. This function is based on the framework of sufficient dimension reduction, that under unconfoundedness, reduces dimension of the covariate vector. A two-step procedure searching for a sufficient subset of the covariate vector is implemented in the form of algorithms. This function uses MCH (if type="dr") or KS (if type="np") in the form of two backward elimination algorithms, Algorithm A and Algorithm B proposed by de Luna, Waernbaum and Richardson (2011).

Algorithm A (alg = 1): First the covariates conditionally independent of the treatment, T, given the rest of the variables (X.T) are removed. Then the covariates conditionally independent of the potential outcomes (in each of the treatment groups) given the rest of the covariates are removed. This yields two subsets of covariates; Q.1 and Q.0 for the treatment and control group respectively.

Algorithm B (alg = 2): First the covariates conditionally independent of the potential outcome (in each of the treatment groups), given the rest of the covariates (X.0 and X.1) are removed. Then the covariates conditionally independent of the treatment, T, given the rest of the covariates are removed. This yields two subsets of covariates; Z.1 and Z.0 for the treatment and control group respectively.

alg=3 runs both Algorithm A and B.

In KS the bandwidth range for unordered discrete covariates is [0, 1/#levels] while for ordered discrete covariates, no matter how many levels, the range is [0, 1]. For continuous covariates bandwidths ranges from 0 to infinity. Ordered discrete and continuous covariates are removed if their bandwidths exceed their respective thresholds. Unordered discrete covariates are removed if their bandwidths are larger than thru times the maximum bandwidth.

In case of MCH one can choose between sliced inverse regression, SIR, or sliced average variance estimation, SAVE. For KS the regression type can be set to local constant kernel or local linear and the bandwidth type can be set to fixed, generalized nearest neighbors or adaptive nearest neighbors. See dr and npregbw for details. Since type="np" results in a fully nonparametric covariate selection procedure this can be much slower than if type="dr".

Value

cov.sel returns a list with the following content:

`X.T`	The of covariates with minimum cardinality such that $P($ `T`\|`X` $) = P($ `T`\|`X.T` $)$ .
`Q.0`	The set of covariates with minimum cardinality such that $P($ `Y.0`\|`X.T` $) = P($ `Y.0`\|`Q.0` $)$ . Where `Y.0` is the response in the control group.
`Q.1`	The set of covariates with minimum cardinality such that $P($ `Y.1`\|`X.T` $) = P($ `Y.1`\|`Q.1` $)$ . Where `Y.1` is the response in the treatment group.
`X.0`	The set of covariates with minimum cardinality such that $P($ `Y.0`\|`X` $) = P($ `Y.0`\|`X.0` $)$ .
`X.1`	The set of covariates with minimum cardinality such that $P($ `Y.1`\|`X` $) = P($ `Y.1`\|`X.1` $)$ .
`Z.0`	The set of covariates with minimum cardinality such that $P($ `T`\|`X.0` $) = P($ `T`\|`Z.0` $)$ .
`Z.1`	The set of covariates with minimum cardinality such that $P($ `T`\|`X.1` $) = P($ `T`\|`Z.1` $)$ .

If type="dr" the following type-specific content is returned:

`evectorsQ.0`	The eigenvectors of the matrix whose columns span the reduced subspace `Q.0`.
`evectorsQ.1`	The eigenvectors of the matrix whose columns span the reduced subspace `Q.1`.
`evectorsZ.0`	The eigenvectors of the matrix whose columns span the reduced subspace `Z.0`.
`evectorsZ.1`	The eigenvectors of the matrix whose columns span the reduced subspace `Z.1`.
`method`	The method used, either `"sir"` or `"save"`.

If type="np" the following type-specific content is returned:

`bandwidthsQ.0`	The selected bandwidths for the covariates in the reduced subspace `Q.0`.
`bandwidthsQ.1`	The selected bandwidths for the covariates in the reduced subspace `Q.1`.
`bandwidthsZ.0`	The selected bandwidths for the covariates in the reduced subspace `Z.0`.
`bandwidthsZ.1`	The selected bandwidths for the covariates in the reduced subspace `Z.1`.
`regtype`	The regression method used, either `"lc"` or `"ll"`.
`bwtype`	Type of bandwidth used, `"fixed"`, `"generalized_nn"` or `"adaptive_nn"`
`covar`	Names of all covariates given as input `X`.

For marginal co-ordinate hypothesis test, type="dr", as a side effect a data frame of labels, tests, and p.values is printed.

Note

cov.sel calls the functions dr, dr.step and npregbw so the packages dr and np are required.

Author(s)

Emma Persson, <[email protected]>, Jenny Häggström, <[email protected]>

References

Cook, R. D. (2004). Testing Predictor contributions in Sufficient Dimension Reduction. The Annals of statistics 32. 1061-1092

de Luna, X., I. Waernbaum, and T. S. Richardson (2011). Covariate selection for the nonparametric estimation of an average treatment effect. Biometrika 98. 861-875

Häggström, J., E. Persson, I. Waernbaum and X. de Luna (2015). An R Package for Covariate Selection When Estimating Average Causal Effects. Journal of Statistical Software 68. 1-20

Hall, P., Q. Li and J.S. Racine (2007). Nonparametric estimation of regression functions in the presence of irrelevant regressors. The Review of Economics and Statistics, 89. 784-789

Li, L., R. D. Cook, and C. J. Nachtsheim (2005). Model-free Variable Selection. Journal of the Royal Statistical Society, Series B 67. 285-299

Examples

## Marginal co-ordinate hypothesis test, continuous covariates only

data(datc)


##Algorithm A, keeping x6 and x7
  
ans <- cov.sel(T = datc$T, Y = datc$y, X = datc[,1:8], type="dr",
               alpha = 0.1, alg = 1, scope=c("x6","x7"))

summary(ans)

##Algorithm B, method "save"
  
ans <- cov.sel(T = datc$T, Y = datc$y, X = datc[,1:10], type="dr",
               alg = 2, method = "save", alpha = 0.3, na.action = "na.omit")

## Kernel-based smoothing, both categorical and continuous covariates

data(datfc)
##The example below with default setting takes about 9 minutes to run.
## ans <- cov.sel(T = datfc$T, Y = datfc$y, X = datfc[,1:8], type="np",
##               alpha = 0.1, alg = 3, scope=NULL, thru=0.5, thro=0.25, thrc=100)

## For illustration purposes we run Algorithm A using only the first 100 observations 
##and x1, x2, x3, x4 in datfc
ans <- cov.sel(T = datfc$T[1:100], Y = datfc$y[1:100], X = datfc[1:100,1:4], 
      type="np",alpha = 0.1, alg = 1, scope=NULL, thru=0.5, thro=0.25, thrc=100)

##The example below running Algorithm A, keeping x6 and x7 with regtype="ll"
##takes about 7 minutes to run.
##ans <- cov.sel(T = datfc$T, Y = datfc$y, X = datfc[,1:8], type="np",
##               alpha = 0.1, alg = 3, scope=c("x6","x7"), thru=0.5, thro=0.25, 
##               thrc=100, regtype="ll")

## Marginal co-ordinate hypothesis test, continuous covariates only

data(datc)


##Algorithm A, keeping x6 and x7
  
ans <- cov.sel(T = datc$T, Y = datc$y, X = datc[,1:8], type="dr",
               alpha = 0.1, alg = 1, scope=c("x6","x7"))

summary(ans)

##Algorithm B, method "save"
  
ans <- cov.sel(T = datc$T, Y = datc$y, X = datc[,1:10], type="dr",
               alg = 2, method = "save", alpha = 0.3, na.action = "na.omit")

## Kernel-based smoothing, both categorical and continuous covariates

data(datfc)
##The example below with default setting takes about 9 minutes to run.
## ans <- cov.sel(T = datfc$T, Y = datfc$y, X = datfc[,1:8], type="np",
##               alpha = 0.1, alg = 3, scope=NULL, thru=0.5, thro=0.25, thrc=100)

## For illustration purposes we run Algorithm A using only the first 100 observations 
##and x1, x2, x3, x4 in datfc
ans <- cov.sel(T = datfc$T[1:100], Y = datfc$y[1:100], X = datfc[1:100,1:4], 
      type="np",alpha = 0.1, alg = 1, scope=NULL, thru=0.5, thro=0.25, thrc=100)

##The example below running Algorithm A, keeping x6 and x7 with regtype="ll"
##takes about 7 minutes to run.
##ans <- cov.sel(T = datfc$T, Y = datfc$y, X = datfc[,1:8], type="np",
##               alpha = 0.1, alg = 3, scope=c("x6","x7"), thru=0.5, thro=0.25, 
##               thrc=100, regtype="ll")

cov.sel.np

Description

Function called by cov.sel if type="np". Not meant to be used on its own.

Usage

cov.sel.np(T, Y, X, alg, scope, thru, thro, thrc, dat, data.0,
		data.1, covar, ...)
cov.sel.np(T, Y, X, alg, scope, thru, thro, thrc, dat, data.0,
		data.1, covar, ...)

Arguments

`T`	A vector, containing `0` and `1`, indicating the binary treatment variable.
`Y`	A vector of observed outcomes.
`X`	A matrix or data frame containing columns of covariates. The covariates may be a mix of continuous, unordered discrete (to be specified in the data frame using `factor`), and ordered discrete (to be specified in the data frame using `ordered`).
`alg`	Specifying which algorithm to be use. `1` indicates Algorithm A, `2` indicates Algorithm B and `3` runs them both. See Details. `alg = 3` is default.
`scope`	A character string giving the name of one (or several) covariate(s) that must not be removed.
`thru`	Bandwidth threshold for unordered discrete covariates. Values in $[0,1]$ are valid. `thru=0` removes all unordered discrete covariates and `thru=1` removes none of them. Default is `thru=0.5`.
`thro`	Bandwidth threshold for ordered discrete covariates. Values in $[0,1]$ are valid. `thro=0` removes all unordered discrete covariates and `thro=1` removes none of them. Default is `thro=0.25`.
`thrc`	Bandwidth threshold for continuous covariates. Non-negative values are valid. Default is `thr=100`.
`dat`	Passed on from `cov.sel`
`data.0`	Passed on from `cov.sel`
`data.1`	Passed on from `cov.sel`
`covar`	Passed on from `cov.sel`
`...`	Additional arguments passed on to `npregbw`. `regtype` can be set to `"lc"` or `"ll"`, the first being default and `bwtype` can be set to `"fixed"`, `"generalized_nn"` or `"adaptive_nn"`, defaults to `"fixed"`.

Details

See cov.sel for details.

Value

Function returns subsets, methods and removed covariates. See cov.sel for details.

Note

cov.sel.np calls the function npregbw so the package np is required.

Author(s)

Jenny Häggström, <[email protected]>

References

de Luna, X., I. Waernbaum, and T. S. Richardson (2011). Covariate selection for the nonparametric estimation of an average treatment effect. Biometrika 98. 861-875

Häggström, J., E. Persson, I. Waernbaum and X. de Luna (2015). An R Package for Covariate Selection When Estimating Average Causal Effects. Journal of Statistical Software 68. 1-20

Hall, P., Q. Li and J.S. Racine (2007). Nonparametric estimation of regression functions in the presence of irrelevant regressors. The Review of Economics and Statistics, 89. 784-789

Simulated Data, Continuous

Description

This data is simulated. The covariates, X, are all generated from a standard normal distribution and they are all independent except for $x_7$ and $x_8$ (cor( $x_7$ , $x_8$ )=0.5). The code generating the data is

library(MASS)
set.seed(9327529)
n<-1000
eta<-mvrnorm(n,rep(0,2),diag(1,2,2))
Sigma=diag(1,10,10)
Sigma[7,8]<-Sigma[8,7]<-0.5
X<-mvrnorm(n,rep(0,10),Sigma)
y0<-2+2*X[,1]+2*X[,2]+2*X[,5]+2*X[,6]+2*X[,8]+eta[,1]
y1<-4+2*X[,1]+2*X[,2]+2*X[,5]+2*X[,6]+2*X[,8]+eta[,2]
e<-1/(1+exp(-0.5*X[,1]-0.5*X[,2]-0.5*X[,3]-0.5*X[,4]-0.5*X[,7]))
T<-rbinom(n,1,e)
y<-y1*T+y0*(1-T)
datc<-data.frame(x1=X[,1],x2=X[,2],x3=X[,3],x4=X[,4],x5=X[,5],x6=X[,6],
x7=X[,7],x8=X[,8],x9=X[,9],x10=X[,10],y0,y1,y,T)

Usage

data(datc)data(datc)

Format

A data frame with 1000 observations on the following 14 variables.

x1: a numeric vector
x2: a numeric vector
x3: a numeric vector
x4: a numeric vector
x5: a numeric vector
x6: a numeric vector
x7: a numeric vector
x8: a numeric vector
x9: a numeric vector
x10: a numeric vector
y0: a numeric vector
y1: a numeric vector
y: a numeric vector
T: a numeric vector

Simulated Data, Factors

Description

This data is simulated. The covariates, X, and the treatment, T, are all generated by simulating independent bernoulli distributions or from a multivariate normal distribution and then dichotomizing to get binary variables with a certain dependence structure.The code generating the data is

library(bindata)
set.seed(9327529)
n<-500
x1 <- rbinom(n, 1, prob = 0.5)
x25 <- rmvbin(n, bincorr=cbind(c(1,0.7),c(0.7,1)), margprob=c(0.5,0.5))
x34 <- rmvbin(n, bincorr=cbind(c(1,0.7),c(0.7,1)), margprob=c(0.5,0.5))
x2 <- x25[,1]
x3 <- x34[,1]
x4 <- x34[,2]
x5 <- x25[,2]
x6 <- rbinom(n, 1, prob = 0.5)
x7<- rbinom(n, 1, prob = 0.5)
x8 <- rbinom(n, 1, prob = 0.5)
e0<-rnorm(n)
e1<-rnorm(n)
p <- 1/(1 + exp(3 - 1.5 * x1 - 1.5 * x2 - 1.5 * x3 - 0.1 * x4 - 0.1 * x5 - 1.3 * x8))
T <- rbinom(n, 1, prob = p)
y0 <- 4 + 2 * x1 + 3 * x4 + 5 * x5 + 2 * x6 + e0
y1 <- 2 + 2 * x1 + 3 * x4+ 5 * x5 + 2 * x6 + e1
y <- y1 * T + y0 * (1 - T)
datf <- data.frame(x1, x2, x3, x4, x5, x6, x7, x8, y0, y1, y, T)
datf[, 1:8] <- lapply(datf[, 1:8], factor)
datf[, 12] <- as.numeric(datf[, 12])

Usage

data(datf)data(datf)

Format

A data frame with 500 observations on the following 12 variables.

x1: a factor with two levels
x2: a factor with two levels
x3: a factor with two levels
x4: a factor with two levels
x5: a factor with two levels
x6: a factor with two levels
x7: a factor with two levels
x8: a factor with two levels
y0: a numeric vector
y1: a numeric vector
y: a numeric vector
T: a numeric vector

Simulated Data, Mixed

Description

This data is simulated. The covariates, X, and the treatment, T, are all generated by simulating from independent or multivariate normal distributions and then some variables are dichotomized to get binary variables with a certain dependence structure. The code generating the data is

library(bindata)
set.seed(9327529)
n<-500
x1 <- rnorm(n, mean = 0, sd = 1)
x2 <- rbinom(n, 1, prob = 0.5)
x25 <- rmvbin(n, bincorr=cbind(c(1,0.7),c(0.7,1)), margprob=c(0.5,0.5))
x2 <- x25[,1]
Sigma <- matrix(c(1,0.5,0.5,1),ncol=2)
x34 <- mvrnorm(n, rep(0, 2), Sigma)
x3 <- x34[,1]
x4 <- x34[,2]
x5 <- x25[,2]
x6 <- rbinom(n, 1, prob = 0.5)
x7<- rnorm(n, mean = 0, sd = 1)
x8 <- rbinom(n, 1, prob = 0.5)
e0<-rnorm(n)
e1<-rnorm(n)
p <- 1/(1 + exp(3 - 1.2 * x1 - 3.7 * x2 - 1.5 * x3 - 0.3 * x4 - 0.3 * x5 - 1.9 * x8))
T <- rbinom(n, 1, prob = p)
y0 <- 4 + 2 * x1 + 3 * x4 + 5 * x5 + 2 * x6 + e0
y1 <- 2 + 2 * x1 + 3 * x4+ 5 * x5 + 2 * x6 + e1
y <- y1 * T + y0 * (1 - T)
datfc <- data.frame(x1, x2, x3, x4, x5, x6, x7, x8, y0, y1, y, T)
datfc[, c(2, 5, 6, 8)] <- lapply(datfc[, c(2, 5, 6, 8)], factor)
datfc[, 12] <- as.numeric(datfc[, 12])

Usage

data(datfc)data(datfc)

Format

A data frame with 500 observations on the following 12 variables.

x1: a numeric vector
x2: a factor with two levels
x3: a numeric vector
x4: a numeric vector
x5: a factor with two levels
x6: a factor with two levels
x7: a numeric vector
x8: a factor with two levels
y0: a numeric vector
y1: a numeric vector
y: a numeric vector
T: a numeric vector

Real data, Lalonde

Description

In order for the code used to create this data frame to work text files available on Dehejia's webpage http://www.nber.org/~rdehejia/data/nswdata2.html need to be downloaded and stored in the working directory. The data frame consists of 297 treated units from a randomized evaluation of a labor training program, the National Supported Work (NSW) Demonstration, and 314 nonexperimental comparison units drawn from survey datasets.

treated <- read.table(file = "nswre74_treated.txt")
controls <- read.table(file = "cps3_controls.txt")
nsw <- rbind(treated, controls)
ue <- function(x) factor(ifelse(x > 0, 0, 1))
UE74 <- mapply(ue, nsw[, 8])
UE75 <- mapply(ue, nsw[, 9])
nsw[, 4:7] <- lapply(nsw[, 4:7], factor)
lalonde <- cbind(nsw[, 1:9], UE74, UE75, nsw[, 10])
colnames(lalonde) <- c("treat", "age", "educ", "black", "hisp", "married",
"nodegr", "re74", "re75", "u74", "u75", "re78")

Usage

data(lalonde)data(lalonde)

Format

A data frame with 614 observations on the following 12 variables.

treat: a numeric vector
age: a numeric vector
educ: a numeric vector
black: a factor with two levels
hisp: a factor with two levels
married: a factor with two levels
nodegr: a factor with two levels
re74: a numeric vector
re75: a numeric vector
u74: a factor with two levels
u75: a factor with two levels
re78: a numeric vector

Summary

Description

This function produce a summary of the results of the covariate selection done by invoking cov.sel.

Usage

## S3 method for class 'cov.sel'
summary(object, ...)
## S3 method for class 'cov.sel'
summary(object, ...)

Arguments

`object`	The list that `cov.sel` returns
`...`	additional arg

Details

Function gives subsets, method and removed variables.

Value

`X.T`	subset `X.T`
`X.0`	subset `X.0`
`X.1`	subset `X.1`
`Q.0`	subset `Q.0`
`Q.1`	subset `Q.1`
`Z.0`	subset `Z.0`
`Z.1`	subset `Z.1`
`method`	The method
`Q.0comp`	The complement subset of covariates to `Q.0`
`Q.1comp`	The complement subset of covariates to `Q.1`
`Z.0comp`	The complement subset of covariates to `Z.0`
`Z.1comp`	The complement subset of covariates to `Z.1`

Author(s)

Emma Persson, <[email protected]>

Package 'CovSel'

Help Index

Model-Free Selection of Covariate Sets

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

cov.sel.np

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Simulated Data, Continuous

Description

Usage

Format

Simulated Data, Factors

Description

Usage

Format

Simulated Data, Mixed

Description

Usage

Format

Real data, Lalonde

Description

Usage

Format

Summary

Description

Usage

Arguments

Details

Value

Author(s)