R: Counterfactual Evaluation

whatif {WhatIf}

R Documentation

Counterfactual Evaluation

Description

Implements the methods described in King and Zeng (2006a, 2006b) for evaluating counterfactuals.

Usage

whatif(formula = NULL, data, cfact, range = NULL, freq = NULL, nearby = 1, 
distance = "gower", miss = "list", choice = "both", return.inputs = FALSE, 
return.distance = FALSE, mc.cores = detectCores(), ...)

Arguments

`formula`	An optional formula without a dependent variable that is of class "formula" and that follows standard `R` conventions for formulas, e.g. ~ x1 + x2. Allows you to transform or otherwise re-specify combinations of the variables in both `data` and `cfact`. To use this parameter, both `data` and `cfact` must be coercable to data frames; the variables of both `data` and `cfact` must be labeled; and all variables appearing in `formula` must also appear in both `data` and `cfact`. Otherwise, errors are returned. The intercept is automatically dropped. Default is `NULL`.
`data`	May take one of the following forms: A `R` model output object, such as the output from calls to `lm`, `glm`, and `zelig`. If it is not a `zelig` object, such an output object must be a list. It must additionally have either a `formula` or `terms` component and either a `data` or `model` component; if it does not, an error is returned. Of the latter, `whatif` first looks for `data`, which should contain either the original data set supplied as part of the model call (as in `glm`) or the name of this data set (as in `zelig`), which is assumed to reside in the global environment. If `data` does not exist, `whatif` then looks for `model`, which should contain the model frame (as in `lm`). The intercept is automatically dropped from the extracted observed covariate data set if the original model included one. A `n`-by-`k` non-character (logical or numeric) matrix or data frame of observed covariate data with `n` data points or units and `k` covariates. All desired variable transformations and interaction terms should be included in this set of `k` covariates unless `formula` is alternatively used to produce them. However, an intercept should not be. Such a matrix may be obtained by passing model output (e.g., output from a call to `lm`) to `model.matrix` and excluding the intercept from the resulting matrix if one was fit. Note that `whatif` will attempt to coerce data frames to their internal numeric values. Hence, data frames should only contain logical, numeric, and factor columns; character columns will lead to an error being returned. A string. Either the complete path (including file name) of the file containing the data or the path relative to your working directory. This file should be a white space delimited text file. If it contains a header, you must include a column of row names as discussed in the help file for the `R` function `read.table`. The data in the file should be as otherwise described in (2). Missing data is allowed and will be dealt with via the argument `missing`. It should be flagged using `R`'s standard representation for missing data, `NA`.
`cfact`	A `R` object or a string. If a `R` object, a `m`-by-`k` non-character matrix or data frame of counterfactuals with `m` counterfactuals and the same `k` covariates (in the same order) as in `data`. However, if `formula` is used to select a subset of the `k` covariates, then `cfact` may contain either only these `j \leq k` covariates or the complete set of `k` covariates. An intercept should not be included as one of the covariates. It will be automatically dropped from the counterfactuals generated by Zelig if the original model contained one. Data frames will again be coerced to their internal numeric values if possible. If a string, either the complete path (including file name) of the file containing the counterfactuals or the path relative to your working directory. This file should be a white space delimited text file. See the discussion under `data` for instructions on dealing with a header. All counterfactuals should be fully observed: if you supply counterfactuals with missing data, they will be list-wise deleted and a warning message will be printed to the screen.
`range`	An optional numeric vector of length `k`, where `k` is the number of covariates. Each element represents the range of the corresponding covariate for use in calculating Gower distances. Use this argument when covariate data do not represent the population of interest, such as selection by stratification or experimental manipulation. By default, the range of each covariate is calculated from the data (the difference of its maximum and minimum values in the sample), which is appropriate when a simple random sampling design was used. To supply your own range for the `k`th covariate, set the `k`th element of the vector equal to the desired range and all other elements equal to `NA`. Default is `NULL`.
`freq`	An optional numeric vector of any positive length, the elements of which comprise a set of distances. Used in calculating cumulative frequency distributions for the distances of the data points from each counterfactual. For each such distance and counterfactual, the cumulative frequency is the fraction of observed covariate data points with distance to the counterfactual less than or equal to the supplied distance value. The default varies with the distance measure used. When the Gower distance measure is employed, frequencies are calculated for the sequence of Gower distances from 0 to 1 in increments of 0.05. When the Euclidian distance measure is employed, frequencies are calculated for the sequence of Euclidian distances from the minimum to the maximum observed distances in twenty equal increments, all rounded to two decimal places. Default is `NULL`.
`nearby`	An optional scalar indicating which observed data points are considered to be nearby (i.e., withing ‘nearby’ geometric variances of) the counterfactuals. Used to calculate the summary statistic returned by the function: the fraction of the observed data nearby each counterfactual. By default, the geometric variance of the covariate data is used. For example, setting `nearby` to 2 will identify the proportion of data points within two geometric variances of a counterfactual. Default is `NULL`.
`distance`	An optional string indicating which of two distance measures to employ. The choices are either `"gower"`, Gower's non-parametric distance measure (`G^2`), which is suitable for both qualitative and quantitative data; or `"euclidian"`, squared Euclidian distance, which is only suitable for quantitative data. The default is `"gower"`.
`miss`	An optional string indicating the strategy for dealing with missing data in the observed covariate data set. `whatif` supports two possible missing data strategies: `"list"`, list-wise deletion of missing cases; and `"case"`, ignoring missing data case-by-case. Note that if `"case"` is selected, cases with missing values are deleted listwise for the convex hull test and for computing Euclidian distances, but pairwise deletion is used in computing the Gower distances to maximally use available information. The user is strongly encouraged to treat missing data using specialized tools such as Amelia prior to feeding the data to `whatif`. Default is `"list"`.
`choice`	An optional string indicating which analyses to undertake. The options are either `"hull"`, only perform the convex hull membership test; `"distance"`, do not perform the convex hull test but do everything else, such as calculating the distance between each counterfactual and data point; or `"both"`, undertake both the convex hull test and the distance calculations (i.e., do everything). Default is `"both"`.
`return.inputs`	A Boolean; should the processed observed covariate and counterfactual data matrices on which all `whatif` computations are performed be returned? Processing refers to internal `whatif` operations such as the subsetting of covariates via `formula`, the deletion of cases with missing values, and the coercion of data frames to numeric matrices. Primarily intended for diagnostic purposes. If `TRUE`, these matrices are returned as a list. Default is `FALSE`.
`return.distance`	A Boolean; should the matrix of distances between each counterfactual and data point be returned? If `TRUE`, this matrix is returned as part of the output; if `FALSE`, it is not. Default is `FALSE` due to the large size that this matrix may attain.
`mc.cores`	The number of cores to use for the convex hull test, i.e. at most how many child processes will be run simultaneously. Must be at least one, and parallelization requires at least two cores. The default is set by `detectCores`

...

Further arguments passed to and from other methods.

Details

This function is the primary tool for evaluating your counterfactuals. Specifically, it:

Determines whether or not your counterfactuals are in the convex hull of the observed covariate data.
Computes the distance of your counterfactuals from each of the n observed covariate data points. The default distance function used is Gower's non-parametric measure.
Computes a summary statistic for each counterfactual based on the distances in (2): the fraction of observed covariate data points with distances to your counterfactual less than a value you supply. By default, this value is taken to be the geometric variability of the observed data.
Computes the cumulative frequency distribution of each counterfactual for the distances in (2) using values that you supply. By default, Gower distances from 0 to 1 in increments of 0.05 are used.

Value

An object of class "whatif", a list consisting of the following six or seven elements:

`call`	The original call to `whatif`.
`inputs`	A list with two elements, `data` and `cfact`. Only present if `return.inputs` was set equal to `TRUE` in the call to `whatif`. The first element is the processed observed covariate data matrix on which all `whatif` computations were performed. The second element is the processed counterfactual data matrix.
`in.hull`	A logical vector of length `m`, where `m` is the number of counterfactuals. Each element of the vector is `TRUE` if the corresponding counterfactual is in the convex hull and `FALSE` otherwise.
`dist`	A `m`-by-`n` numeric matrix, where `m` is the number of counterfactuals and `n` is the number of data points (units). Only present if `return.distance` was set equal to `TRUE` in the call to `whatif`. The `[i, j]`th entry of the matrix contains the distance between the `i`th counterfactual and the `j`th data point.
`geom.var`	A scalar. The geometric variability of the observed covariate data.
`sum.stat`	A numeric vector of length `m`, where `m` is the number of counterfactuals. The `m`th element contains the summary statistic for the corresponding counterfactual. This summary statistic is the fraction of data points with distances to the counterfactual less than the argument `nearby`, which by default is the geometric variability of the covariates.
`cum.freq`	A numeric matrix. By default, the matrix has dimension `m`-by-21, where `m` is the number of counterfactuals; however, if you supplied your own frequencies via the argument `freq`, the matrix has dimension `m`-by-`f`, where `f` is the length of `freq`. Each row of the matrix contains the cumulative frequency distribution for the corresponding counterfactual calculated using either the distance measure-specific default set of distance values or the set that you supplied (see the discussion under the argument `freq`). Hence, the `[i, j]`th entry of the matrix is the fraction of data points with distances to the `i`th counterfactual less than or equal to the value represented by the `j`th column. The column names contain these values.

Note

This function requires the lpSolve package.

Author(s)

Stoll, Heather hstoll@polsci.ucsb.edu, King, Gary king@harvard.edu and Zeng, Langche zeng@ucsd.edu

References

King, Gary and Langche Zeng. 2006. "The Dangers of Extreme Counterfactuals." Political Analysis 14 (2). Available from https://gking.harvard.edu.

King, Gary and Langche Zeng. 2007. "When Can History Be Our Guide? The Pitfalls of Counterfactual Inference." International Studies Quarterly 51 (March). Available from https://gking.harvard.edu.

Examples

##  Create example data sets and counterfactuals
my.cfact <- matrix(rnorm(3*5), ncol = 5)
my.data <- matrix(rnorm(100*5), ncol = 5)

##  Evaluate counterfactuals
my.result <- whatif(data = my.data, cfact = my.cfact, mc.cores = 1)

##  Evaluate counterfactuals and supply own gower distances for 
##  cumulative frequency distributions
my.result <- whatif(cfact = my.cfact, data = my.data, 
                    freq = c(0, .25, .5, 1, 1.25, 1.5), mc.cores = 1)

[Package WhatIf version 1.5-10 Index]