lmw_iv: Compute instrumental variable regression-implied weights

In ngreifer/lmw: Linear Model Weights

Compute instrumental variable regression-implied weights

Description

Computes the weights implied by an instrumental variable (IV) model that would estimate a weighted difference in outcome means equal to the treatment effect resulting from the supplied model fit with two-stage least squares.

Usage

lmw_iv(
  formula,
  data = NULL,
  estimand = "ATE",
  method = "URI",
  treat = NULL,
  iv,
  base.weights = NULL,
  s.weights = NULL,
  obj = NULL,
  fixef = NULL,
  target = NULL,
  target.weights = NULL,
  contrast = NULL,
  focal = NULL
)

Arguments

formula	a one-sided formula with the treatment and covariates on the right-hand side corresponding to the second-stage (reduced form) outcome regression model to be fit. If an outcome variable is supplied on the left-hand side, it will be ignored. This model should not include an IV. See Details for how this formula is interpreted in light of other options.
data	a data frame containing the variables named in formula, treat, and iv.
estimand	the estimand of interest, which determines how covariates are centered. Should be one of "ATE" for the average treatment effect, "ATT" for the average treatment effect in the treated, "ATC" for the average treatment effect in the control, or "CATE" for the conditional average treatment effect. When estimand = "CATE", an argument to target must be supplied. This argument also affects what summary.lmw() considers to be the target population. Default is "ATE" unless obj is specified, in which case it takes its value from the supplied object.
method	the method used to estimate the weights; either "URI" (the default) for uni-regression imputation weights, where a single model is fit to the whole dataset, or "MRI" for multi-regression imputation, where the covariates fully interact with the treatment. This affects the interpretation of formula. See Details.
treat	the name of the treatment variable in data. If unspecified, the first variable present in formula will be taken as the treatment variable with a message. Currently, only binary treatments are supported. See Details.
iv	a character vector or one-sided formula containing the names of the IVs in data. These variables should not appear in formula. Multiple IVs are allowed. See Details. This argument is required.
base.weights	a vector of base weights. See Details. If omitted and obj is specified, the weights from the supplied object will be used. Can be supplied as a numeric vector, a string containing the name of the variable in data containing the base weights, or the unquoted name of the variable in data containing the base weights.
s.weights	a vector of sampling weights. See Details. If omitted and obj is specified, the sampling weights from the supplied object will be used. Can be supplied as a numeric vector, a string containing the name of the variable in data containing the sampling weights, or the unquoted name of the variable in data containing the sampling weights.
obj	a matchit or weightit object corresponding to the matched or weighted sample in which the implied IV regression would take place. See Details.
fixef	optional; a string or one-sided formula containing the name of the fixed effects variable in data. See Details.
target	a list or data frame containing the target values for each covariate included in formula. Ignored with a warning when estimand is not "CATE".
target.weights	a vector of sampling weights to be applied to target when supplied as a data frame. Ignored with a warning when estimand is not "CATE".
contrast	ignored.
focal	the level of the treatment variable to be considered "focal" (i.e., the "treated" level when estimand = "ATT" or the control level when estimand = "ATC"). Ignored when estimand is "ATE" or "CATE". For binary treatments, this generally does not need to be supplied.

Details

lmw_iv() computes weights that make the weighted difference in outcome means between the treatment groups equal to the two-stage least squares (2SLS) estimate of the treatment effect. formula corresponds to the second-stage (reduced form) model, with the treatment replaced by its fitted values resulting from the first stage model. The first stage is fit by replacing the treatment in the supplied formula with the IVs named in iv and using the treatment as the outcome. The treatment is assumed to be endogenous and the supplied instrumental variables assumed to be instruments conditional on the other covariates, which are assumed to to be exogenous.

When any treatment-by-covariate interactions are present in formula or when method = "MRI", covariates are centered at specific values to ensure the resulting weights correspond to the desired estimand as supplied to the estimand argument. For the ATE, the covariates are centered at their means in the full sample. For the ATT and ATC, the covariates are centered at their means in the treatment or control group (i.e., the focal group), respectively. For the CATE, the covariates are centered according to the argument supplied to target (see below). Note that when covariate-by-covariate interactions are present, they will be centered after computing the interaction rather than the interaction being computed on the centered covariates unless estimand = "CATE", in which case the covariates will be centered at the values specified in target prior to involvement in interactions. Note that the resulting effect estimate does not actually correspond to the estimand supplied unless all effect heterogeneity is due to the included covariates.

When treatment-by-covariate interactions are included in formula, additional instruments will be formed as the product of the supplied IVs and the interacting covariates. When method = "MRI", instruments will be formed as the product of the supplied IVs and each of the covariates. All treatment-by-covariate interactions are considered endogenous.

Base weights and sampling weights

Base weights (base.weights) and sampling weights (s.weights) are similar in that they both involve combining weights with an outcome regression model. However, they differ in a few ways. Sampling weights are primarily used to adjust the target population; when the outcome model is fit, it is fit using weighted least squares, and when target balance is assessed, it is assessed using the sampling weighted population as the target population. Centering of covariates in the outcome model is done using the sampling weighted covariate means. Base weights are primarily used to offer a second level of balancing beyond the implied regression weights, i.e., to fit the 2SLS models in the base-weighted sample. Base weights do not change the target population, so when target balance is assessed, it is assessed using the unweighted population as the target population.

Some forms of weights both change the target population and provide an extra layer of balancing, like propensity score weights that target estimands other than the ATT, ATC, or ATE (e.g., overlap weights), or matching weights where the target population is defined by the matching (e.g., matching with a caliper, cardinality matching, or coarsened exact matching). Because these weights change the target population, they should be supplied to s.weights to ensure covariates are appropriately centered. In lmw_iv(), whether weights are supplied to base.weights or s.weights will not matter for the estimation of the weights but will affect the target population in balance assessment.

When both base.weights and s.weights are supplied, e.g., when the base weights are the result of a propensity score model fit with sampling weights, it is assumed the base weights do not incorporate the sampling weights; that is, it is assumed that to estimate a treatment effect without regression adjustment, the base weights and the sampling weights would have to be multiplied together. This is true, for example, for the weights in a matchit or weightit object (see below) but not for weights in the output of MatchIt::match.data() unless called with include.s.weights = FALSE or weights resulting from CBPS::CBPS().

2SLS after using MatchIt or WeightIt

Instrumental variable regression weights can be computed in a matched or weighted sample by supplying a matchit or weightit object (from MatchIt or WeightIt, respectively) to the obj argument of lmw(). The estimand, base weights, and sampling weights (if any) will be taken from the supplied object and used in the calculation of the implied regression weights, unless these have been supplied separately to lmw_iv(). The weights component of the supplied object containing the matching or balancing weights will be passed to base.weights and the s.weights component will be passed to s.weights. Arguments supplied to lmw_iv() will take precedence over the corresponding components in the obj object.

Multi-category treatments

Multi-category treatments are not currently supported for lmw_iv().

Fixed effects

A fixed effects variable can be supplied to the fixef argument. This is equivalent to adding the fixed effects variable as an exogenous predictor that does not interact with the treatment, IV, or any other covariate. The difference is that computation is much faster when the fixed effect has many levels because demeaning is used rather than including the fixed effect variable as a collection of dummy variables. When using URI, the weights will be the same regardless of whether the fixed effect variable is included as a covariate or supplied to fixef; when using MRI, results will differ because the fixed effect variable does not interact with treatment. The fixed effects variable will not appear in the summary.lmw() output (but can be added using addlvariables argument) or in the model output of lmw_est() or summary.lmw_est(). Because it does not interact with the treatment, the distribution of the fixed effect variable may not correspond to the target population, so caution should be used if it is expected the treatment effect varies across levels of this variable (in which case it should be included as a predictor). Currently only one fixed effect variable is allowed.

Value

An lmw_iv object, which inherits from lmw objects and contains the following components:

treat	the treatment variable, given as a factor.
weights	the computed implied regression weights.
covs	a data frame containing the covariates included the model formula.
estimand	the requested estimand.
method	the method used to estimate the weights ("URI" or "MRI").
base.weights	the weights supplied to base.weights.
s.weights	the weights supplied to s.weights.
call	the original call to lmw_iv().
fixef	the fixed effects variable if supplied to fixef.
formula	the model formula.
iv	the instrumental variables, given as a one-sided formula.
target	the supplied covariate target values when estimand = "CATE", after some initial processing.
contrast	the contrasted treatment groups.
focal	the focal treatment levels when estimand is "ATT" or "ATC".

All functions that lack a specific lmw_iv method work with lmw_iv objects as they do for lmw objects, such as summary.lmw(), plot.lmw(), etc.

References

Chattopadhyay, A., & Zubizarreta, J. R. (2023). On the implied weights of linear regression for causal inference. Biometrika, 110(3), 615–629. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/asac058")}

See Also

summary.lmw() for summarizing balance and representativeness; plot.lmw() for plotting features of the weights; lmw_est() for estimating treatment effects from lmw_iv objects; influence.lmw() for influence measures; ivreg() in the ivreg package for fitting 2SLS models.

Examples

# URI for the ATT using instrument `Ins`
lmw.out <- lmw_iv(~ treat + age + education + race +
                    re74, data = lalonde,
                  estimand = "ATT", method = "URI",
                  treat = "treat", iv = ~Ins)
lmw.out
summary(lmw.out, addlvariables = ~married + re75)

ngreifer/lmw documentation built on Feb. 14, 2024, 10:53 p.m.