lmw_est: Estimate a treatment effect from a linear model
In ngreifer/lmw: Linear Model Weights
lmw_est R Documentation
Estimate a treatment effect from a linear model
Description
lmw_est() fits the outcome regression corresponding to the model used
to compute the weights in the supplied lmw object and returns the
model coefficients and their covariance matrix. Use
summary.lmw_est() to compute and view the treatment effect and
potential outcome mean estimates and their standard errors.
Usage
lmw_est(x, ...)
## S3 method for class 'lmw'
lmw_est(x, outcome, data = NULL, robust = TRUE, cluster = NULL, ...)
## S3 method for class 'lmw_aipw'
lmw_est(x, outcome, data = NULL, robust = TRUE, cluster = NULL, ...)
## S3 method for class 'lmw_iv'
lmw_est(x, outcome, data = NULL, robust = TRUE, cluster = NULL, ...)
Arguments
x
an lmw or lmw_iv object; the output of a call to
lmw() or lmw_iv().
...
other arguments passed to sandwich::vcovHC() or
sandwich::vcovCL().
outcome
the name of the outcome variable. Can be supplied as a string
containing the name of the outcome variable or as the outcome variable
itself. If not supplied, the outcome variable in the formula supplied
to lmw() or lmw_iv(), if any, will be used.
data
an optional data frame containing the outcome variable named in
outcome and the cluster variable(s) when cluster is supplied
as a formula.
robust
whether to compute the robust covariance matrix for the model
coefficients. Allowable values include those allowed for the type
argument of sandwich::vcovHC() or sandwich::vcovCL()
when cluster is specified. Can also be specified as TRUE (the
default), which means "HC3" or "HC1" when cluster is
specified, or FALSE, which means "const" (i.e., the standard
non-robust covariance). When cluster is specified, robust will
be set to TRUE if FALSE. When AIPW is used, robust is
ignored; the HC0 robust covariance matrix is used.
cluster
the clustering variable(s) for computing a cluster-robust
covariance matrix. See sandwich::vcovCL(). If supplied as a
formula, the clustering variables must be present in the original
dataset used to compute the weights or data. When AIPW is used,
cluster is ignored.
Details
lmw_est() uses lm.fit() or lm.wfit() to fit
the outcome regression model (and first stage model for lmw_iv
objects) and returns the output of these functions augmented with other
components related to the estimation of the weights. Unlike with
lm.[w]fit(), the covariance matrix of the parameter estimates is also
included in the output.
For lmw objects, the model fit is that supplied to the formula
input to lmw() except that it is fit in a dataset appropriately
centered to ensure the estimand corresponds with the one requested. When
method = "MRI" in the call to lmw(), the model is fit as an
interaction between the treatment and all the (centered) terms in the model
formula. The results will be similar to those from using lm() on
this model and supplied data except that the covariates are centered
beforehand. The product of the sampling weights and base weights supplied to
lmw(), if any, will be supplied to lm.wfit() to fit the model
using weighted least squares.
For lmw_aipw objects, the model is fit as above except that base
weights are not included in the model fitting and are instead used to
compute additional augmentation terms that are added to the estimated
potential outcome means from the outcome regression. The variance-covariance
matrix is computed using M-estimation; this corresponds to the HC0 robust
covariance matrix for the model parameters with the base weights treated as
fixed, which yields conservative standard errors for the ATE. Inference is
only approximate for the ATT and ATC.
For lmw_iv objects, the first stage model is constructed by removing
the treatment from the supplied model formula, adding the instrumental
variable as a main effect, and using the treatment variable as the outcome.
For the second stage (reduced form) model, the fitted values of the
treatment from the first stage model are used in place of the treatment in
the outcome model. The results are similar to those from using
ivreg::ivreg(), and the coefficients estimates will be the same
except for the intercept due to the centering of covariates.
Although some coefficients in the model may be interpretable as treatment
effect estimates, summary.lmw_est() should be used to view and
extract the treatment effect and potential outcome mean estimates, standard
errors, and other model statistics. The output of lmw_est() should
rarely be used except to be supplied to summary().
Value
An lmw_est object with the following components:
coefficients, residuals, fitted.values, effects, weights, rank,
df.residual, qr
for lmw objects, the output of the
lm.fit() or lm.wfit() call used to fit the outcome
model. For lmw_iv objects, the output of the lm.fit() or
lm.wfit() call used to fit the the second stage model, with
residuals corresponding to the residuals computed when substituting
the true treatment variable in place of the fitted treatment values in the
model.
model.matrix
the model matrix (supplied to the x
argument of lm.fit).
vcov
the estimated covariance matrix of
the parameter estimates as produced by sandwich::vcovHC() or
sandwich::vcovCL().
lmw.weights
the implied regression
weights computed by lmw_est().
call
the call to
lmw_est().
estimand
the requested estimand.
focal
the
focal treatment level when estimand is "ATT" or "ATC".
method
the method used to estimate the weights ("URI" or
"MRI").
robust
the type standard error used.
outcome
the name of the outcome variable.
treat_levels
the
levels of the treatment.
When AIPW is used, the object will be of class lmw_est_aipw, which
inherits from lmw_est, and contains the additional components:
coef_aipw
the model-predicted potential outcome means (mu) and
the augmentation terms (aug).
vcov_aipw
the covariance matrix
of the quantities in coef_aipw.
When weights are included in the estimation (i.e., base.weights or
s.weights supplied to lmw() or lmw_iv()), any units
will weights equal to zero will be removed from the data prior to model
fitting.
Methods exist for lmw_est objects for model.matrix(),
vcov(), hatvalues(), sandwich::bread(),
and sandwich::estfun(), all of which are used internally to
compute the parameter estimate covariance matrix. The first two simply
extract the corresponding component from the lmw_est object and the
last three imitate the corresponding methods for lm objects (or
ivreg objects for lmw_iv inputs). Other regression-related
functions, such as coef(), residuals(), and
fitted(), use the default methods and should work correctly with
lmw_est objects.
Note that when fixed effects are supplied through the fixef argument
to lmw() or lmw_iv(), standard error estimates computed using
functions outside lmw may not be accurate due to issues relating to
degrees of freedom. In particular, this affects conventional and HC1-robust
standard errors. Otherwise, sandwich::vcovHC() can be used to compute
standard errors (setting type = "const" for conventional standard
errors), though sandwich::vcovCL() may not work as expected and
should not be used. To calculate cluster-robust standard errors, supply an
argument to cluster in lmw_est().
Note
lmw_est() uses non-standard evaluation to interpret its
outcome argument. For programmers who wish to use lmw_est()
inside other functions, an effective way to pass the name of an arbitrary
outcome (e.g., y passed as a string) is to use do.call(),
for example:
fun <- function(model, outcome, data) {
do.call("lmw_est", list(model, outcome, data)) } When using
lmw_est() inside lapply() or purrr::map to loop
over outcomes, this syntax must be used as well.
See Also
summary.lmw_est() for viewing and extracting the
treatment effect and potential outcome mean estimates, standard errors, and
other model statistics; lmw() or lmw_iv() for
estimating the weights that correspond to the model estimated by
lmw_est(); lm() and lm.fit() for fitting the
corresponding model; ivreg() in the ivreg package for fitting
2SLS models; influence.lmw_est() for influence measures
Examples
data("lalonde")
# MRI regression for ATT
lmw.out1 <- lmw(~ treat + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
estimand = "ATT", method = "MRI",
treat = "treat")
lmw.fit1 <- lmw_est(lmw.out1, outcome = "re78")
lmw.fit1
summary(lmw.fit1)
# MRI regression for ATT after propensity score matching
m.out <- MatchIt::matchit(treat ~ age + education + race +
married + nodegree + re74 + re75,
data = lalonde, method = "nearest",
estimand = "ATT")
lmw.out2 <- lmw(~ treat + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
method = "MRI", treat = "treat", obj = m.out)
## Using a cluster-robust SE with subclass (pair membership)
## as the cluster variable
lmw.fit2 <- lmw_est(lmw.out2, outcome = "re78", cluster = ~subclass)
lmw.fit2
summary(lmw.fit2)
# AIPW for ATE with MRI regression after propensity score
# weighting
ps <- glm(treat ~ age + education + race + married + nodegree +
re74 + re75, data = lalonde,
family = binomial)$fitted
ipw <- ifelse(lalonde$treat == 1, 1/ps, 1/(1-ps))
lmw.out3 <- lmw(re78 ~ treat + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
method = "MRI", treat = "treat",
base.weights = ipw, dr.method = "AIPW")
lmw.fit3 <- lmw_est(lmw.out3)
lmw.fit3
summary(lmw.fit3)
# MRI for multi-category treatment ATE
lmw.out3 <- lmw(~ treat_multi + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
estimand = "ATE", method = "MRI",
treat = "treat_multi")
lmw.fit3 <- lmw_est(lmw.out3, outcome = "re78")
lmw.fit3
summary(lmw.fit3)
ngreifer/lmw documentation built on Feb. 14, 2024, 10:53 p.m.
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| lmw_est | R Documentation |
Estimate a treatment effect from a linear model
Description
lmw_est() fits the outcome regression corresponding to the model used
to compute the weights in the supplied lmw object and returns the
model coefficients and their covariance matrix. Use
summary.lmw_est() to compute and view the treatment effect and
potential outcome mean estimates and their standard errors.
Usage
lmw_est(x, ...)
## S3 method for class 'lmw'
lmw_est(x, outcome, data = NULL, robust = TRUE, cluster = NULL, ...)
## S3 method for class 'lmw_aipw'
lmw_est(x, outcome, data = NULL, robust = TRUE, cluster = NULL, ...)
## S3 method for class 'lmw_iv'
lmw_est(x, outcome, data = NULL, robust = TRUE, cluster = NULL, ...)
Arguments
x |
an |
... |
other arguments passed to |
outcome |
the name of the outcome variable. Can be supplied as a string
containing the name of the outcome variable or as the outcome variable
itself. If not supplied, the outcome variable in the |
data |
an optional data frame containing the outcome variable named in
|
robust |
whether to compute the robust covariance matrix for the model
coefficients. Allowable values include those allowed for the |
cluster |
the clustering variable(s) for computing a cluster-robust
covariance matrix. See |
Details
lmw_est() uses lm.fit() or lm.wfit() to fit
the outcome regression model (and first stage model for lmw_iv
objects) and returns the output of these functions augmented with other
components related to the estimation of the weights. Unlike with
lm.[w]fit(), the covariance matrix of the parameter estimates is also
included in the output.
For lmw objects, the model fit is that supplied to the formula
input to lmw() except that it is fit in a dataset appropriately
centered to ensure the estimand corresponds with the one requested. When
method = "MRI" in the call to lmw(), the model is fit as an
interaction between the treatment and all the (centered) terms in the model
formula. The results will be similar to those from using lm() on
this model and supplied data except that the covariates are centered
beforehand. The product of the sampling weights and base weights supplied to
lmw(), if any, will be supplied to lm.wfit() to fit the model
using weighted least squares.
For lmw_aipw objects, the model is fit as above except that base
weights are not included in the model fitting and are instead used to
compute additional augmentation terms that are added to the estimated
potential outcome means from the outcome regression. The variance-covariance
matrix is computed using M-estimation; this corresponds to the HC0 robust
covariance matrix for the model parameters with the base weights treated as
fixed, which yields conservative standard errors for the ATE. Inference is
only approximate for the ATT and ATC.
For lmw_iv objects, the first stage model is constructed by removing
the treatment from the supplied model formula, adding the instrumental
variable as a main effect, and using the treatment variable as the outcome.
For the second stage (reduced form) model, the fitted values of the
treatment from the first stage model are used in place of the treatment in
the outcome model. The results are similar to those from using
ivreg::ivreg(), and the coefficients estimates will be the same
except for the intercept due to the centering of covariates.
Although some coefficients in the model may be interpretable as treatment
effect estimates, summary.lmw_est() should be used to view and
extract the treatment effect and potential outcome mean estimates, standard
errors, and other model statistics. The output of lmw_est() should
rarely be used except to be supplied to summary().
Value
An lmw_est object with the following components:
coefficients, residuals, fitted.values, effects, weights, rank,
df.residual, qr |
for |
model.matrix |
the model matrix (supplied to the |
vcov |
the estimated covariance matrix of
the parameter estimates as produced by |
lmw.weights |
the implied regression
weights computed by |
call |
the call to
|
estimand |
the requested estimand. |
focal |
the
focal treatment level when |
method |
the method used to estimate the weights ( |
robust |
the type standard error used. |
outcome |
the name of the outcome variable. |
treat_levels |
the levels of the treatment. |
When AIPW is used, the object will be of class lmw_est_aipw, which
inherits from lmw_est, and contains the additional components:
coef_aipw |
the model-predicted potential outcome means ( |
vcov_aipw |
the covariance matrix
of the quantities in |
When weights are included in the estimation (i.e., base.weights or
s.weights supplied to lmw() or lmw_iv()), any units
will weights equal to zero will be removed from the data prior to model
fitting.
Methods exist for lmw_est objects for model.matrix(),
vcov(), hatvalues(), sandwich::bread(),
and sandwich::estfun(), all of which are used internally to
compute the parameter estimate covariance matrix. The first two simply
extract the corresponding component from the lmw_est object and the
last three imitate the corresponding methods for lm objects (or
ivreg objects for lmw_iv inputs). Other regression-related
functions, such as coef(), residuals(), and
fitted(), use the default methods and should work correctly with
lmw_est objects.
Note that when fixed effects are supplied through the fixef argument
to lmw() or lmw_iv(), standard error estimates computed using
functions outside lmw may not be accurate due to issues relating to
degrees of freedom. In particular, this affects conventional and HC1-robust
standard errors. Otherwise, sandwich::vcovHC() can be used to compute
standard errors (setting type = "const" for conventional standard
errors), though sandwich::vcovCL() may not work as expected and
should not be used. To calculate cluster-robust standard errors, supply an
argument to cluster in lmw_est().
Note
lmw_est() uses non-standard evaluation to interpret its
outcome argument. For programmers who wish to use lmw_est()
inside other functions, an effective way to pass the name of an arbitrary
outcome (e.g., y passed as a string) is to use do.call(),
for example:
fun <- function(model, outcome, data) {
do.call("lmw_est", list(model, outcome, data)) } When using
lmw_est() inside lapply() or purrr::map to loop
over outcomes, this syntax must be used as well.
See Also
summary.lmw_est() for viewing and extracting the
treatment effect and potential outcome mean estimates, standard errors, and
other model statistics; lmw() or lmw_iv() for
estimating the weights that correspond to the model estimated by
lmw_est(); lm() and lm.fit() for fitting the
corresponding model; ivreg() in the ivreg package for fitting
2SLS models; influence.lmw_est() for influence measures
Examples
data("lalonde")
# MRI regression for ATT
lmw.out1 <- lmw(~ treat + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
estimand = "ATT", method = "MRI",
treat = "treat")
lmw.fit1 <- lmw_est(lmw.out1, outcome = "re78")
lmw.fit1
summary(lmw.fit1)
# MRI regression for ATT after propensity score matching
m.out <- MatchIt::matchit(treat ~ age + education + race +
married + nodegree + re74 + re75,
data = lalonde, method = "nearest",
estimand = "ATT")
lmw.out2 <- lmw(~ treat + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
method = "MRI", treat = "treat", obj = m.out)
## Using a cluster-robust SE with subclass (pair membership)
## as the cluster variable
lmw.fit2 <- lmw_est(lmw.out2, outcome = "re78", cluster = ~subclass)
lmw.fit2
summary(lmw.fit2)
# AIPW for ATE with MRI regression after propensity score
# weighting
ps <- glm(treat ~ age + education + race + married + nodegree +
re74 + re75, data = lalonde,
family = binomial)$fitted
ipw <- ifelse(lalonde$treat == 1, 1/ps, 1/(1-ps))
lmw.out3 <- lmw(re78 ~ treat + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
method = "MRI", treat = "treat",
base.weights = ipw, dr.method = "AIPW")
lmw.fit3 <- lmw_est(lmw.out3)
lmw.fit3
summary(lmw.fit3)
# MRI for multi-category treatment ATE
lmw.out3 <- lmw(~ treat_multi + age + education + race + married +
nodegree + re74 + re75, data = lalonde,
estimand = "ATE", method = "MRI",
treat = "treat_multi")
lmw.fit3 <- lmw_est(lmw.out3, outcome = "re78")
lmw.fit3
summary(lmw.fit3)
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