predict.msel: Predict method for msel function
In switchSelection: Endogenous Switching and Sample Selection Regression Models
predict.msel R Documentation
Predict method for msel function
Description
Predicted values based on the object of class 'msel'.
Usage
## S3 method for class 'msel'
predict(
object,
...,
newdata = NULL,
given_ind = numeric(),
group = NA,
group2 = NA,
group3 = NA,
type = ifelse(any(is.na(group2)), "prob", "val"),
me = NULL,
eps = NULL,
control = list(),
test = FALSE,
exogenous = NULL
)
Arguments
object
an object of class "msel".
...
further arguments (currently ignored)
newdata
an optional data frame in which to look for variables
with which to predict. If omitted, the original data frame used.
This data frame should contain values of dependent variables even if
they are not actually needed for prediction
(simply assign them with 0 values).
given_ind
a numeric vector of indexes of conditioned components.
group
a numeric vector which i-th element represents a value of the
i-th dependent variable. If this value equals -1 then this component
will be ignored (useful for estimation of marginal probabilities).
group2
a numeric vector which i-th element represents a value of the
i-th dependent variable of the continuous equation.
If this value equals -1 then this component will be ignored.
group3
an integer representing the index of the alternative of the
multinomial equation. If this value equals -1 then this component will be
ignored.
type
a string representing a type of the prediction.
See 'Details' for more information.
me
a string representing the name of the variable for which marginal
effect should be estimated. See 'Details' for more information.
eps
a numeric vector of length 1 or 2 used for calculation of
the marginal effects. See 'Details' for more information.
control
a list of additional arguments. Currently is not intended
for the users.
test
a logical, function or integer. If test = TRUE then the
output of the function is supplied to
test_msel before return to perform a t-test.
If test is a function it will be applied to the output of the
predict before test_msel is called.
If test is an integer then test_msel
will be applied only to the test-th column of the output.
exogenous
a list such that exogenous[[i]] represents the value
(or a vector of values of the same size as nrow(newdata)) which will
be exogenously assigned to the variable names(exogenous)[[i]] in
newdata i.e., newdata[, names(exogenous)[i]] <- exogenous[[i]].
If newdata is NULL and exogenous is not NULL then
newdata is set to object$data.
This argument is especially useful for the casual inference when some
endogenous (dependent) variables should be exogenously assigned with some
values i.e., in the right hand side of the formula, formula2
and formula3. The purpose of exogeneous argument is just a
convenience so equivalently it is possible to exogenously provide the values
to variables via the newdata argument.
Details
See 'Examples' section of msel
for the examples of this function application.
Probabilities of the multivariate ordinal equations
If type = "prob" then the function returns a joint probability that
the ordinal outcomes will have values assigned in group. To calculate
marginal probabilities set unnecessary group values to -1.
To estimate conditional probabilities provide indexes of the conditioned
outcomes through the given_ind argument.
For example, if z_{1i}, z_{2i} and z_{3i} are the ordinal
outcomes then to estimate
P(z_{1i}=2 | z_{3i} = 0, w_{1i}, w_{2i}, w_{3i}) set
given_ind = 3 and groups = c(2, -1, 0).
Linear predictors (indexes) of the multivariate ordinal equations
If type = "li" or type = "lp" then the function returns a
matrix which columns are linear predictors (indexes) of the corresponding
equations. If group[j] = -1 then linear predictors (indexes)
associated with the j-th ordinal equation will be omitted from the
output.
For example, if group = c(0, -1, 1) then the function returns a
matrix which first column is w_{1i}\hat{\gamma}_{1} and the second
column is w_{3i}\hat{\gamma}_{3}.
Standard deviations of the multivariate ordinal equations
If type = "sd" then the function returns a matrix which columns are
the estimates of the standard deviations of the random errors for
the corresponding equations.
If group[j] = -1 then the standard deviations associated with the
j-th ordinal equation will be omitted from the output.
For example, if group = c(0, -1, 1) then the function returns a
matrix which first column is \hat{\sigma}_{1i}^{*} and the second
column is \hat{\sigma}_{3i}^{*}.
Predictions of the continuous outcomes
If type = "val" then the function returns the predictions of the
conditional (on group) expectation of the continuous outcomes in the
regimes determined by the group2 argument. To predict unconditional
expectations set group to a vector of -1 values.
For example, suppose that there is a single continuous equation y_{i}
and two ordinal equations z_{1i} and z_{2i}.
To estimate E(y_{2i}|x_{i}) set group = c(-1, -1) and
group2 = 2.
To estimate E(y_{1i}|x_{i}, z_{1i} = 2, z_{2i} = 0) set
group = c(2, 0) and group2 = 1.
To estimate E(y_{0i}|x_{i}, z_{2i} = 1) set
group = c(-1, 1) and group2 = 0.
Suppose that there are two continuous y_{i}^{(1)},
y_{i}^{(2)} and two ordinal z_{1i}, z_{2i} equations.
If group2 = c(1, 3) and group = c(3, 0) then the function
returns a matrix which first column are the estimates of
E(y_{1i}^{(1)}|z_{1i} = 3, z_{2i} = 0, x_{i}^{(1)}) and the second
column are the estimates of
E(y_{3i}^{(2)}|z_{1i} = 3, z_{2i} = 0, x_{i}^{(2)}).
Selectivity terms
If type = "lambda" then the function returns a matrix which
j-th column is a numeric vector of estimates of the selectivity terms
\lambda_{ji} associated with the ordinal equations.
Similarly if type = "lambda_mn" then the
function returns a numeric matrix with the selectivity terms of the
multinomial equations.
Probabilities of the multinomial equation
If type = "prob_mn" and group3 = j then the function returns
a vector of the estimates of the probabilities
P(\tilde{z}_{i}=j|\tilde{w}_{i}).
Linear indexes (predictors) of the multinomial equation
If type = "li_mn" or type = "lp_mn" then the function returns a
numeric matrix which j-th column is a numeric vector of estimates of
the linear predictor (index) associated with the (j-1)-th alternative
\tilde{w}_{i}\tilde{\gamma}_{(j-1)}.
Estimation of the marginal effects
If me is provided then the function returns marginal effect
of variable me respect to the statistic determined by the type
argument.
For example, if me = "x1" and type = "prob" then the function
returns a marginal effect of x1 on the corresponding probability
i.e., one that would be estimated if me is NULL.
If length(eps) = 1 then eps is an increment in
numeric differentiation procedure.
If eps is NULL then this increment will be selected
automatically taking into account scaling of variables.
If length(eps) = 2 then marginal effects will be estimated as the
difference of predicted value when variable me equals eps[2]
and eps[1] correspondingly.
For example, suppose that
type = "prob", me = "x1", given_ind = 3 and
groups = c(2, -1, 0). Then if eps is a NULL or a
small number (something like eps = 0.0001) then the following marginal
effect will be estimated (via the numeric differentiation):
\frac{\partial P(z_{1i}=2 | z_{3i} = 0)}{\partial x_{1i}}.
If eps = c(1, 3) then the function estimates the following difference
(useful for estimation of marginal effects of ordered covariates):
P(z_{1i}=2 | z_{3i} = 0, x_{1i} = 3) -
P(z_{1i}=2 | z_{3i} = 0, x_{1i} = 1).
Notice that the conditioning on w_{ji} has been omitted for brevity.
Causal inference
Argument exogenous is useful for the causal inference.
For example, suppose that there are two binary outcomes z_{1i} and
z_{2i}. Also z_{1i} is the endogenous regressor for z_{2i}.
That is z_{1i} appears both on the left hand side of
formula[[1]] and on the right hand side of formula[[2]].
Consider the estimation of the average treatment effect:
ATE = P(z_{2i} = 1|do(z_{1i}) = 1) -
P(z_{2i} = 1|do(z_{1i}) = 0),
where do is a do-calculus operator.
The estimate of the average treatment effect is as follows:
\widehat{ATE} = \frac{1}{n}\sum\limits_{i=1}^{n}p_{1i}-p_{0i},
where:
p_{1i} = \hat{P}(z_{2i} = 1|do(z_{1i}) = 1, w_{1i}, w_{2i}^{(*)}),
p_{0i} = \hat{P}(z_{2i} = 1|do(z_{1i}) = 0, w_{1i}, w_{2i}^{(*)}).
Vector w_{2i}^{(*)} denotes all the regressors w_{2i} except
the endogenous one z_{1i}.
To get \widehat{ATE} it is sufficient to make the following steps.
First, calculate p_{1i} by setting type = "prob",
group = c(-1, 1) and providing the value 1 to z_{1i}
through the exogenous argument.
Second, calculate p_{0i} by setting type = "prob",
group = c(-1, 0) and providing the value 0 to z_{1i}
through the exogenous argument. Third, take the average value of
p_{1i}-p_{0i}.
Value
This function returns predictions for each row of newdata
or for each observation in the model if newdata is NULL.
Structure of the output depends on the type argument
(see 'Details' section).
switchSelection documentation built on Sept. 26, 2024, 5:07 p.m.
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| predict.msel | R Documentation |
Predict method for msel function
Description
Predicted values based on the object of class 'msel'.
Usage
## S3 method for class 'msel'
predict(
object,
...,
newdata = NULL,
given_ind = numeric(),
group = NA,
group2 = NA,
group3 = NA,
type = ifelse(any(is.na(group2)), "prob", "val"),
me = NULL,
eps = NULL,
control = list(),
test = FALSE,
exogenous = NULL
)
Arguments
object |
an object of class "msel". |
... |
further arguments (currently ignored) |
newdata |
an optional data frame in which to look for variables with which to predict. If omitted, the original data frame used. This data frame should contain values of dependent variables even if they are not actually needed for prediction (simply assign them with 0 values). |
given_ind |
a numeric vector of indexes of conditioned components. |
group |
a numeric vector which i-th element represents a value of the i-th dependent variable. If this value equals -1 then this component will be ignored (useful for estimation of marginal probabilities). |
group2 |
a numeric vector which i-th element represents a value of the i-th dependent variable of the continuous equation. If this value equals -1 then this component will be ignored. |
group3 |
an integer representing the index of the alternative of the multinomial equation. If this value equals -1 then this component will be ignored. |
type |
a string representing a type of the prediction. See 'Details' for more information. |
me |
a string representing the name of the variable for which marginal effect should be estimated. See 'Details' for more information. |
eps |
a numeric vector of length 1 or 2 used for calculation of the marginal effects. See 'Details' for more information. |
control |
a list of additional arguments. Currently is not intended for the users. |
test |
a logical, function or integer. If |
exogenous |
a list such that |
Details
See 'Examples' section of msel
for the examples of this function application.
Probabilities of the multivariate ordinal equations
If type = "prob" then the function returns a joint probability that
the ordinal outcomes will have values assigned in group. To calculate
marginal probabilities set unnecessary group values to -1.
To estimate conditional probabilities provide indexes of the conditioned
outcomes through the given_ind argument.
For example, if z_{1i}, z_{2i} and z_{3i} are the ordinal
outcomes then to estimate
P(z_{1i}=2 | z_{3i} = 0, w_{1i}, w_{2i}, w_{3i}) set
given_ind = 3 and groups = c(2, -1, 0).
Linear predictors (indexes) of the multivariate ordinal equations
If type = "li" or type = "lp" then the function returns a
matrix which columns are linear predictors (indexes) of the corresponding
equations. If group[j] = -1 then linear predictors (indexes)
associated with the j-th ordinal equation will be omitted from the
output.
For example, if group = c(0, -1, 1) then the function returns a
matrix which first column is w_{1i}\hat{\gamma}_{1} and the second
column is w_{3i}\hat{\gamma}_{3}.
Standard deviations of the multivariate ordinal equations
If type = "sd" then the function returns a matrix which columns are
the estimates of the standard deviations of the random errors for
the corresponding equations.
If group[j] = -1 then the standard deviations associated with the
j-th ordinal equation will be omitted from the output.
For example, if group = c(0, -1, 1) then the function returns a
matrix which first column is \hat{\sigma}_{1i}^{*} and the second
column is \hat{\sigma}_{3i}^{*}.
Predictions of the continuous outcomes
If type = "val" then the function returns the predictions of the
conditional (on group) expectation of the continuous outcomes in the
regimes determined by the group2 argument. To predict unconditional
expectations set group to a vector of -1 values.
For example, suppose that there is a single continuous equation y_{i}
and two ordinal equations z_{1i} and z_{2i}.
To estimate E(y_{2i}|x_{i}) set group = c(-1, -1) and
group2 = 2.
To estimate E(y_{1i}|x_{i}, z_{1i} = 2, z_{2i} = 0) set
group = c(2, 0) and group2 = 1.
To estimate E(y_{0i}|x_{i}, z_{2i} = 1) set
group = c(-1, 1) and group2 = 0.
Suppose that there are two continuous y_{i}^{(1)},
y_{i}^{(2)} and two ordinal z_{1i}, z_{2i} equations.
If group2 = c(1, 3) and group = c(3, 0) then the function
returns a matrix which first column are the estimates of
E(y_{1i}^{(1)}|z_{1i} = 3, z_{2i} = 0, x_{i}^{(1)}) and the second
column are the estimates of
E(y_{3i}^{(2)}|z_{1i} = 3, z_{2i} = 0, x_{i}^{(2)}).
Selectivity terms
If type = "lambda" then the function returns a matrix which
j-th column is a numeric vector of estimates of the selectivity terms
\lambda_{ji} associated with the ordinal equations.
Similarly if type = "lambda_mn" then the
function returns a numeric matrix with the selectivity terms of the
multinomial equations.
Probabilities of the multinomial equation
If type = "prob_mn" and group3 = j then the function returns
a vector of the estimates of the probabilities
P(\tilde{z}_{i}=j|\tilde{w}_{i}).
Linear indexes (predictors) of the multinomial equation
If type = "li_mn" or type = "lp_mn" then the function returns a
numeric matrix which j-th column is a numeric vector of estimates of
the linear predictor (index) associated with the (j-1)-th alternative
\tilde{w}_{i}\tilde{\gamma}_{(j-1)}.
Estimation of the marginal effects
If me is provided then the function returns marginal effect
of variable me respect to the statistic determined by the type
argument.
For example, if me = "x1" and type = "prob" then the function
returns a marginal effect of x1 on the corresponding probability
i.e., one that would be estimated if me is NULL.
If length(eps) = 1 then eps is an increment in
numeric differentiation procedure.
If eps is NULL then this increment will be selected
automatically taking into account scaling of variables.
If length(eps) = 2 then marginal effects will be estimated as the
difference of predicted value when variable me equals eps[2]
and eps[1] correspondingly.
For example, suppose that
type = "prob", me = "x1", given_ind = 3 and
groups = c(2, -1, 0). Then if eps is a NULL or a
small number (something like eps = 0.0001) then the following marginal
effect will be estimated (via the numeric differentiation):
\frac{\partial P(z_{1i}=2 | z_{3i} = 0)}{\partial x_{1i}}.
If eps = c(1, 3) then the function estimates the following difference
(useful for estimation of marginal effects of ordered covariates):
P(z_{1i}=2 | z_{3i} = 0, x_{1i} = 3) -
P(z_{1i}=2 | z_{3i} = 0, x_{1i} = 1).
Notice that the conditioning on w_{ji} has been omitted for brevity.
Causal inference
Argument exogenous is useful for the causal inference.
For example, suppose that there are two binary outcomes z_{1i} and
z_{2i}. Also z_{1i} is the endogenous regressor for z_{2i}.
That is z_{1i} appears both on the left hand side of
formula[[1]] and on the right hand side of formula[[2]].
Consider the estimation of the average treatment effect:
ATE = P(z_{2i} = 1|do(z_{1i}) = 1) -
P(z_{2i} = 1|do(z_{1i}) = 0),
where do is a do-calculus operator.
The estimate of the average treatment effect is as follows:
\widehat{ATE} = \frac{1}{n}\sum\limits_{i=1}^{n}p_{1i}-p_{0i},
where:
p_{1i} = \hat{P}(z_{2i} = 1|do(z_{1i}) = 1, w_{1i}, w_{2i}^{(*)}),
p_{0i} = \hat{P}(z_{2i} = 1|do(z_{1i}) = 0, w_{1i}, w_{2i}^{(*)}).
Vector w_{2i}^{(*)} denotes all the regressors w_{2i} except
the endogenous one z_{1i}.
To get \widehat{ATE} it is sufficient to make the following steps.
First, calculate p_{1i} by setting type = "prob",
group = c(-1, 1) and providing the value 1 to z_{1i}
through the exogenous argument.
Second, calculate p_{0i} by setting type = "prob",
group = c(-1, 0) and providing the value 0 to z_{1i}
through the exogenous argument. Third, take the average value of
p_{1i}-p_{0i}.
Value
This function returns predictions for each row of newdata
or for each observation in the model if newdata is NULL.
Structure of the output depends on the type argument
(see 'Details' section).
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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