ictregBayes: Item Count Technique
In list: Statistical Methods for the Item Count Technique and List Experiment
ictregBayes R Documentation
Item Count Technique
Description
Function to conduct multivariate regression analyses of survey data with the
item count technique, also known as the list experiment and the unmatched
count technique.
Usage
ictregBayes(
formula,
data = parent.frame(),
treat = "treat",
J,
constrained.single = "full",
constrained.multi = TRUE,
fit.start = "lm",
n.draws = 10000,
burnin = 5000,
thin = 0,
delta.start,
psi.start,
Sigma.start,
Phi.start,
delta.mu0,
psi.mu0,
delta.A0,
psi.A0,
Sigma.df,
Sigma.scale,
Phi.df,
Phi.scale,
delta.tune,
psi.tune,
gamma.tune,
zeta.tune,
formula.mixed,
group.mixed,
verbose = TRUE,
sensitive.model = "logit",
df = 5,
endorse.options,
...
)
Arguments
formula
An object of class "formula": a symbolic description of the
model to be fitted.
data
A data frame containing the variables in the model
treat
Name of treatment indicator as a string. For single sensitive
item models, this refers to a binary indicator, and for multiple sensitive
item models it refers to a multi-valued variable with zero representing the
control condition. This can be an integer (with 0 for the control group) or
a factor (with "control" for the control group).
J
Number of non-sensitive (control) survey items. This will be set
automatically to the maximum value of the outcome variable in the treatment
group if no input is sent by the user.
constrained.single
A string indicating whether the control group
parameters are constrained to be equal in the single sensitive item design,
either setting all parameters to be equal (full) or only the
intercept (intercept). If neither, set to none.
constrained.multi
A logical value indicating whether the
non-sensitive item count is included as a predictor in the sensitive item
fits for the multiple sensitive item design.
fit.start
Fit method for starting values. The options are lm,
glm, nls, and ml, which use OLS, logistic regression,
non-linear least squares, and maximum likelihood estimation to generate
starting values, respectively. The default is lm.
n.draws
Number of MCMC iterations after the burnin.
burnin
The number of initial MCMC iterations that are discarded.
thin
The interval of thinning, in which every other (thin = 1)
or more iterations are discarded in the output object
delta.start
Optional starting values for the sensitive item fit. This
should be a vector with the length of the number of covariates for the
single sensitive item design, and either a vector or a list with a vector of
starting values for each of the sensitive items. The default runs an
ictreg fit with the method set by the fit.start option.
psi.start
Optional starting values for the control items fit. This
should be a vector of length the number of covariates for the constrained
models. The default runs an ictreg fit with the method set by the
fit.start option.
Sigma.start
Optional starting values for Sigma parameter for mixed
effects models for sensitive item.
Phi.start
Optional starting values for the Phi parameter for mixed
effects models for control item.
delta.mu0
Optional vector of prior means for the sensitive item fit
parameters, a vector of length the number of covariates.
psi.mu0
Optional vector of prior means for the control item fit
parameters, a vector of length the number of covariates.
delta.A0
Optional matrix of prior precisions for the sensitive item
fit parameters, a matrix of dimension the number of covariates.
psi.A0
Optional matrix of prior precisions for the control items fit
parameters, a matrix of dimension the number of covariates.
Sigma.df
Optional prior degrees of freedom parameter for mixed
effects models for sensitive item.
Sigma.scale
Optional prior scale parameter for mixed effects models
for sensitive item.
Phi.df
Optional prior degress of freedom parameter for mixed effects
models for control item.
Phi.scale
Optional prior scale parameter for mixed effects models for
control item.
delta.tune
A required vector of tuning parameters for the Metropolis
algorithm for the sensitive item fit. This must be set and refined by the
user until the acceptance ratios are approximately .4 (reported in the
output).
psi.tune
A required vector of tuning parameters for the Metropolis
algorithm for the control item fit. This must be set and refined by the user
until the acceptance ratios are approximately .4 (reported in the output).
gamma.tune
An optional vector of tuning parameters for the Metropolis
algorithm for the control item fit for the random effects. This can be set
and refined by the user until the acceptance ratios are approximately .4
(reported in the output).
zeta.tune
An optional vector of tuning parameters for the Metropolis
algorithm for the sensitive item fit for the random effects. This can be set
and refined by the user until the acceptance ratios are approximately .4
(reported in the output).
formula.mixed
To specify a mixed effects model, include this formula
object for the group-level fit. ~1 allows intercepts to vary, and including
covariates in the formula allows the slopes to vary also.
group.mixed
A numerical group indicator specifying which group each
individual belongs to for a mixed effects model.
verbose
A logical value indicating whether model diagnostics are
printed out during fitting.
sensitive.model
A logical value indicating which model is used for
the sensitive item fit, logistic regression (logit, default), robit
regression (robit), or probit regression (probit).
df
Degrees of freedom for the robit model for the sensitive item fit,
only used if robit is set to TRUE.
endorse.options
A list of inputs and options for running the combined
list experiment and endorsement experiment model. Options documented more
fully in endorse package.
...
further arguments to be passed to NLS regression commands.
Details
This function allows the user to perform regression analysis on data from
the item count technique, also known as the list experiment and the
unmatched count technique using a Bayesian MCMC algorithm.
Unlike the maximum likelihood and least squares estimators in the
ictreg function, the Metropolis algorithm for the Bayesian MCMC
estimators in this function must be tuned to work correctly. The
delta.tune and psi.tune are required, and the values, one for
each estimated parameter, will need to be manipulated. The output of the
ictregBayes function, and of the summary function run on an
ictregBayes object display the acceptance ratios from the Metropolis
algorithm. If these values are far from 0.4, the tuning parameters should be
changed until the ratios approach 0.4.
For the single sensitive item design, the model can constrain all control
parameters to be equal (constrained = "full"), or just the intercept
(constrained = "intercept") or all the control fit parameters can be
allowed to vary across the potential sensitive item values
(constrained = "none").
For the multiple sensitive item design, the model can include the estimated
number of affirmative responses to the control items as a covariate in the
sensitive item model fit (constrained set to TRUE) or exclude
it (FALSE).
The function also allows the user to perform combined list experiment and
endorsement experiment regression. Setting endorse.options to a list
with the options from the endorse package for endorsement experiment
regression, the function will return the combined model in which the
relationship between covariates and the sensitive item in the list
experiment model is set to be identical to the relationship between
covariates and support for endorsers in the endorsement experiment model.
For more details on endorsement experiment regression, see the help for the
endorse package.
Convergence is at times difficult to achieve, so we recommend running
multiple chains from overdispersed starting values by, for example, running
an MLE or linear model using the ictreg() function, and then generating a
set of overdispersed starting values using those estimates and their
estimated variance-covariance matrix. An example is provided below for each
of the possible designs. Running summary() after such a procedure
will output the Gelman-Rubin convergence statistics in addition to the
estimates. If the G-R statistics are all below 1.1, the model is said to
have converged.
Value
ictregBayes returns an object of class "ictregBayes". The
function summary is used to obtain a table of the results, using the
coda package. Two attributes are also included, the data ("x"), the
call ("call"), which can be extracted using the command, e.g.,
attr(ictregBayes.object, "x").
mcmc
an object of class "mcmc" that can be analyzed using the
coda package.
x
the design matrix
multi
a logical
value indicating whether the data included multiple sensitive items.
constrained
a logical or character value indicating whether the
control group parameters are constrained to be equal in the single sensitive
item design, and whether the non-sensitive item count is included as a
predictor in the sensitive item fits for the multiple sensitive item
design.
delta.start
Optional starting values for the sensitive item
fit. This should be a vector with the length of the number of covariates.
The default runs an ictreg fit with the method set by the
fit.start option.
psi.start
Optional starting values for the
control items fit. This should be a vector of length the number of
covariates. The default runs an ictreg fit with the method set by the
fit.start option.
delta.mu0
Optional vector of prior means
for the sensitive item fit parameters, a vector of length the number of
covariates.
psi.mu0
Optional vector of prior means for the control
item fit parameters, a vector of length the number of covariates.
delta.A0
Optional matrix of prior precisions for the sensitive item
fit parameters, a matrix of dimension the number of covariates.
psi.A0
Optional matrix of prior precisions for the control items fit
parameters, a matrix of dimension the number of covariates.
delta.tune
A required vector of tuning parameters for the Metropolis
algorithm for the sensitive item fit. This must be set and refined by the
user until the acceptance ratios are approximately .4 (reported in the
output).
psi.tune
A required vector of tuning parameters for the
Metropolis algorithm for the control item fit. This must be set and refined
by the user until the acceptance ratios are approximately .4 (reported in
the output).
J
Number of non-sensitive (control) survey items set by
the user or detected.
treat.labels
a vector of the names used by the
treat vector for the sensitive item or items. This is the names from
the treat indicator if it is a factor, or the number of the item if
it is numeric.
control.label
a vector of the names used by the
treat vector for the control items. This is the names from the
treat indicator if it is a factor, or the number of the item if it is
numeric.
call
the matched call
If the data includes multiple sensitive items, the following object is also
included:
treat.values
a vector of the values used in the
treat vector for the sensitive items, either character or numeric
depending on the class of treat. Does not include the value for the
control status
Author(s)
Graeme Blair, UCLA, graeme.blair@ucla.edu
and Kosuke Imai, Princeton University, kimai@princeton.edu
References
Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis of
List Experiments." Political Analysis, Vol. 20, No 1 (Winter). available at
http://imai.princeton.edu/research/listP.html
Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item Count
Technique.” Journal of the American Statistical Association, Vol. 106, No.
494 (June), pp. 407-416. available at
http://imai.princeton.edu/research/list.html
Blair, Graeme, Jason Lyall and Kosuke Imai. (2013) “Comparing and Combining
List and Experiments: Evidence from Afghanistan." Working paper. available
at http://imai.princeton.edu/research/comp.html
See Also
predict.ictreg for fitted values
Examples
data(race)
## Not run:
## Multiple chain MCMC list experiment regression
## starts with overdispersed MLE starting values
## Standard single sensitive-item design
## Control item parameters fully constrained
mle.estimates <- ictreg(y ~ male + college + age + south, data = race)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = draws[1, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full")
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = draws[2, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full")
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = draws[3, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full")
bayesSingleConstrained <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesSingleConstrained)
## Control item parameters unconstrained
mle.estimates <- ictreg(y ~ male + college + age + south, data = race,
constrained = FALSE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = list(psi0 = draws[1, 6:10],
psi1 = draws[1, 11:15]), burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5),
psi.tune = list(psi0 = diag(.0017, 5), psi1 = diag(.00005, 5)),
constrained.single = "none")
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = list(psi0 = draws[2, 6:10],
psi1 = draws[2, 11:15]), burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5),
psi.tune = list(psi0 = diag(.0017, 5), psi1 = diag(.00005, 5)),
constrained.single = "none")
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = list(psi0 = draws[3, 6:10],
psi1 = draws[3, 11:15]), burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5),
psi.tune = list(psi0 = diag(.0017, 5), psi1 = diag(.00005, 5)),
constrained.single = "none")
bayesSingleUnconstrained <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesSingleUnconstrained)
## Control item parameters constrained except intercept
mle.estimates <- ictreg(y ~ male + college + age + south, data = race,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = c(draws[1, 6:10],0),
burnin = 10000, n.draws = 100000, delta.tune = diag(.002, 5),
psi.tune = diag(.0004, 6), constrained.single = "intercept")
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = c(draws[2, 6:10],0),
burnin = 10000, n.draws = 100000, delta.tune = diag(.002, 5),
psi.tune = diag(.0004, 6), constrained.single = "intercept")
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = c(draws[3, 6:10],0),
burnin = 10000, n.draws = 100000, delta.tune = diag(.002, 5),
psi.tune = diag(.0004, 6), constrained.single = "intercept")
bayesSingleInterceptOnly <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesSingleInterceptOnly)
## Multiple sensitive item design
## Constrained (estimated control item count not included in sensitive fit)
mle.estimates.multi <- ictreg(y ~ male + college + age + south, data = multi,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesMultiDraws.1 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[1, 6:10], draws[1, 11:15]),
psi.start = draws[1, 1:5], burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5), psi.tune = diag(.001, 5),
constrained.multi = TRUE)
bayesMultiDraws.2 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[2, 6:10], draws[2, 11:15]),
psi.start = draws[2, 1:5], burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5), psi.tune = diag(.001, 5),
constrained.multi = TRUE)
bayesMultiDraws.3 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[3, 6:10], draws[3, 11:15]),
psi.start = draws[3, 1:5], burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5), psi.tune = diag(.001, 5),
constrained.multi = TRUE)
bayesMultiConstrained <- as.list(bayesMultiDraws.1, bayesMultiDraws.2,
bayesMultiDraws.3)
summary(bayesMultiConstrained)
## Unconstrained (estimated control item count is included in sensitive fit)
mle.estimates.multi <- ictreg(y ~ male + college + age + south, data = multi,
constrained = FALSE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesMultiDraws.1 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[1, 6:10], draws[1, 11:15]),
psi.start = draws[1, 1:5], burnin = 50000, n.draws = 300000,
delta.tune = diag(.0085, 6), psi.tune = diag(.00025, 5),
constrained.multi = FALSE)
bayesMultiDraws.2 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[2, 6:10], draws[2, 11:15]),
psi.start = draws[2, 1:5], burnin = 50000, n.draws = 300000,
delta.tune = diag(.0085, 6), psi.tune = diag(.00025, 5),
constrained.multi = FALSE)
bayesMultiDraws.3 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[3, 6:10], draws[3, 11:15]),
psi.start = draws[3, 1:5], burnin = 50000, n.draws = 300000,
delta.tune = diag(.0085, 6), psi.tune = diag(.00025, 5),
constrained.multi = FALSE)
bayesMultiUnconstrained <- as.list(bayesMultiDraws.1, bayesMultiDraws.2,
bayesMultiDraws.3)
summary(bayesMultiUnconstrained)
## Mixed effects models
## Varying intercepts
mle.estimates <- ictreg(y ~ male + college + age + south, data = race)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = draws[1, 6:10], burnin = 100,
n.draws = 1000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full", group.mixed = "state", formula.mixed = ~ 1)
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = draws[2, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full", group.mixed = "state", formula.mixed = ~ 1)
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = draws[3, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full", group.mixed = "state", formula.mixed = ~ 1)
bayesMixed <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesMixed)
## End(Not run)
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| ictregBayes | R Documentation |
Item Count Technique
Description
Function to conduct multivariate regression analyses of survey data with the item count technique, also known as the list experiment and the unmatched count technique.
Usage
ictregBayes(
formula,
data = parent.frame(),
treat = "treat",
J,
constrained.single = "full",
constrained.multi = TRUE,
fit.start = "lm",
n.draws = 10000,
burnin = 5000,
thin = 0,
delta.start,
psi.start,
Sigma.start,
Phi.start,
delta.mu0,
psi.mu0,
delta.A0,
psi.A0,
Sigma.df,
Sigma.scale,
Phi.df,
Phi.scale,
delta.tune,
psi.tune,
gamma.tune,
zeta.tune,
formula.mixed,
group.mixed,
verbose = TRUE,
sensitive.model = "logit",
df = 5,
endorse.options,
...
)
Arguments
formula |
An object of class "formula": a symbolic description of the model to be fitted. |
data |
A data frame containing the variables in the model |
treat |
Name of treatment indicator as a string. For single sensitive item models, this refers to a binary indicator, and for multiple sensitive item models it refers to a multi-valued variable with zero representing the control condition. This can be an integer (with 0 for the control group) or a factor (with "control" for the control group). |
J |
Number of non-sensitive (control) survey items. This will be set automatically to the maximum value of the outcome variable in the treatment group if no input is sent by the user. |
constrained.single |
A string indicating whether the control group
parameters are constrained to be equal in the single sensitive item design,
either setting all parameters to be equal ( |
constrained.multi |
A logical value indicating whether the non-sensitive item count is included as a predictor in the sensitive item fits for the multiple sensitive item design. |
fit.start |
Fit method for starting values. The options are |
n.draws |
Number of MCMC iterations after the burnin. |
burnin |
The number of initial MCMC iterations that are discarded. |
thin |
The interval of thinning, in which every other ( |
delta.start |
Optional starting values for the sensitive item fit. This
should be a vector with the length of the number of covariates for the
single sensitive item design, and either a vector or a list with a vector of
starting values for each of the sensitive items. The default runs an
|
psi.start |
Optional starting values for the control items fit. This
should be a vector of length the number of covariates for the constrained
models. The default runs an |
Sigma.start |
Optional starting values for Sigma parameter for mixed effects models for sensitive item. |
Phi.start |
Optional starting values for the Phi parameter for mixed effects models for control item. |
delta.mu0 |
Optional vector of prior means for the sensitive item fit parameters, a vector of length the number of covariates. |
psi.mu0 |
Optional vector of prior means for the control item fit parameters, a vector of length the number of covariates. |
delta.A0 |
Optional matrix of prior precisions for the sensitive item fit parameters, a matrix of dimension the number of covariates. |
psi.A0 |
Optional matrix of prior precisions for the control items fit parameters, a matrix of dimension the number of covariates. |
Sigma.df |
Optional prior degrees of freedom parameter for mixed effects models for sensitive item. |
Sigma.scale |
Optional prior scale parameter for mixed effects models for sensitive item. |
Phi.df |
Optional prior degress of freedom parameter for mixed effects models for control item. |
Phi.scale |
Optional prior scale parameter for mixed effects models for control item. |
delta.tune |
A required vector of tuning parameters for the Metropolis algorithm for the sensitive item fit. This must be set and refined by the user until the acceptance ratios are approximately .4 (reported in the output). |
psi.tune |
A required vector of tuning parameters for the Metropolis algorithm for the control item fit. This must be set and refined by the user until the acceptance ratios are approximately .4 (reported in the output). |
gamma.tune |
An optional vector of tuning parameters for the Metropolis algorithm for the control item fit for the random effects. This can be set and refined by the user until the acceptance ratios are approximately .4 (reported in the output). |
zeta.tune |
An optional vector of tuning parameters for the Metropolis algorithm for the sensitive item fit for the random effects. This can be set and refined by the user until the acceptance ratios are approximately .4 (reported in the output). |
formula.mixed |
To specify a mixed effects model, include this formula object for the group-level fit. ~1 allows intercepts to vary, and including covariates in the formula allows the slopes to vary also. |
group.mixed |
A numerical group indicator specifying which group each individual belongs to for a mixed effects model. |
verbose |
A logical value indicating whether model diagnostics are printed out during fitting. |
sensitive.model |
A logical value indicating which model is used for
the sensitive item fit, logistic regression ( |
df |
Degrees of freedom for the robit model for the sensitive item fit,
only used if |
endorse.options |
A list of inputs and options for running the combined
list experiment and endorsement experiment model. Options documented more
fully in |
... |
further arguments to be passed to NLS regression commands. |
Details
This function allows the user to perform regression analysis on data from the item count technique, also known as the list experiment and the unmatched count technique using a Bayesian MCMC algorithm.
Unlike the maximum likelihood and least squares estimators in the
ictreg function, the Metropolis algorithm for the Bayesian MCMC
estimators in this function must be tuned to work correctly. The
delta.tune and psi.tune are required, and the values, one for
each estimated parameter, will need to be manipulated. The output of the
ictregBayes function, and of the summary function run on an
ictregBayes object display the acceptance ratios from the Metropolis
algorithm. If these values are far from 0.4, the tuning parameters should be
changed until the ratios approach 0.4.
For the single sensitive item design, the model can constrain all control
parameters to be equal (constrained = "full"), or just the intercept
(constrained = "intercept") or all the control fit parameters can be
allowed to vary across the potential sensitive item values
(constrained = "none").
For the multiple sensitive item design, the model can include the estimated
number of affirmative responses to the control items as a covariate in the
sensitive item model fit (constrained set to TRUE) or exclude
it (FALSE).
The function also allows the user to perform combined list experiment and
endorsement experiment regression. Setting endorse.options to a list
with the options from the endorse package for endorsement experiment
regression, the function will return the combined model in which the
relationship between covariates and the sensitive item in the list
experiment model is set to be identical to the relationship between
covariates and support for endorsers in the endorsement experiment model.
For more details on endorsement experiment regression, see the help for the
endorse package.
Convergence is at times difficult to achieve, so we recommend running
multiple chains from overdispersed starting values by, for example, running
an MLE or linear model using the ictreg() function, and then generating a
set of overdispersed starting values using those estimates and their
estimated variance-covariance matrix. An example is provided below for each
of the possible designs. Running summary() after such a procedure
will output the Gelman-Rubin convergence statistics in addition to the
estimates. If the G-R statistics are all below 1.1, the model is said to
have converged.
Value
ictregBayes returns an object of class "ictregBayes". The
function summary is used to obtain a table of the results, using the
coda package. Two attributes are also included, the data ("x"), the
call ("call"), which can be extracted using the command, e.g.,
attr(ictregBayes.object, "x").
mcmc |
an object of class "mcmc" that can be analyzed using the
|
x |
the design matrix |
multi |
a logical value indicating whether the data included multiple sensitive items. |
constrained |
a logical or character value indicating whether the control group parameters are constrained to be equal in the single sensitive item design, and whether the non-sensitive item count is included as a predictor in the sensitive item fits for the multiple sensitive item design. |
delta.start |
Optional starting values for the sensitive item
fit. This should be a vector with the length of the number of covariates.
The default runs an |
psi.start |
Optional starting values for the
control items fit. This should be a vector of length the number of
covariates. The default runs an |
delta.mu0 |
Optional vector of prior means for the sensitive item fit parameters, a vector of length the number of covariates. |
psi.mu0 |
Optional vector of prior means for the control item fit parameters, a vector of length the number of covariates. |
delta.A0 |
Optional matrix of prior precisions for the sensitive item fit parameters, a matrix of dimension the number of covariates. |
psi.A0 |
Optional matrix of prior precisions for the control items fit parameters, a matrix of dimension the number of covariates. |
delta.tune |
A required vector of tuning parameters for the Metropolis algorithm for the sensitive item fit. This must be set and refined by the user until the acceptance ratios are approximately .4 (reported in the output). |
psi.tune |
A required vector of tuning parameters for the Metropolis algorithm for the control item fit. This must be set and refined by the user until the acceptance ratios are approximately .4 (reported in the output). |
J |
Number of non-sensitive (control) survey items set by the user or detected. |
treat.labels |
a vector of the names used by the
|
control.label |
a vector of the names used by the
|
call |
the matched call |
If the data includes multiple sensitive items, the following object is also included:
treat.values |
a vector of the values used in the
|
Author(s)
Graeme Blair, UCLA, graeme.blair@ucla.edu and Kosuke Imai, Princeton University, kimai@princeton.edu
References
Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis of List Experiments." Political Analysis, Vol. 20, No 1 (Winter). available at http://imai.princeton.edu/research/listP.html
Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item Count Technique.” Journal of the American Statistical Association, Vol. 106, No. 494 (June), pp. 407-416. available at http://imai.princeton.edu/research/list.html
Blair, Graeme, Jason Lyall and Kosuke Imai. (2013) “Comparing and Combining List and Experiments: Evidence from Afghanistan." Working paper. available at http://imai.princeton.edu/research/comp.html
See Also
predict.ictreg for fitted values
Examples
data(race)
## Not run:
## Multiple chain MCMC list experiment regression
## starts with overdispersed MLE starting values
## Standard single sensitive-item design
## Control item parameters fully constrained
mle.estimates <- ictreg(y ~ male + college + age + south, data = race)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = draws[1, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full")
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = draws[2, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full")
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = draws[3, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full")
bayesSingleConstrained <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesSingleConstrained)
## Control item parameters unconstrained
mle.estimates <- ictreg(y ~ male + college + age + south, data = race,
constrained = FALSE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = list(psi0 = draws[1, 6:10],
psi1 = draws[1, 11:15]), burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5),
psi.tune = list(psi0 = diag(.0017, 5), psi1 = diag(.00005, 5)),
constrained.single = "none")
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = list(psi0 = draws[2, 6:10],
psi1 = draws[2, 11:15]), burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5),
psi.tune = list(psi0 = diag(.0017, 5), psi1 = diag(.00005, 5)),
constrained.single = "none")
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = list(psi0 = draws[3, 6:10],
psi1 = draws[3, 11:15]), burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5),
psi.tune = list(psi0 = diag(.0017, 5), psi1 = diag(.00005, 5)),
constrained.single = "none")
bayesSingleUnconstrained <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesSingleUnconstrained)
## Control item parameters constrained except intercept
mle.estimates <- ictreg(y ~ male + college + age + south, data = race,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = c(draws[1, 6:10],0),
burnin = 10000, n.draws = 100000, delta.tune = diag(.002, 5),
psi.tune = diag(.0004, 6), constrained.single = "intercept")
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = c(draws[2, 6:10],0),
burnin = 10000, n.draws = 100000, delta.tune = diag(.002, 5),
psi.tune = diag(.0004, 6), constrained.single = "intercept")
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = c(draws[3, 6:10],0),
burnin = 10000, n.draws = 100000, delta.tune = diag(.002, 5),
psi.tune = diag(.0004, 6), constrained.single = "intercept")
bayesSingleInterceptOnly <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesSingleInterceptOnly)
## Multiple sensitive item design
## Constrained (estimated control item count not included in sensitive fit)
mle.estimates.multi <- ictreg(y ~ male + college + age + south, data = multi,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesMultiDraws.1 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[1, 6:10], draws[1, 11:15]),
psi.start = draws[1, 1:5], burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5), psi.tune = diag(.001, 5),
constrained.multi = TRUE)
bayesMultiDraws.2 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[2, 6:10], draws[2, 11:15]),
psi.start = draws[2, 1:5], burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5), psi.tune = diag(.001, 5),
constrained.multi = TRUE)
bayesMultiDraws.3 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[3, 6:10], draws[3, 11:15]),
psi.start = draws[3, 1:5], burnin = 10000, n.draws = 100000,
delta.tune = diag(.002, 5), psi.tune = diag(.001, 5),
constrained.multi = TRUE)
bayesMultiConstrained <- as.list(bayesMultiDraws.1, bayesMultiDraws.2,
bayesMultiDraws.3)
summary(bayesMultiConstrained)
## Unconstrained (estimated control item count is included in sensitive fit)
mle.estimates.multi <- ictreg(y ~ male + college + age + south, data = multi,
constrained = FALSE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesMultiDraws.1 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[1, 6:10], draws[1, 11:15]),
psi.start = draws[1, 1:5], burnin = 50000, n.draws = 300000,
delta.tune = diag(.0085, 6), psi.tune = diag(.00025, 5),
constrained.multi = FALSE)
bayesMultiDraws.2 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[2, 6:10], draws[2, 11:15]),
psi.start = draws[2, 1:5], burnin = 50000, n.draws = 300000,
delta.tune = diag(.0085, 6), psi.tune = diag(.00025, 5),
constrained.multi = FALSE)
bayesMultiDraws.3 <- ictregBayes(y ~ male + college + age + south,
data = multi, delta.start = list(draws[3, 6:10], draws[3, 11:15]),
psi.start = draws[3, 1:5], burnin = 50000, n.draws = 300000,
delta.tune = diag(.0085, 6), psi.tune = diag(.00025, 5),
constrained.multi = FALSE)
bayesMultiUnconstrained <- as.list(bayesMultiDraws.1, bayesMultiDraws.2,
bayesMultiDraws.3)
summary(bayesMultiUnconstrained)
## Mixed effects models
## Varying intercepts
mle.estimates <- ictreg(y ~ male + college + age + south, data = race)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates),
Sigma = vcov(mle.estimates) * 9)
bayesDraws.1 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[1, 1:5], psi.start = draws[1, 6:10], burnin = 100,
n.draws = 1000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full", group.mixed = "state", formula.mixed = ~ 1)
bayesDraws.2 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[2, 1:5], psi.start = draws[2, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full", group.mixed = "state", formula.mixed = ~ 1)
bayesDraws.3 <- ictregBayes(y ~ male + college + age + south, data = race,
delta.start = draws[3, 1:5], psi.start = draws[3, 6:10], burnin = 10000,
n.draws = 100000, delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5),
constrained.single = "full", group.mixed = "state", formula.mixed = ~ 1)
bayesMixed <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesMixed)
## End(Not run)
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