ictregBayesHier: Item Count Technique
In list: Statistical Methods for the Item Count Technique and List Experiment
View source: R/ictregBayesHier.R
ictregBayesHier R Documentation
Item Count Technique
Description
Function to conduct multilevel, multivariate regression analyses of survey
data with the item count technique, also known as the list experiment and
the unmatched count technique.
Usage
ictregBayesHier(
formula,
data = parent.frame(),
group.level.2,
group.level.3,
group.level.4,
formula.level.2,
formula.level.3,
formula.level.4,
treat = "treat",
J,
fit.start = "lm",
n.draws = 10000,
burnin = 5000,
thin = 0,
delta.start.level.1,
delta.mu0.level.1,
delta.A0.level.1,
delta.start.level.2,
delta.mu0.level.2,
delta.A0.level.2,
delta.start.level.3,
delta.mu0.level.3,
delta.A0.level.3,
delta.start.level.4,
delta.mu0.level.4,
delta.A0.level.4,
sigma.start.level.1,
sigma.df.level.1,
sigma.scale.level.1,
sigma.start.level.2,
sigma.df.level.2,
sigma.scale.level.2,
sigma.start.level.3,
sigma.df.level.3,
sigma.scale.level.3,
sigma.start.level.4,
sigma.df.level.4,
sigma.scale.level.4,
delta.tune,
alpha.tune,
verbose = TRUE,
...
)
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
group.level.2
Name of second level group variable from the data frame
indicating which group each individual belongs to as a string
group.level.3
Name of third level group variable from the data frame
indicating which group each individual belongs to as a string
group.level.4
Name of fourth level group variable from the data frame
indicating which group each individual belongs to as a string
formula.level.2
An object of class "formula" for the second level of
the hierarchical model
formula.level.3
An object of class "formula" for the third level of
the hierarchical model
formula.level.4
An object of class "formula" for the fourth level of
the hierarchical 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.
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.level.1
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.
delta.mu0.level.1
Optional vector of prior means for the sensitive
item fit parameters, a vector of length the number of covariates.
delta.A0.level.1
Optional matrix of prior precisions for the
sensitive item fit parameters, a matrix of dimension the number of
covariates.
delta.start.level.2
Optional starting values for the sensitive item
fit for the second level of the hierarchical model. 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.
delta.mu0.level.2
Optional vector of prior means for the sensitive
item fit parameters for the second level of the hierarchical model, a vector
of length the number of covariates.
delta.A0.level.2
Optional matrix of prior precisions for the
sensitive item fit parameters for the second level of the hierarchical
model, a matrix of dimension the number of covariates.
delta.start.level.3
Optional starting values for the sensitive item
fit for the third level of the hierarchical model. 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.
delta.mu0.level.3
Optional vector of prior means for the sensitive
item fit parameters for the third level of the hierarchical model, a vector
of length the number of covariates.
delta.A0.level.3
Optional matrix of prior precisions for the
sensitive item fit parameters for the third level of the hierarchical model,
a matrix of dimension the number of covariates.
delta.start.level.4
Optional starting values for the sensitive item
fit for the fourth level of the hierarchical model. 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.
delta.mu0.level.4
Optional vector of prior means for the sensitive
item fit parameters for the fourth level of the hierarchical model, a vector
of length the number of covariates.
delta.A0.level.4
Optional matrix of prior precisions for the
sensitive item fit parameters for the fourth level of the hierarchical
model, a matrix of dimension the number of covariates.
sigma.start.level.1
Optional list of length the number of sensitive
items with the starting values for the sigma parameters.
sigma.df.level.1
Optional prior degrees of freedom parameter.
sigma.scale.level.1
Optional prior scale parameter.
sigma.start.level.2
Optional list of length the number of sensitive
items with the starting values for the sigma parameters for the second level
of the hierarchical model.
sigma.df.level.2
Optional prior degrees of freedom parameter for the
second level of the hierarchical model.
sigma.scale.level.2
Optional prior scale parameter for the second
level of the hierarchical model.
sigma.start.level.3
Optional list of length the number of sensitive
items with the starting values for the sigma parameters for the third level
of the hierarchical model.
sigma.df.level.3
Optional prior degrees of freedom parameter for the
third level of the hierarchical model.
sigma.scale.level.3
Optional prior scale parameter for the third
level of the hierarchical model.
sigma.start.level.4
Optional list of length the number of sensitive
items with the starting values for the sigma parameters for the fourth level
of the hierarchical model.
sigma.df.level.4
Optional prior degrees of freedom parameter for the
fourth level of the hierarchical model.
sigma.scale.level.4
Optional prior scale parameter for the fourth
level of the hierarchical model.
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).
alpha.tune
An optional vector of tuning parameters for the Metropolis
algorithm for the random effects.
verbose
A logical value indicating whether model diagnostics are
printed out during fitting.
...
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).
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
See Also
predict.ictreg for fitted values
Examples
data(race)
## Not run:
## Multiple chain MCMC list experiment regression
## starts with overdispersed MLE starting values
## Multiple item two level hierarchical model - varying intercepts
mle.estimates.multi <- ictreg(y ~ male + college, data = multi,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesDraws.1 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ 1,
delta.start.level.1 = list(draws[1, 8:9], draws[1, 2:3], draws[1, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.2 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ 1,
delta.start.level.1 = list(draws[2, 8:9], draws[2, 2:3], draws[2, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.3 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ 1,
delta.start.level.1 = list(draws[3, 8:9], draws[3, 2:3], draws[3, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesHierTwoLevel <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesHierTwoLevel)
## Multiple item two level hierarchical model - including covariates
mle.estimates.multi <- ictreg(y ~ male + college, data = multi,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesDraws.1 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ age,
delta.start.level.1 = list(draws[1, 8:9], draws[1, 2:3], draws[1, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.2 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ age,
delta.start.level.1 = list(draws[2, 8:9], draws[2, 2:3], draws[2, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.3 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ age,
delta.start.level.1 = list(draws[3, 8:9], draws[3, 2:3], draws[3, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesHierTwoLevel <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesHierTwoLevel)
## End(Not run)
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| ictregBayesHier | R Documentation |
Item Count Technique
Description
Function to conduct multilevel, multivariate regression analyses of survey data with the item count technique, also known as the list experiment and the unmatched count technique.
Usage
ictregBayesHier(
formula,
data = parent.frame(),
group.level.2,
group.level.3,
group.level.4,
formula.level.2,
formula.level.3,
formula.level.4,
treat = "treat",
J,
fit.start = "lm",
n.draws = 10000,
burnin = 5000,
thin = 0,
delta.start.level.1,
delta.mu0.level.1,
delta.A0.level.1,
delta.start.level.2,
delta.mu0.level.2,
delta.A0.level.2,
delta.start.level.3,
delta.mu0.level.3,
delta.A0.level.3,
delta.start.level.4,
delta.mu0.level.4,
delta.A0.level.4,
sigma.start.level.1,
sigma.df.level.1,
sigma.scale.level.1,
sigma.start.level.2,
sigma.df.level.2,
sigma.scale.level.2,
sigma.start.level.3,
sigma.df.level.3,
sigma.scale.level.3,
sigma.start.level.4,
sigma.df.level.4,
sigma.scale.level.4,
delta.tune,
alpha.tune,
verbose = TRUE,
...
)
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 |
group.level.2 |
Name of second level group variable from the data frame indicating which group each individual belongs to as a string |
group.level.3 |
Name of third level group variable from the data frame indicating which group each individual belongs to as a string |
group.level.4 |
Name of fourth level group variable from the data frame indicating which group each individual belongs to as a string |
formula.level.2 |
An object of class "formula" for the second level of the hierarchical model |
formula.level.3 |
An object of class "formula" for the third level of the hierarchical model |
formula.level.4 |
An object of class "formula" for the fourth level of the hierarchical 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. |
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.level.1 |
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 |
delta.mu0.level.1 |
Optional vector of prior means for the sensitive item fit parameters, a vector of length the number of covariates. |
delta.A0.level.1 |
Optional matrix of prior precisions for the sensitive item fit parameters, a matrix of dimension the number of covariates. |
delta.start.level.2 |
Optional starting values for the sensitive item
fit for the second level of the hierarchical model. 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 |
delta.mu0.level.2 |
Optional vector of prior means for the sensitive item fit parameters for the second level of the hierarchical model, a vector of length the number of covariates. |
delta.A0.level.2 |
Optional matrix of prior precisions for the sensitive item fit parameters for the second level of the hierarchical model, a matrix of dimension the number of covariates. |
delta.start.level.3 |
Optional starting values for the sensitive item
fit for the third level of the hierarchical model. 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 |
delta.mu0.level.3 |
Optional vector of prior means for the sensitive item fit parameters for the third level of the hierarchical model, a vector of length the number of covariates. |
delta.A0.level.3 |
Optional matrix of prior precisions for the sensitive item fit parameters for the third level of the hierarchical model, a matrix of dimension the number of covariates. |
delta.start.level.4 |
Optional starting values for the sensitive item
fit for the fourth level of the hierarchical model. 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 |
delta.mu0.level.4 |
Optional vector of prior means for the sensitive item fit parameters for the fourth level of the hierarchical model, a vector of length the number of covariates. |
delta.A0.level.4 |
Optional matrix of prior precisions for the sensitive item fit parameters for the fourth level of the hierarchical model, a matrix of dimension the number of covariates. |
sigma.start.level.1 |
Optional list of length the number of sensitive items with the starting values for the sigma parameters. |
sigma.df.level.1 |
Optional prior degrees of freedom parameter. |
sigma.scale.level.1 |
Optional prior scale parameter. |
sigma.start.level.2 |
Optional list of length the number of sensitive items with the starting values for the sigma parameters for the second level of the hierarchical model. |
sigma.df.level.2 |
Optional prior degrees of freedom parameter for the second level of the hierarchical model. |
sigma.scale.level.2 |
Optional prior scale parameter for the second level of the hierarchical model. |
sigma.start.level.3 |
Optional list of length the number of sensitive items with the starting values for the sigma parameters for the third level of the hierarchical model. |
sigma.df.level.3 |
Optional prior degrees of freedom parameter for the third level of the hierarchical model. |
sigma.scale.level.3 |
Optional prior scale parameter for the third level of the hierarchical model. |
sigma.start.level.4 |
Optional list of length the number of sensitive items with the starting values for the sigma parameters for the fourth level of the hierarchical model. |
sigma.df.level.4 |
Optional prior degrees of freedom parameter for the fourth level of the hierarchical model. |
sigma.scale.level.4 |
Optional prior scale parameter for the fourth level of the hierarchical model. |
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). |
alpha.tune |
An optional vector of tuning parameters for the Metropolis algorithm for the random effects. |
verbose |
A logical value indicating whether model diagnostics are printed out during fitting. |
... |
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).
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
See Also
predict.ictreg for fitted values
Examples
data(race)
## Not run:
## Multiple chain MCMC list experiment regression
## starts with overdispersed MLE starting values
## Multiple item two level hierarchical model - varying intercepts
mle.estimates.multi <- ictreg(y ~ male + college, data = multi,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesDraws.1 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ 1,
delta.start.level.1 = list(draws[1, 8:9], draws[1, 2:3], draws[1, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.2 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ 1,
delta.start.level.1 = list(draws[2, 8:9], draws[2, 2:3], draws[2, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.3 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ 1,
delta.start.level.1 = list(draws[3, 8:9], draws[3, 2:3], draws[3, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesHierTwoLevel <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesHierTwoLevel)
## Multiple item two level hierarchical model - including covariates
mle.estimates.multi <- ictreg(y ~ male + college, data = multi,
constrained = TRUE)
draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),
Sigma = vcov(mle.estimates.multi) * 9)
bayesDraws.1 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ age,
delta.start.level.1 = list(draws[1, 8:9], draws[1, 2:3], draws[1, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.2 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ age,
delta.start.level.1 = list(draws[2, 8:9], draws[2, 2:3], draws[2, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesDraws.3 <- ictregBayesHier(y ~ male + college,
formula.level.2 = ~ age,
delta.start.level.1 = list(draws[3, 8:9], draws[3, 2:3], draws[3, 5:6]),
data = multi, treat = "treat",
delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),
alpha.tune = rep(0.001, length(unique(multi$state))),
J = 3, group.level.2 = "state",
n.draws = 100000, burnin = 50000, thin = 100)
bayesHierTwoLevel <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)
summary(bayesHierTwoLevel)
## End(Not run)
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