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.
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, ...)
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 multivalued 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 nonsensitive (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 nonsensitive 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 grouplevel 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. 
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").
an object of class "mcmc" that can be analyzed using the
coda
package.
the design matrix
a logical value indicating whether the data included multiple sensitive items.
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 nonsensitive item count is included as a predictor in the sensitive item fits for the multiple sensitive item design.
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.
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.
Optional vector of prior means for the sensitive item fit parameters, a vector of length the number of covariates.
Optional vector of prior means for the control item fit parameters, a vector of length the number of covariates.
Optional matrix of prior precisions for the sensitive item fit parameters, a matrix of dimension the number of covariates.
Optional matrix of prior precisions for the control items fit parameters, a matrix of dimension the number of covariates.
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).
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).
Number of nonsensitive (control) survey items set by the user or detected.
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.
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.
the matched call
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
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 variancecovariance matrix. An example is provided below for each
of the possible designs. Running summary()
after such a procedure
will output the GelmanRubin convergence statistics in addition to the
estimates. If the GR statistics are all below 1.1, the model is said to
have converged.
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. 407416. 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
predict.ictreg
for fitted values
data(race)# NOT RUN { ## Multiple chain MCMC list experiment regression ## starts with overdispersed MLE starting values ## Standard single sensitiveitem 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) # }