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The 1991 National Race and Politics Survey

Description

This dataset is a subset of the 1991 National Race and Politics Survey andcontains the item count technique or the list experiment. The main questionreads as follows:⁠ Now I'm going to read you four things thatsometimes make people angry or upset. After I read all (three/four), justtell me HOW MANY of them upset you. (I don't want to know which ones, justhow many.) (1) "the federal government increasing the tax on gasoline;" (2)"professional athletes getting million-dollar-plus salaries;" (3) "largecorporations polluting the environment;" (4) "black leaders asking thegovernment for affirmative action."⁠

Format

A data frame containing the following 6 variables for 1171observations.

Details

where the last item is presented only with the treatment group and thecontrol list only contains the first three items.

Source

The full data set is available at SDA (Survey Documentation andAnalysis;https://sda.berkeley.edu/D3/Natlrace/Doc/nrac.htm)

Combined List Estimator

Description

This function implements the combined list estimator described in Aronow,Coppock, Crawford, and Green (2015): Combining List Experiment and DirectQuestion Estimates of Sensitive Behavior Prevalence

Usage

combinedListDirect(  formula,  data = parent.frame(),  treat = "treat",  direct = "direct")

Arguments

Value

a list containing conventional, direct, and combined prevalenceestimates with associated standard errors as well as the results of twoplacebo tests.

Examples

# Load data from Aronow, Coppock, Crawford, and Green (2015)data("combinedListExps")# complete case analysiscombinedListExps <- na.omit(combinedListExps)# Conduct estimation without covariate adjustmentout.1 <- combinedListDirect(list1N ~ list1treat,                             data = subset(combinedListExps, directsfirst==1),                             treat = "list1treat", direct = "direct1")summary(out.1)# Conduct estimation with covariate adjustmentout.2 <- combinedListDirect(list1N ~ list1treat + gender +                             ideology + education + race,                             data = subset(combinedListExps, directsfirst==1),                             treat = "list1treat", direct = "direct1")summary(out.2)

Five List Experiments with Direct Questions

Description

A dataset containing the five list experiments in Aronow, Coppock, Crawford, and Green (2015)

A dataset containing the five list experiments in Aronow, Coppock, Crawford,and Green (2015)

Usage

data(combinedListExps)

Format

A data frame with 1023 observations and 23 variables

A data frame with 1023 observations and 23 variables

Comparing List and Endorsement Experiment Data

Description

Function to conduct a statistical test with the null hypothesis that thereis no difference between the correlation coefficients between listexperiment and endorsement experiment data.

Usage

comp.listEndorse(  y.endorse,  y.list,  treat,  n.draws = 10000,  alpha = 0.05,  endorse.mean = FALSE,  method = "pearson")

Arguments

Details

This function allows the user to calculate the correlation between list andendorsement experiment data within the control group and the treatmentgroup, and to conduct a statistical test with the null hypothesis of nodifference between the two correlation coefficients.

Value

comp.listEndorse returns a list with four elements: thecorrelation statistic (rho or tau) for the treatment group ascor.treat, the correlation statistic for the control group ascor.control, the p.value for the statistical test comparing the twocorrelation statistics asp.value, and the bootstrapped confidenceinterval of the difference asci.

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme, Jason Lyall and Kosuke Imai. (2014) “Comparingand Combining List and Experiments: Evidence from Afghanistan." AmericanJournal of Political Science. available athttp://imai.princeton.edu/research/comp.html

Hausman Specification Test for Two List Experiment Regression Fit Objects

Description

Hausman Specification Test for Two List Experiment Regression Fit Objects

Usage

ict.hausman.test(ml, nls, abs = FALSE, psd = FALSE)

Arguments

Value

List containing Hausman statistic, p-value, and the degrees of freedom of the test.

Item Count Technique

Description

Function to conduct a statistical test with the null hypothesis that thereis no "design effect" in a list experiment, a failure of the experiment.

Usage

ict.test(  y,  treat,  J = NA,  alpha = 0.05,  n.draws = 250000,  gms = TRUE,  pi.table = TRUE)

Arguments

Details

This function allows the user to perform a statistical test on data from alist experiment or item count technique with the null hypothesis of nodesign effect. A design effect occurs when an individual's response to thenon-sensitive items changes depending upon the respondent's treatmentstatus.

Value

ict.test returns a numerical scalar with theBonferroni-corrected minimum p-value of the statistical test.

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

See Also

ictreg for list experiment regression based on theassumption of no design effect

Examples

data(affirm)data(race)# Conduct test with null hypothesis that there is no design effect# Replicates results on Blair and Imai (2012) pg. 69test.value.affirm <- ict.test(affirm$y, affirm$treat, J = 3, gms = TRUE)print(test.value.affirm)test.value.race <- ict.test(race$y, race$treat, J = 3, gms = TRUE)print(test.value.race)

Item Count Technique

Description

Function to conduct multivariate regression analyses of survey data with theitem count technique, also known as the list experiment and the unmatchedcount technique.

Usage

ictreg(  formula,  data = parent.frame(),  treat = "treat",  J,  method = "ml",  weights,  h = NULL,  group = NULL,  matrixMethod = "efficient",  robust = FALSE,  error = "none",  overdispersed = FALSE,  constrained = TRUE,  floor = FALSE,  ceiling = FALSE,  ceiling.fit = "glm",  floor.fit = "glm",  ceiling.formula = ~1,  floor.formula = ~1,  fit.start = "lm",  fit.sensitive = "glm",  fit.nonsensitive = "nls",  multi.condition = "none",  maxIter = 5000,  verbose = FALSE,  ...)

Arguments

Details

This function allows the user to perform regression analysis on data fromthe item count technique, also known as the list experiment and theunmatched count technique.

Three list experiment designs are accepted by this function: the standarddesign; the multiple sensitive item standard design; and the modified designproposed by Corstange (2009).

For the standard design, three methods are implemented in this function: thelinear model; the Maximum Likelihood (ML) estimation for theExpectation-Maximization (EM) algorithm; the nonlinear least squares (NLS)estimation with the two-step procedure both proposed in Imai (2010); and theMaximum Likelihood (ML) estimator in the presence of two types of dishonestresponses, "ceiling" and "floor" liars. The ceiling model, floor model, orboth, as described in Blair and Imai (2010) can be activated by using theceiling andfloor options. The constrained and unconstrainedML models presented in Imai (2010) are available through theconstrained option, and the user can specify if overdispersion ispresent in the data for the no liars models using theoverdispersedoption to control whether a beta-binomial or binomial model is used in theEM algorithm to model the item counts.

The modified design and the multiple sensitive item design are automaticallydetected by the function, and only the binomial model without overdispersionis available.

Value

ictreg returns an object of class "ictreg". The functionsummary is used to obtain a table of the results. The objectictreg is a list that contains the following components. Some ofthese elements are not available depending on which method is used(lm,nls orml), which design is used (standard,modified), whether multiple sensitive items are include(multi), and whether the constrained model is used (constrained= TRUE).

For the maximum likelihood models, an additional output object is included:

For the floor/ceiling models, several additional output objects areincluded:

For the multiple sensitive item design, thepar.treat andse.treat vectors are returned as lists of vectors, one for eachsensitive item.

For the unconstrained model, thepar.control andse.controloutput is replaced by:

Depending upon the estimator requested by the user, model fit statistics arealso included:

When using the auxiliary data functionality, the following objects areincluded:

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis. Forthcoming. available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://imai.princeton.edu/research/list.html

See Also

predict.ictreg for fitted values

Examples

data(race)set.seed(1)# Calculate list experiment difference in meansdiff.in.means.results <- ictreg(y ~ 1, data = race,              treat = "treat", J=3, method = "lm")summary(diff.in.means.results)# Fit linear regression# Replicates Table 1 Columns 1-2 Imai (2011); note that age is divided by 10lm.results <- ictreg(y ~ south + age + male + college, data = race,              treat = "treat", J=3, method = "lm")summary(lm.results)# Fit two-step non-linear least squares regression# Replicates Table 1 Columns 3-4 Imai (2011); note that age is divided by 10nls.results <- ictreg(y ~ south + age + male + college, data = race,              treat = "treat", J=3, method = "nls")summary(nls.results)## Not run: # Fit EM algorithm ML model with constraint# Replicates Table 1 Columns 5-6, Imai (2011); note that age is divided by 10ml.constrained.results <- ictreg(y ~ south + age + male + college, data = race,           treat = "treat", J=3, method = "ml",  overdispersed = FALSE, constrained = TRUE)summary(ml.constrained.results)# Fit EM algorithm ML model with no constraint# Replicates Table 1 Columns 7-10, Imai (2011); note that age is divided by 10ml.unconstrained.results <- ictreg(y ~ south + age + male + college, data = race,        treat = "treat", J=3, method = "ml",    overdispersed = FALSE, constrained = FALSE)summary(ml.unconstrained.results)# Fit EM algorithm ML model for multiple sensitive items# Replicates Table 3 in Blair and Imai (2010)multi.results <- ictreg(y ~ male + college + age + south + south:age, treat = "treat",        J = 3, data = multi, method = "ml", multi.condition = "level")summary(multi.results)# Fit standard design ML model# Replicates Table 7 Columns 1-2 in Blair and Imai (2010)noboundary.results <- ictreg(y ~ age + college + male + south, treat = "treat",           J = 3, data = affirm, method = "ml",      overdispersed = FALSE)summary(noboundary.results)# Fit standard design ML model with ceiling effects alone# Replicates Table 7 Columns 3-4 in Blair and Imai (2010)ceiling.results <- ictreg(y ~ age + college + male + south, treat = "treat",      J = 3, data = affirm, method = "ml", fit.start = "nls",  ceiling = TRUE, ceiling.fit = "bayesglm",  ceiling.formula = ~ age + college + male + south)summary(ceiling.results)# Fit standard design ML model with floor effects alone# Replicates Table 7 Columns 5-6 in Blair and Imai (2010)floor.results <- ictreg(y ~ age + college + male + south, treat = "treat",        J = 3, data = affirm, method = "ml", fit.start = "glm", floor = TRUE, floor.fit = "bayesglm",floor.formula = ~ age + college + male + south)summary(floor.results)# Fit standard design ML model with floor and ceiling effects# Replicates Table 7 Columns 7-8 in Blair and Imai (2010)both.results <- ictreg(y ~ age + college + male + south, treat = "treat",             J = 3, data = affirm, method = "ml",        floor = TRUE, ceiling = TRUE,        floor.fit = "bayesglm", ceiling.fit = "bayesglm",       floor.formula = ~ age + college + male + south,       ceiling.formula = ~ age + college + male + south)summary(both.results)# Response error models (Blair, Imai, and Chou 2018)top.coded.error <- ictreg(   y ~ age + college + male + south, treat = "treat",   J = 3, data = race, method = "ml", error = "topcoded")   uniform.error <- ictreg(   y ~ age + college + male + south, treat = "treat",   J = 3, data = race, method = "ml", error = "topcoded")   # Robust models, which constrain sensitive item proportion#   to difference-in-means estimaterobust.ml <- ictreg(   y ~ age + college + male + south, treat = "treat",   J = 3, data = affirm, method = "ml", robust = TRUE)robust.nls <- ictreg(   y ~ age + college + male + south, treat = "treat",   J = 3, data = affirm, method = "nls", robust = TRUE)   ## End(Not run)

Item Count Technique: Outcome Models

Description

Function to conduct multivariate regression analyses of survey data with theitem count technique, also known as the list experiment, using predictedresponses from list experiments as predictors in outcome regression models.

Usage

ictreg.joint(  formula,  data = parent.frame(),  treat = "treat",  J,  outcome = "outcome",  outcome.reg = "logistic",  constrained = FALSE,  maxIter = 1000)

Arguments

Details

This function allows the user to perform regression analysis on survey datawith the item count technique, also known as the list experiment, usingpredicted responses from list experiments as predictors in outcomeregression models.

Value

ictreg.joint returns an object of class "ictreg.joint". Thefunctionsummary is used to obtain a table of the results. The objectictreg.joint is a list that contains the following components.

References

Imai, Kosuke, Bethany Park, and Kenneth F. Greene. (2014)“Using the Predicted Responses from List Experiments as ExplanatoryVariables in Regression Models.” available athttp://imai.princeton.edu/research/files/listExp.pdf

Examples

## Not run: data(mexico)loyal <- mexico[mexico$mex.loyal == 1,]notloyal <- mexico[mexico$mex.loyal == 0,]## Logistic outcome regression## (effect of vote-selling on turnout)## This replicates Table 4 in Imai et al. 2014loyalreg <- ictreg.joint(formula = mex.y.all ~ mex.male + mex.age + mex.age2 + mex.education +                           mex.interest + mex.married +                         mex.wealth + mex.urban + mex.havepropoganda + mex.concurrent, data = loyal,                         treat = "mex.t", outcome = "mex.votecard", J = 3, constrained = TRUE,                         outcome.reg = "logistic", maxIter = 1000)summary(loyalreg)## Linear outcome regression## (effect of vote-selling on candidate approval)## This replicates Table 5 in Imai et al. 2014approvalreg <- ictreg.joint(formula = mex.y.all ~ mex.male + mex.age + mex.age2 +                            mex.education +                            mex.interest + mex.married +                            mex.urban +                             mex.cleanelections + mex.cleanelectionsmiss +                            mex.havepropoganda +                            mex.wealth + mex.northregion +                            mex.centralregion + mex.metro + mex.pidpriw2 +     mex.pidpanw2 + mex.pidprdw2,                            data = mexico, treat = "mex.t", outcome = "mex.epnapprove",                            J = 3, constrained = TRUE,                            outcome.reg = "linear", maxIter = 1000)summary(approvalreg)## End(Not run)

Item Count Technique

Description

Function to conduct multivariate regression analyses of survey data with theitem count technique, also known as the list experiment and the unmatchedcount 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

Details

This function allows the user to perform regression analysis on data fromthe item count technique, also known as the list experiment and theunmatched count technique using a Bayesian MCMC algorithm.

Unlike the maximum likelihood and least squares estimators in theictreg function, the Metropolis algorithm for the Bayesian MCMCestimators in this function must be tuned to work correctly. Thedelta.tune andpsi.tune are required, and the values, one foreach estimated parameter, will need to be manipulated. The output of theictregBayes function, and of thesummary function run on anictregBayes object display the acceptance ratios from the Metropolisalgorithm. If these values are far from 0.4, the tuning parameters should bechanged until the ratios approach 0.4.

For the single sensitive item design, the model can constrain all controlparameters to be equal (constrained = "full"), or just the intercept(constrained = "intercept") or all the control fit parameters can beallowed to vary across the potential sensitive item values(constrained = "none").

For the multiple sensitive item design, the model can include the estimatednumber of affirmative responses to the control items as a covariate in thesensitive item model fit (constrained set toTRUE) or excludeit (FALSE).

The function also allows the user to perform combined list experiment andendorsement experiment regression. Settingendorse.options to a listwith the options from theendorse package for endorsement experimentregression, the function will return the combined model in which therelationship between covariates and the sensitive item in the listexperiment model is set to be identical to the relationship betweencovariates and support for endorsers in the endorsement experiment model.For more details on endorsement experiment regression, see the help for theendorse package.

Convergence is at times difficult to achieve, so we recommend runningmultiple chains from overdispersed starting values by, for example, runningan MLE or linear model using the ictreg() function, and then generating aset of overdispersed starting values using those estimates and theirestimated variance-covariance matrix. An example is provided below for eachof the possible designs. Runningsummary() after such a procedurewill output the Gelman-Rubin convergence statistics in addition to theestimates. If the G-R statistics are all below 1.1, the model is said tohave converged.

Value

ictregBayes returns an object of class "ictregBayes". Thefunctionsummary is used to obtain a table of the results, using thecoda package. Two attributes are also included, the data ("x"), thecall ("call"), which can be extracted using the command, e.g.,attr(ictregBayes.object, "x").

If the data includes multiple sensitive items, the following object is alsoincluded:

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://imai.princeton.edu/research/list.html

Blair, Graeme, Jason Lyall and Kosuke Imai. (2013) “Comparing and CombiningList and Experiments: Evidence from Afghanistan." Working paper. availableathttp://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 constrainedmle.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 unconstrainedmle.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 interceptmle.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 interceptsmle.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)

Item Count Technique

Description

Function to conduct multilevel, multivariate regression analyses of surveydata with the item count technique, also known as the list experiment andthe 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

Details

This function allows the user to perform regression analysis on data fromthe item count technique, also known as the list experiment and theunmatched count technique using a Bayesian MCMC algorithm.

Unlike the maximum likelihood and least squares estimators in theictreg function, the Metropolis algorithm for the Bayesian MCMCestimators in this function must be tuned to work correctly. Thedelta.tune andpsi.tune are required, and the values, one foreach estimated parameter, will need to be manipulated. The output of theictregBayes function, and of thesummary function run on anictregBayes object display the acceptance ratios from the Metropolisalgorithm. If these values are far from 0.4, the tuning parameters should bechanged until the ratios approach 0.4.

For the single sensitive item design, the model can constrain all controlparameters to be equal (constrained = "full"), or just the intercept(constrained = "intercept") or all the control fit parameters can beallowed to vary across the potential sensitive item values(constrained = "none").

For the multiple sensitive item design, the model can include the estimatednumber of affirmative responses to the control items as a covariate in thesensitive item model fit (constrained set toTRUE) or excludeit (FALSE).

Convergence is at times difficult to achieve, so we recommend runningmultiple chains from overdispersed starting values by, for example, runningan MLE or linear model using the ictreg() function, and then generating aset of overdispersed starting values using those estimates and theirestimated variance-covariance matrix. An example is provided below for eachof the possible designs. Runningsummary() after such a procedurewill output the Gelman-Rubin convergence statistics in addition to theestimates. If the G-R statistics are all below 1.1, the model is said tohave converged.

Value

ictregBayes returns an object of class "ictregBayes". Thefunctionsummary is used to obtain a table of the results, using thecoda package. Two attributes are also included, the data ("x"), thecall ("call"), which can be extracted using the command, e.g.,attr(ictregBayes.object, "x").

If the data includes multiple sensitive items, the following object is alsoincluded:

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://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 interceptsmle.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$state))),                        J = 3, group.level.2 = "state",                        n.draws = 100000, burnin = 50000, thin = 100)bayesHierTwoLevel <- as.list(bayesDraws.1, bayesDraws.2, bayesDraws.3)summary(bayesHierTwoLevel)## Multiple item two level hierarchical model - including covariatesmle.estimates.multi <- ictreg(y ~ male + college, data = multi,  constrained = TRUE)draws <- mvrnorm(n = 3, mu = coef(mle.estimates.multi),   Sigma = vcov(mle.estimates.multi) * 9)bayesDraws.1 <- ictregBayesHier(y ~ male + college,                        formula.level.2 = ~ age,                         delta.start.level.1 = list(draws[1, 8:9], draws[1, 2:3], draws[1, 5:6]),                        data = multi, treat = "treat",                        delta.tune = list(rep(0.005, 2), rep(0.05, 2), rep(0.05, 2)),                        alpha.tune = rep(0.001, length(unique(multi$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)

The 2012 Mexico Elections Panel Study

Description

This dataset is a subset of the 2012 Mexico Elections Panel Study andcontains a list experiment question. It reads as follows:⁠ I am goingto read you a list of four activities that appear on this card and I wantyou to tell me how many of these activities you have done in recent weeks.Please don''t tell me which ones, just HOW MANY. The four activities are...(SHOW CARD AND READ) a. See television news that mentions a candidate b.Attend a campaign event c. Exchange your vote for a gift, favor, or accessto a service d. Talk about politics with other people⁠

Format

A data frame containing the following variables for 1004observations.

Details

where item c. is presented only to the treatment group, and the control listonly contains the other three items.

Source

The full data set is available at the Mexico Panel Study website(http://mexicopanelstudy.mit.edu/)

The 1994 Multi-Investigator Survey

Description

This dataset is a subset of the 1994 Multi-Investigator Survey and containsthe item count technique or the list experiment. The main question reads asfollows:⁠ Now I'm going to read you four things that sometimes makepeople angry or upset. After I read all (three/four), just tell me HOW MANYof them upset you. (I don't want to know which ones, just how many.) (1)"the federal government increasing the tax on gasoline;" (2) "professionalathletes getting million-dollar-plus salaries;" (3) "requiring seatbelts beused when driving;" (4) "large corporations polluting the environment;" (5)"black leaders asking the government for affirmative action."⁠

Format

A data frame containing the following 6 variables for 1171observations.

Details

where the last item is presented only with the treatment group and thecontrol list only contains the first three items.

The survey also includes a question in which attitudes toward the sensitiveitem are asked directly.

⁠ Now I'm going to ask you about another thing that sometimes makespeople angry or upset. Do you get angry or upset when black leaders ask thegovernment for affirmative action?⁠

Source

The full data set is available at SDA (Survey Documentation andAnalysis;https://sda.berkeley.edu/D3/Multi/Doc/mult.htm)

The 1991 National Race and Politics Survey

Description

This dataset is a subset of the 1991 National Race and Politics Survey andcontains a list experiment with two sensitive items. The main questionsread as follows:⁠ Now I'm going to read you four things that sometimesmake people angry or upset. After I read all (three/four), just tell me HOWMANY of them upset you. (I don't want to know which ones, just how many.)(1) "the federal government increasing the tax on gasoline;" (2)"professional athletes getting million-dollar-plus salaries;" (3) "largecorporations polluting the environment;" (4) "a black family moving nextdoor to you."⁠

Format

A data frame containing the following 6 variables for 1795observations.

Details

where the last item is presented only with the treatment group and thecontrol list only contains the first three items.

The second sensitive item replaces item (4) with⁠ (4) "black leadersasking the government for affirmative action." ⁠

Treatment status one (treat == 1) is the "black family" item and status twois the "affirmative action" item.

Source

The full data set is available at SDA (Survey Documentation andAnalysis;https://sda.berkeley.edu/D3/Natlrace/Doc/nrac.htm)

Plot Method for the Item Count Technique

Description

Function to plot predictions and confidence intervals of predictions fromestimates from multivariate regression analysis of survey data with the itemcount technique.

Usage

## S3 method for class 'predict.ictreg'plot(  x,  labels = NA,  axes.ict = TRUE,  xlim = NULL,  ylim = NULL,  xlab = NULL,  ylab = "Estimated Proportion",  axes = F,  pch = 19,  xvec = NULL,  ...)

Arguments

Details

plot.predict.ictreg produces plots with estimated populationproportions of respondents answering the sensitive item in a list experimentin the affirmative, with confidence intervals.

The function accepts a set ofpredict.ictreg objects calculated inthe following manner:

predict(ictreg.object, avg = TRUE, interval = "confidence")

For each average prediction, a point estimate and its confidence interval isplotted at equally spaced intervals. The x location of the points can bemanipulated with thexvec option.

Either a single predict object can be plotted, or a group of them combinedwithc(predict.object1, predict.object2). Predict objects with thenewdata.diff option, which calculates the mean difference inprobability between two datasets, and thedirect.glm option, whichcalculates the mean difference between the mean predicted support for thesensitive item in the list experiment and in a direct survey item, can alsobe plotted in the same way as otherpredict objects.

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://imai.princeton.edu/research/list.html

See Also

ictreg for model fitting andpredict.ictreg for predictions based on the model fits.

Examples

data(race)race.south <- race.nonsouth <- racerace.south[, "south"] <- 1race.nonsouth[, "south"] <- 0## Not run: # Fit EM algorithm ML model with constraintml.constrained.results <- ictreg(y ~ south + age + male + college,    data = race, treat = "treat", J=3, method = "ml",    overdispersed = FALSE, constrained = TRUE)# Calculate average predictions for respondents in the South # and the the North of the US for the MLE model, replicating the # estimates presented in Figure 1, Imai (2011)avg.pred.south.mle <- predict(ml.constrained.results,    newdata = race.south, avg = TRUE, interval = "confidence")avg.pred.nonsouth.mle <- predict(ml.constrained.results,    newdata = race.nonsouth, avg = TRUE, interval = "confidence")# A plot of a single estimate and its confidence intervalplot(avg.pred.south.mle, labels = "South")# A  plot of the two estimates and their confidence intervals# use c() to combine more than one predict object for plottingplot(c(avg.pred.south.mle, avg.pred.nonsouth.mle), labels = c("South", "Non-South"))# The difference option can also be used to simultaneously# calculate separate estimates of the two sub-groups# and the estimated difference. This can also be plotted.avg.pred.diff.mle <- predict(ml.constrained.results,    newdata = race.south, newdata.diff = race.nonsouth,   se.fit = TRUE, avg = TRUE, interval="confidence")plot(avg.pred.diff.mle, labels = c("South", "Non-South", "Difference"))# Social desirability bias plots# Estimate logit for direct sensitive questiondata(mis)mis.list <- subset(mis, list.data == 1)mis.sens <- subset(mis, sens.data == 1)# Fit EM algorithm ML modelfit.list <- ictreg(y ~ age + college + male + south,   J = 4, data = mis.list, method = "ml")# Fit logistic regression with directly-asked sensitive questionfit.sens <- glm(sensitive ~ age + college + male + south,    data = mis.sens, family = binomial("logit"))# Predict difference between response to sensitive item# under the direct and indirect questions (the list experiment).# This is an estimate of the revealed social desirability bias# of respondents. See Blair and Imai (2010).avg.pred.social.desirability <- predict(fit.list,    direct.glm = fit.sens, se.fit = TRUE)plot(avg.pred.social.desirability)## End(Not run)

Predict Method for Item Count Technique

Description

Function to calculate predictions and uncertainties of predictions fromestimates from multivariate regression analysis of survey data with the itemcount technique.

Usage

## S3 method for class 'ictreg'predict(  object,  newdata,  newdata.diff,  direct.glm,  newdata.direct,  se.fit = FALSE,  interval = c("none", "confidence"),  level = 0.95,  avg = FALSE,  sensitive.item,  ...)

Arguments

Details

predict.ictreg produces predicted values, obtained by evaluating theregression function in the frame newdata (which defaults tomodel.frame(object). If the logicalse.fit isTRUE,standard errors of the predictions are calculated. Settingintervalspecifies computation of confidence intervals at the specified level or nointervals.

Ifavg is set toTRUE, the mean prediction across allobservations in the dataset will be calculated, and if these.fitoption is set toTRUE a standard error for this mean estimate will beprovided. Theinterval option will output confidence intervalsinstead of only the point estimate if set toTRUE.

Two additional types of mean prediction are also available. The first, if anewdata.diff data frame is provided by the user, calculates the meanpredicted values across two datasets, as well as the mean difference inpredicted value. Standard errors and confidence intervals can also be added.For difference prediction,avg must be set toTRUE.

The second type of prediction, triggered if adirect.glm object isprovided by the user, calculates the mean difference in prediction betweenpredictions based on anictreg fit and aglm fit from a directsurvey item on the sensitive question. This is defined as the revealedsocial desirability bias in Blair and Imai (2010).

Value

predict.ictreg produces a vector of predictions or a matrixof predictions and bounds with column names fit, lwr, and upr if interval isset. If se.fit is TRUE, a list with the following components is returned:

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://imai.princeton.edu/research/list.html

See Also

ictreg for model fitting

Examples

data(race)race.south <- race.nonsouth <- racerace.south[, "south"] <- 1race.nonsouth[, "south"] <- 0## Not run: # Fit EM algorithm ML model with constraint with no covariatesml.results.south.nocov <- ictreg(y ~ 1,    data = race[race$south == 1, ], method = "ml", treat = "treat",    J = 3, overdispersed = FALSE, constrained = TRUE)ml.results.nonsouth.nocov <- ictreg(y ~ 1,    data = race[race$south == 0, ], method = "ml", treat = "treat",    J = 3, overdispersed = FALSE, constrained = TRUE)# Calculate average predictions for respondents in the South # and the the North of the US for the MLE no covariates # model, replicating the estimates presented in Figure 1, # Imai (2010)avg.pred.south.nocov <- predict(ml.results.south.nocov,   newdata = as.data.frame(matrix(1, 1, 1)), se.fit = TRUE,    avg = TRUE)avg.pred.nonsouth.nocov <- predict(ml.results.nonsouth.nocov,   newdata = as.data.frame(matrix(1, 1, 1)), se.fit = TRUE,    avg = TRUE)# Fit linear regressionlm.results <- ictreg(y ~ south + age + male + college,    data = race, treat = "treat", J=3, method = "lm")# Calculate average predictions for respondents in the # South and the the North of the US for the lm model, # replicating the estimates presented in Figure 1, Imai (2010)avg.pred.south.lm <- predict(lm.results, newdata = race.south,    se.fit = TRUE, avg = TRUE)avg.pred.nonsouth.lm <- predict(lm.results, newdata = race.nonsouth,    se.fit = TRUE, avg = TRUE)# Fit two-step non-linear least squares regressionnls.results <- ictreg(y ~ south + age + male + college,    data = race, treat = "treat", J=3, method = "nls")# Calculate average predictions for respondents in the South # and the the North of the US for the NLS model, replicating# the estimates presented in Figure 1, Imai (2010)avg.pred.nls <- predict(nls.results, newdata = race.south,    newdata.diff = race.nonsouth, se.fit = TRUE, avg = TRUE)# Fit EM algorithm ML model with constraintml.constrained.results <- ictreg(y ~ south + age + male + college,    data = race, treat = "treat", J=3, method = "ml",    overdispersed = FALSE, constrained = TRUE)# Calculate average predictions for respondents in the South # and the the North of the US for the MLE model, replicating the # estimates presented in Figure 1, Imai (2010)avg.pred.diff.mle <- predict(ml.constrained.results,    newdata = race.south, newdata.diff = race.nonsouth,   se.fit = TRUE, avg = TRUE)# Calculate average predictions from the item count technique# regression and from a direct sensitive item modeled with# a logit.# Estimate logit for direct sensitive questiondata(mis)mis.list <- subset(mis, list.data == 1)mis.sens <- subset(mis, sens.data == 1)# Fit EM algorithm ML modelfit.list <- ictreg(y ~ age + college + male + south,   J = 4, data = mis.list, method = "ml")# Fit logistic regression with directly-asked sensitive questionfit.sens <- glm(sensitive ~ age + college + male + south,    data = mis.sens, family = binomial("logit"))# Predict difference between response to sensitive item# under the direct and indirect questions (the list experiment).# This is an estimate of the revealed social desirability bias# of respondents. See Blair and Imai (2010).avg.pred.social.desirability <- predict(fit.list,    direct.glm = fit.sens, se.fit = TRUE)## End(Not run)

Predict Method for Item Count Technique, Outcome Regressions

Description

Function to calculate predictions and uncertainties of predictions fromestimates from multivariate regression analysis of survey data with the itemcount technique, using predicted responses to list experiments as predictorsin outcome regressions.

Usage

## S3 method for class 'ictreg.joint'predict(  object,  newdata,  newdata.diff,  se.fit = FALSE,  interval = c("none", "confidence"),  level = 0.95,  avg = FALSE,  sensitive.value = c("0", "1", "both"),  sensitive.diff = FALSE,  return.draws = FALSE,  predict.sensitive = FALSE,  ...)

Arguments

Details

predict.ictreg.joint produces predicted values, obtained byevaluating the regression function in the frame newdata (which defaults tomodel.frame(object)). By using sensitive.value, users must set the value ofz – the latent response to the sensitive item – to be either zero or one,depending on the prediction that the user requires.

Two additional types of mean prediction are also available. The first, if anewdata.diff data frame is provided by the user, calculates the meanpredicted values across two datasets, as well as the mean difference inpredicted value. Standard errors and confidence intervals are also added.For newdata.diff predictions, sensitive.value must be set to 1 or 0, not"both" (and sensitive.diff must also be set to FALSE). Users may also setthe logical sensitive.diff to TRUE and sensitive.value to "both", which willoutput the mean predicted values across all observations for z = 0 as wellas z = 1, in addition to the mean difference in predicted value. Standarderrors and confidence intervals are also added. For difference predictions(sensitive.diff and newdata.diff), the option avg must be set to TRUE.

Users can also use the predict.sensitive = TRUE option to generatepredictions of responses to the sensitive item, with standard errors andconfidence intervals.

NOTE: In order to generate predictions from user-provided data frames(newdata and newdata.diff), users MUST run models usingictreg.jointon data that does not contain any missingness. Further, the data framesprovided topredict.ictreg.joint must also not contain anymissingness.

Value

predict.ictreg.joint produces a vector of predictions or amatrix of predictions and bounds with column names fit, lwr, and upr ifinterval is set. If sensitive.value = "both",predict.ictreg.jointwill produce a list, where the first element corresponds to when thesensitive item = 0 and the second element corresponds to when the sensitiveitem = 1. If sensitive.diff = TRUE, the third element in the listcorresponds to the difference (sensitive = 0 subtracted from sensitive = 1).If se.fit is TRUE, a list with the following components is returned:

If return.draws is TRUE, the list includes

If predict.sensitive = TRUE, the list also includes

References

Imai, Kosuke, Bethany Park, and Kenneth F. Greene. (2014)“Using the Predicted Responses from List Experiments as ExplanatoryVariables in Regression Models.” available athttp://imai.princeton.edu/research/files/listExp.pdf

Examples

data(mexico)loyal <- mexico[mexico$mex.loyal == 1,]notloyal <- mexico[mexico$mex.loyal == 0,]## Not run: ## Logistic outcome regression## (effect of vote-selling on turnout)## This replicates Table 4 in Imai et al. 2014loyalreg <- ictreg.joint(formula = mex.y.all ~ mex.male + mex.age + mex.age2 + mex.education +                           mex.interest + mex.married +                         mex.wealth + mex.urban + mex.havepropoganda + mex.concurrent, data = loyal,                         treat = "mex.t", outcome = "mex.votecard", J = 3, constrained = TRUE,                         outcome.reg = "logistic", maxIter = 1000)## Linear outcome regression## (effect of vote-selling on candidate approval)## This replicates Table 5 in Imai et al. 2014approvalreg <- ictreg.joint(formula = mex.y.all ~ mex.male + mex.age + mex.age2 +                            mex.education +                            mex.interest + mex.married +                            mex.urban +                             mex.cleanelections + mex.cleanelectionsmiss +                            mex.havepropoganda +                            mex.wealth + mex.northregion +                            mex.centralregion + mex.metro + mex.pidpriw2 +     mex.pidpanw2 + mex.pidprdw2,                            data = mexico, treat = "mex.t", outcome = "mex.epnapprove",                            J = 3, constrained = TRUE,                            outcome.reg = "linear", maxIter = 1000)summary(approvalreg)## Generate predicted probability of turnout, averaged over the whole sample,## for vote sellers (z = 1), non-vote sellers (z = 0), and the difference## between vote sellers and non-vote sellers, in the sample of party supporters.## This replicates the results in the righthand panel of Figure 2 in Imai et al. 2014loyalpred <- predict.ictreg.joint(loyalreg, se.fit = TRUE, interval = "confidence", level = 0.95, avg = TRUE, sensitive.value = "both", sensitive.diff = TRUE, return.draws = TRUE,    predict.sensitive = TRUE)loyalpred$fit## View predicted probability of vote selling, in the sample of party supporters.## This replicates the results in the lefthand panel of Figure 2 in Imai et al. 2014loyalpred$fitsens## End(Not run)

Predict Method for the Item Count Technique with Bayesian MCMC

Description

Function to calculate predictions and uncertainties of predictions fromestimates from multivariate regression analysis of survey data with the itemcount technique.

Usage

## S3 method for class 'ictregBayes'predict(  object,  newdata,  newdata.diff,  direct.glm,  se.fit = FALSE,  interval = c("none", "confidence"),  level = 0.95,  sensitive.item,  ...)

Arguments

Details

predict.ictregBayes produces predicted values, obtained by evaluatingthe regression function in the frame newdata (which defaults tomodel.frame(object). If the logicalse.fit isTRUE,standard errors of the predictions are calculated. Settingintervalspecifies computation of confidence intervals at the specified level or nointervals.

The mean prediction across all observations in the dataset is calculated,and if these.fit option is set toTRUE a standard error forthis mean estimate will be provided. Theinterval option will outputconfidence intervals instead of only the point estimate if set toTRUE.

Two additional types of mean prediction are also available. The first, if anewdata.diff data frame is provided by the user, calculates the meanpredicted values across two datasets, as well as the mean difference inpredicted value. Standard errors and confidence intervals can also be added.For difference prediction,avg must be set toTRUE.

The second type of prediction, triggered if adirect.glm object isprovided by the user, calculates the mean difference in prediction betweenpredictions based on anictreg fit and aglm fit from a directsurvey item on the sensitive question. This is defined as the revealedsocial desirability bias in Blair and Imai (2010).

In the multiple sensitive item design, prediction can only be based on thecoefficients from one of the sensitive item fits. Thesensitive.itemoption allows you to specify which is used, using integers from 1 to thenumber of sensitive items.

Value

predict.ictreg produces a vector of predictions or a matrixof predictions and bounds with column names fit, lwr, and upr if interval isset. If se.fit is TRUE, a list with the following components is returned:

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://imai.princeton.edu/research/list.html

See Also

ictreg for model fitting

Examples

data(race)## Not run: bayes.fit <- ictregBayes(y ~ age + college + male + south, data = multi,   treat = "treat", delta.tune = diag(.002, 5), psi.tune = diag(.00025, 5))bayes.predict <- predict(bayes.fit, interval = "confidence", se.fit = TRUE)## End(Not run)

Predict Method for the Item Count Technique with Bayesian HierarchicalRegression

Description

Function to calculate predictions and uncertainties of predictions fromestimates from hierarchical multivariate regression analysis of survey datawith the item count technique.

Usage

## S3 method for class 'ictregBayesHier'predict(  object,  newdata,  se.fit = FALSE,  interval = c("none", "confidence"),  level = 0.95,  sensitive.item,  ...)

Arguments

Details

predict.ictregBayesHier produces predicted values, obtained byevaluating the regression function in the frame newdata (which defaults tomodel.frame(object). If the logicalse.fit isTRUE,standard errors of the predictions are calculated. Settingintervalspecifies computation of confidence intervals at the specified level or nointervals.

The mean prediction across all observations in the dataset is calculated,and if these.fit option is set toTRUE a standard error forthis mean estimate will be provided. Theinterval option will outputconfidence intervals instead of only the point estimate if set toTRUE.

In the multiple sensitive item design, prediction can only be based on thecoefficients from one of the sensitive item fits. Thesensitive.itemoption allows you to specify which is used, using integers from 1 to thenumber of sensitive items.

Value

predict.ictreg produces a vector of predictions or a matrixof predictions and bounds with column names fit, lwr, and upr if interval isset. If se.fit is TRUE, a list with the following components is returned:

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://imai.princeton.edu/research/list.html

See Also

ictreg for model fitting

Examples

data(race)## Not run: 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)bayes.fit <- 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 = 100, burnin = 10, thin = 1)bayes.predict <- predict(bayes.fit, interval = "confidence", se.fit = TRUE)## End(Not run)

The 1991 National Race and Politics Survey

Description

This dataset is a subset of the 1991 National Race and Politics Survey andcontains the item count technique or the list experiment. The main questionreads as follows:⁠ Now I'm going to read you four things thatsometimes make people angry or upset. After I read all (three/four), justtell me HOW MANY of them upset you. (I don't want to know which ones, justhow many.) (1) "the federal government increasing the tax on gasoline;" (2)"professional athletes getting million-dollar-plus salaries;" (3) "largecorporations polluting the environment;" (4) "a black family moving nextdoor to you."⁠

Format

A data frame containing the following 6 variables for 1213observations.

Details

where the last item is presented only with the treatment group and thecontrol list only contains the first three items.

Source

The full data set is available at SDA (Survey Documentation andAnalysis;https://sda.berkeley.edu/D3/Natlrace/Doc/nrac.htm)

Summary Method for the Item Count Technique

Description

Function to summarize results from list experiment regression based on theictreg() function, and to produce proportions of liars estimates.

Usage

## S3 method for class 'ictreg'summary(object, boundary.proportions = FALSE, n.draws = 10000, ...)

Arguments

Details

predict.ictreg produces a summary of the results from anictreg object. It displays the coefficients, standard errors, and fitstatistics for any model fromictreg.

predict.ictreg also produces estimates of the conditional probabilityof lying and of the population proportion of liars for boundary models fromictreg() ifceiling = TRUE orfloor = TRUE.

The conditional probability of lying for the ceiling model is theprobability that a respondent with true affirmative views of all thesensitive and non-sensitive items lies and responds negatively to thesensitive item. The conditional probability for the floor model is theprobability that a respondent lies to conceal her true affirmative views ofthe sensitive item when she also holds true negative views of all thenon-sensitive items. In both cases, the respondent may believe her privacyis not protected, so may conceal her true affirmative views of the sensitiveitem.

Author(s)

Graeme Blair, UCLA,graeme.blair@ucla.eduand Kosuke Imai, Princeton University,kimai@princeton.edu

References

Blair, Graeme and Kosuke Imai. (2012) “Statistical Analysis ofList Experiments." Political Analysis, Vol. 20, No 1 (Winter). available athttp://imai.princeton.edu/research/listP.html

Imai, Kosuke. (2011) “Multivariate Regression Analysis for the Item CountTechnique.” Journal of the American Statistical Association, Vol. 106, No.494 (June), pp. 407-416. available athttp://imai.princeton.edu/research/list.html

See Also

ictreg for model fitting

Examples

data(race)## Not run: # Fit standard design ML model with ceiling effects# Replicates Table 7 Columns 3-4 in Blair and Imai (2012)ceiling.results <- ictreg(y ~ age + college + male + south, treat = "treat",      J = 3, data = affirm, method = "ml", fit.start = "nls",  ceiling = TRUE, ceiling.fit = "bayesglm",  ceiling.formula = ~ age + college + male + south)# Summarize fit object and generate conditional probability # of ceiling liars the population proportion of ceiling liars,# both with standard errors.# Replicates Table 7 Columns 3-4 last row in Blair and Imai (2012)summary(ceiling.results, boundary.proportions = TRUE)## End(Not run)