ramchoice: Revealed Preference and Attention Analysis in Random Limited Attention Models

Description

Information about socio-economic agent's preference (consumer, firm, organization, voter, etc.) is important not only for understanding the decision-making process, but also for conducting welfare analysis and providing robust policy recommendations. However, it is widely documented in psychology, economics and other disciplines that decision makers may not pay full attention to all available alternatives, rendering standard revealed preference theory invalid.

This package implements the estimation and inference procedures documented in Cattaneo, Ma, Masatlioglu, and Suleymanov (2020), and Cattaneo, Cheung, Ma, and Masatlioglu (2024), which utilize standard choice data to partially identify decision maker's preference and attention. For statistical inference, several simulation-based critical values are provided.

The following functions are provided: revealPref and revealAtte (the main functions for revealed preference and attention analysis), sumData, genMat, logitAtte, logitSimu. A simulated dataset ramdata is also included for illustration purposes.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2024). Attention Overload. Working paper.

Generate Constraint Matrices

Description

genMat generates constraint matrices for a range of preference orderings according to (i) the monotonic attention assumption proposed by Cattaneo, Ma, Masatlioglu, and Suleymanov (2020), (ii) the attention overload assumption proposed by Cattaneo, Cheung, Ma, and Masatlioglu (2021), and (iii) the attentive-at-binaries restriction.

This function is embedded in revealPref.

Usage

genMat(
  sumMenu,
  sumMsize,
  pref_list = NULL,
  RAM = TRUE,
  AOM = TRUE,
  limDataCorr = TRUE,
  attBinary = 1
)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2022). Attention Overload. Working paper.

Examples

# Load data
data(ramdata)

# Generate summary statistics
summaryStats <- sumData(ramdata$menu, ramdata$choice)

# Generate constraint matrices
constraints <- genMat(summaryStats$sumMenu, summaryStats$sumMsize)
constraints$ConstN
constraints$R[1:10, 1:10]

Compute Choice Probabilities and Attention Frequencies for the Logit Attention Rule

Description

logitAtte computes choice probabilities and attention frequencies for the logit attention rule considered by Brady and Rehbeck (2016). To be specific, for a choice problem S and its subset T, the attention that T attracts is assumed to be proportional to its size: |T|^a, where a is a parameter that one can specify. It will be assumed that the first alternative is the most preferred, and that the last alternative is the least preferred.

This function is useful for replicating the simulation results in Cattaneo, Ma, Masatlioglu, and Suleymanov (2020), and Cattaneo, Cheung, Ma, and Masatlioglu (2022).

Usage

logitAtte(mSize = NULL, a = NULL)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

R. L. Brady and J. Rehbeck (2016). Menu-Dependent Stochastic Feasibility. Econometrica 84(3): 1203-1223. doi:10.3982/ECTA12694

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2022). Attention Overload. Working paper.

Examples

logitAtte(mSize = 5, a = 2)

Choice Data Simulation Following the Logit Attention Rule

Description

logitSimu simulates choice data according to the logit attention rule considered by Brady and Rehbeck (2016). To be specific, for a choice problem S and its subset T, the attention that T attracts is assumed to be proportional to its size: |T|^a, where a is a parameter that one can specify. It will be assumed that the first alternative is the most preferred, and that the last alternative is the least preferred.

This function is useful for replicating the simulation results in Cattaneo, Ma, Masatlioglu, and Suleymanov (2020), and Cattaneo, Cheung, Ma, and Masatlioglu (2022).

Usage

logitSimu(n, uSize, mSize, a)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

R. L. Brady and J. Rehbeck (2016). Menu-Dependent Stochastic Feasibility. Econometrica 84(3): 1203-1223. doi:10.3982/ECTA12694

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2022). Attention Overload. Working paper.

Examples

set.seed(42)
logitSimu(n = 5, uSize = 6, mSize = 5, a = 2)

Internal function.

Description

Internal function.

Usage

## S3 method for class 'ramchoiceRevealAtte'
print(x, ...)

Arguments

Internal function.

Description

Internal function.

Usage

## S3 method for class 'ramchoiceRevealPref'
print(x, ...)

Arguments

Internal function.

Description

Internal function.

Usage

## S3 method for class 'ramchoiceRevealPrefModel'
print(x, ...)

Arguments

Revealed Preference Analysis in Random Limited Attention Models

Description

This has been replaced by revealPref.

Usage

rAtte(
  menu,
  choice,
  pref_list = NULL,
  method = "GMS",
  nCritSimu = 2000,
  BARatio2MS = 0.1,
  BARatio2UB = 0.1,
  MNRatioGMS = NULL,
  RAM = TRUE,
  AOM = TRUE,
  limDataCorr = TRUE,
  attBinary = 1
)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2022). Attention Overload. Working paper.

ramdata: Simulated Choice Data

Description

The file contains a standard choice data of 9,000 observations. There are five alternatives in the grand set.

See revealPref for revealed preference analysis, and revealAtte for revealed attention. sumData is a low-level function that computes summary statistics, and genMat generates constraint matrices subject to given preferences.

Format

menu

Numeric matrix of 0s and 1s, choice problems (1 indicates an alternative in the choice problem and 0 otherwise).

choice

Numeric matrix of 0s and 1s, choices (1 indicates an alternative being chosen).

Revealed Attention Analysis in Random Limited Attention Models

Description

Given a random sample of choice problems and choices, revealAtte returns the upper and lower bounds on the attention frequency following the construction of Cattaneo, Cheung, Ma, and Masatlioglu (2024).

sumData is a low-level function that generates summary statistics. For revealed preference analysis, see revealPref.

Usage

revealAtte(
  menu,
  choice,
  alternative = NULL,
  S = NULL,
  lower = TRUE,
  upper = TRUE,
  pref = NULL,
  nCritSimu = 2000,
  level = 0.95
)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2024). Attention Overload. Working paper.

Examples

# Load data
data(ramdata)

# Set seed, to replicate simulated critical values
set.seed(42)

# preference
pref <- matrix(c(1, 2, 3, 4, 5), ncol=5, byrow=TRUE)
# list of choice problems
S <- matrix(c(1, 1, 0, 0, 0,
              1, 1, 1, 0, 0,
              1, 1, 1, 0, 1,
              1, 1, 1, 1, 1), ncol=5, byrow=TRUE)
result <- revealAtte(menu = ramdata$menu, choice = ramdata$choice,
  alternative = c(1,2), S = S,
  lower = TRUE, upper = TRUE,
  pref = pref)
summary(result)

Revealed Preference Analysis in Random Limited Attention Models

Description

Given a random sample of choice problems and choices, revealPref returns test statistics, critical values and p-values against a collection of preferences. Five methods for choosing critical values are available: (i) GMS: generalized moment selection (plug-in (estimated) moment conditions with shrinkage); (ii) PI: critical values based on plug-in estimated moment conditions (this is not uniformly valid); (iii) LF: critical values based on the least favorable model (plug-in 0 for the moment conditions); (iv) 2MS: two-step moment selection; and (v) 2UB: refined moment selection (plug-in upper bound of moment inequalities).

sumData is a low-level function that generates summary statistics, and genMat can be used to construct the constraint matrices. The simulated dataset ramdata is also provided for illustration. For revealed attention analysis, see revealAtte.

Usage

revealPref(
  menu,
  choice,
  pref_list = NULL,
  method = "GMS",
  nCritSimu = 2000,
  BARatio2MS = 0.1,
  BARatio2UB = 0.1,
  MNRatioGMS = NULL,
  RAM = TRUE,
  AOM = TRUE,
  limDataCorr = TRUE,
  attBinary = 1
)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2024). Attention Overload. Working paper.

Examples

# Load data
data(ramdata)

# Set seed, to replicate simulated critical values
set.seed(42)

# list of preferences
pref_list <- matrix(c(1, 2, 3, 4, 5,
                      2, 1, 3, 4, 5,
                      2, 3, 4, 5, 1,
                      5, 4, 3, 2, 1), ncol=5, byrow=TRUE)

# revealed preference using only RAM restrictions
result1 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = TRUE, AOM = FALSE)
summary(result1)

# revealed preference using only AOM restrictions
result2 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = FALSE, AOM = TRUE)
summary(result2)

# revealed preference using both RAM and AOM restrictions
result3 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = TRUE, AOM = TRUE)
summary(result3)

# revealed preference employing additional restrictions for binary choice problems
result4 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = TRUE, AOM = TRUE, attBinary = 2/3)
summary(result4)

Model Falsification with Random Limited Attention

Description

Given a collection of choice problems and corresponding choice probabilities, revealPrefModel determines if they are compatible with the Random Attention Model (RAM) of Cattaneo, Ma, Masatlioglu, and Suleymanov (2020) and/or the Attention Overload Model (AOM) of Cattaneo, Cheung, Ma, and Masatlioglu (2024).

See revealPref for revealed preference analysis with empirical choice data.

Usage

revealPrefModel(
  menu,
  prob,
  pref_list = NULL,
  RAM = TRUE,
  AOM = TRUE,
  limDataCorr = TRUE,
  attBinary = 1
)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2024). Attention Overload. Working paper.

Examples

# Logit attention with parameter 2
# True preference: 1 2 3 4 5 6
menu <- prob <- matrix(c(1, 1, 1, 1, 1, 1,
                         0, 1, 1, 1, 1, 1,
                         1, 0, 1, 1, 1, 1,
                         1, 1, 0, 1, 1, 1,
                         1, 1, 1, 0, 1, 1,
                         1, 1, 1, 1, 0, 1,
                         1, 1, 1, 1, 1, 0), ncol=6, byrow=TRUE)
for (i in 1:nrow(prob)) prob[i, menu[i, ]==1] <- logitAtte(sum(menu[i, ]), 2)$choiceProb

# List of preferences to be tested
pref_list <- matrix(c(1, 2, 3, 4, 5, 6,
                      2, 3, 4, 5, 6, 1), ncol=6, byrow=TRUE)
# RAM only
result1 <- revealPrefModel(menu = menu, prob = prob, pref_list = pref_list, RAM = TRUE, AOM = FALSE)
summary(result1)

# AOM only
result2 <- revealPrefModel(menu = menu, prob = prob, pref_list = pref_list, RAM = FALSE, AOM = TRUE)
summary(result2)

# Both RAM and AOM
result3 <- revealPrefModel(menu = menu, prob = prob, pref_list = pref_list, RAM = TRUE, AOM = TRUE)
summary(result3)

Generate Summary Statistics

Description

sumData generates summary statistics. Given a collection of choice problems and corresponding choices, sumData calculates the number of occurrences of each choice problem, as well as the empirical choice probabilities.

This function is embedded in revealPref.

Usage

sumData(menu, choice)

Arguments

Value

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Paul Cheung, University of Maryland. hycheung@umd.edu

Xinwei Ma (maintainer), University of California San Diego. x1ma@ucsd.edu

Yusufcan Masatlioglu, University of Maryland. yusufcan@umd.edu

Elchin Suleymanov, Purdue University. esuleyma@purdue.edu

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2024). Attention Overload. Working paper.

Examples

# Load data
data(ramdata)

# Generate summary statistics
summaryStats <- sumData(ramdata$menu, ramdata$choice)
nrow(summaryStats$sumMenu)
min(summaryStats$sumN)

summaryStats$sumMenu[1, ]
summaryStats$sumProb[1, ]
summaryStats$sumN[1]

Internal function.

Description

Internal function.

Usage

## S3 method for class 'ramchoiceRevealAtte'
summary(object, ...)

Arguments

Internal function.

Description

Internal function.

Usage

## S3 method for class 'ramchoiceRevealPref'
summary(object, ...)

Arguments

Internal function.

Description

Internal function.

Usage

## S3 method for class 'ramchoiceRevealPrefModel'
summary(object, ...)

Arguments