Title:	SEM Sensitivity Analysis
Version:	0.1.0
Maintainer:	Biying Zhou <biying.zhou@psu.edu>
Description:	Performs sensitivity analysis for Structural Equation Modeling (SEM). It determines which sample points need to be removed for the sign of a specific path in the SEM model to change, thus assessing the robustness of the model. Methodological manuscript in preparation.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.3
Imports:	lavaan, dplyr, R.utils, semfindr, stats, methods,
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2025-10-27 22:43:23 UTC; zby15
Author:	Biying Zhou [aut, cre], Feng Ji [aut]
Repository:	CRAN
Date/Publication:	2025-10-31 18:10:08 UTC

Run Specified Test for SEM Path Sign or Fit Measure Change

Description

This function runs a specified test by method name or method index to determine either (1) when a specific path in a Structural Equation Modeling (SEM) model changes sign (positive or negative) by iteratively removing data points, or (2) whether a fit measure (e.g., CFI, TLI) exceeds or falls below a specified threshold (e.g., 0.9). The function outputs relevant results for the specified test.

Usage

SEMsensitivity(
  df,
  model,
  var_one = NULL,
  var_two = NULL,
  PAR = NULL,
  threshold = 10,
  fit,
  estimates = NULL,
  conc = NULL,
  int = NULL,
  par_value = NULL,
  max_final,
  N,
  signFactor = NULL,
  equalCons = 0L,
  calcMeth = "Hessian",
  ratio = NULL,
  adaptA = NULL,
  alpha = NULL,
  maxTime = NULL,
  pruneNum = NULL,
  measureTest = "cfi",
  fitThreshold = 0.9,
  highGood = TRUE,
  method = 2,
  ...
)

Arguments

Value

A list containing the results of the specified test.

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

# Run specified test by method name
result_by_name <- SEMsensitivity(df, model, var_one, var_two, PAR, threshold, fit,
estimates, conc, int, par_value, max_final, N, signFactor,
method = "Naive Method with Exact Influence")
summary(result_by_name)

# Run specified test by method index
result_by_index <- SEMsensitivity(df, model, var_one, var_two, PAR, threshold, fit,
estimates, conc, int, par_value, max_final, N, signFactor, method = 1)
summary(result_by_index)

Naive Method with Exact Influence

Description

Remove a fixed percentage of samples (determined by the exact influence) at a time and refit the model to observe the change in the path of interest. Use method 1 - Naive Method with Exact Influence.

Usage

Test1(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  ...
)

Arguments

Value

A list of class TestResult containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test1_result <- Test1(df, model, var_one, var_two, PAR, threshold, fit, estimates,
 conc, int, par_value, max_final, N, signFactor)
summary(Test1_result)

Use depth method to drop fit measure below threshold

Description

This function uses the depth method to iteratively remove the most influential data points based on influence scores to reduce the fit measure below a specified threshold. The method is based on approximating the influence of each data point and is similar to TEST 8 but focused on fit metrics like CFI, RMSEA, etc.

Usage

Test10(
  df,
  model,
  fit,
  max_final,
  N,
  measureTest = "cfi",
  fitThreshold = 0.9,
  highGood = TRUE,
  ...
)

Arguments

Value

A list of class TestResult10 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)

# Import data
df <- PoliticalDemocracy

# Build SEM model
model <- '
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
'

fit <- lavaan::sem(model, data = df)
max_final <- ceiling(10 * nrow(df) / 100)  # dropping 10% of the data points
N <- nrow(df)

Test10_result <- Test10(df, model, fit, max_final, N,
measureTest = "cfi", fitThreshold = 0.9, highGood = TRUE)
summary(Test10_result)

Use Simulated Annealing Method to Try to Switch Sign of Parameter

Description

This function uses the simulated annealing method to iteratively remove data points in order to switch the sign of a specific path in a Structural Equation Modeling (SEM) model.

Usage

Test11(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  ...
)

Arguments

Value

A list of class TestResult11 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine the value of the parameter of interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute the max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store the number of observations in df for convenience

# Determine whether the parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test11_result = Test11(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor)
summary(Test11_result)

Use Particle Swarm Optimization (PSO) to Try to Switch Sign of Parameter

Description

This function uses the Particle Swarm Optimization (PSO) method to iteratively remove data points in order to switch the sign of a specific path in a Structural Equation Modeling (SEM) model.

Usage

Test12(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  ...
)

Arguments

Value

A list of class TestResult12 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine the value of the parameter of interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute the max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store the number of observations in df for convenience

# Determine whether the parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test12_result = Test12(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor)
summary(Test12_result)

Use Brute Search with Cut Method to Try to Switch Sign of Parameter

Description

This function uses a brute-force search method with pruning (cutting) to iteratively search for combinations of data points that switch the sign of a specific path in a Structural Equation Modeling (SEM) model.

Usage

Test13(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  ...
)

Arguments

Value

A list of class TestResult13 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine the value of the parameter of interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute the max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store the number of observations in df for convenience

# Determine whether the parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test13_result = Test13(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor)
summary(Test13_result)

Naive Method with Approximate Influence

Description

Remove a fixed percentage of samples (determined by the approximate influence) at a time and refit the model to observe the change in the parameter of interest. Use method 2 - Naive Method with Approximate Influence.

Usage

Test2(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  equalCons = 0L,
  calcMeth = "Hessian",
  ...
)

Arguments

Value

A list of class TestResult containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test2_result <- Test2(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor)
summary(Test2_result)

Specified Approximation Method

Description

This function determines when a specific path in a Structural Equation Modeling (SEM) model changes sign by iteratively removing most influential data points (determined by naive method) and outputs relevant results. Use method 3 - Specified Approximation Method.

Usage

Test3(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  equalCons = 0L,
  calcMeth = "Hessian",
  ...
)

Arguments

Value

A list of class TestResult3 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test3_result = Test3(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor,equalCons = 0L)
summary(Test3_result)

Simple depth method

Description

This function determines a specific path in a Structural Equation Modeling (SEM) model value changing by removing samples iteratively, in which influences are determined by naive method and outputs relevant results. Use method 4 - Simple depth method.

Usage

Test4(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  equalCons = 0L,
  calcMeth = "Hessian",
  ...
)

Arguments

Value

A list of class TestResult containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test4_result = Test4(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor)
summary(Test4_result)

Combined Method

Description

This function determines a specific path in a Structural Equation Modeling (SEM) model value changing by removing samples iteratively, in which influences are determined by both naive method and approximate method and outputs relevant results. Use method 5 - Combined Method.

Usage

Test5(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  equalCons = 0L,
  calcMeth = "Hessian",
  ratio = 2,
  ...
)

Arguments

Value

A list of class TestResult containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test5_result = Test5(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor)
summary(Test5_result)

Finding case deletions required to change fit metric using exact influences

Description

Remove a fixed percentage of samples (determined by the exact influence) at a time and refit the model to observe the change in the path of interest. Use method 1 - Naive Method with Exact Influence.

Usage

Test61(
  df,
  model,
  threshold,
  fit,
  max_final,
  N,
  measureTest = "cfi",
  fitThreshold = 0.9,
  highGood = TRUE,
  ...
)

Arguments

Value

A list of class TestResult61 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100)
N <- nrow(df)

Test61_result <- Test61(df, model, threshold, fit, max_final, N,
 measureTest = "cfi", fitThreshold = 0.9, highGood = TRUE)
summary(Test61_result)

Finding case deletions required to change fit metric using approximate method

Description

Remove a fixed percentage of samples (determined by the approximate influence) at a time and refit the model to observe the change in the fit metric of interest. Use method 2 - Approximate Method.

Usage

Test62(
  df,
  model,
  threshold,
  fit,
  max_final,
  N,
  equalCons = 0L,
  measureTest = "cfi",
  fitThreshold = 0.9,
  highGood = TRUE,
  ...
)

Arguments

Value

A list of class TestResult62 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100)
N <- nrow(df)

Test62_result <- Test62(df, model, threshold, fit, max_final, N, equalCons = 0L,
 measureTest = "cfi", fitThreshold = 0.9, highGood = TRUE)
summary(Test62_result)

Negamax Search Algorithm Function

Description

Utilizes a Negamax search algorithm to iteratively drop data points and update the SEM, ultimately aiming to minimize the parameter value of interest. Use method 7 - Negamax Search Algorithm Function.

Usage

Test7(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  equalCons = 0L,
  calcMeth = "Hessian",
  adaptA = FALSE,
  alpha = 0.25,
  maxTime = 300,
  pruneNum = 3,
  ...
)

Arguments

Value

A list of class TestResult7 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

  Test7_result = Test7(df, model, var_one, var_two, PAR, threshold, fit, estimates,
  conc, int, par_value, max_final, N, signFactor,equalCons = 0,calcMeth = "Hessian",
  adaptA = FALSE, alpha= 0.25, maxTime = 300, pruneNum = 3)
summary(Test7_result)

Use Depth Method to Try to Switch Sign of Parameter

Description

This function uses a depth method to iteratively remove data points in order to switch the sign of a specific path in a Structural Equation Modeling (SEM) model.

Usage

Test8(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  equalCons = 0L,
  calcMeth = "Hessian",
  ...
)

Arguments

Value

A list of class TestResult8 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

  Test8_result = Test8(df, model, var_one, var_two, PAR, threshold, fit, estimates,
  conc, int, par_value, max_final, N, signFactor,equalCons=0,calcMeth = "Hessian")
summary(Test8_result)

Use Depth Method to Try to Switch Sign of Parameter

Description

This function uses a depth method combined with a Negamax search algorithm to iteratively remove data points in order to switch the sign of a specific path in a Structural Equation Modeling (SEM) model.

Usage

Test9(
  df,
  model,
  var_one,
  var_two,
  PAR,
  threshold,
  fit,
  estimates,
  conc,
  int,
  par_value,
  max_final,
  N,
  signFactor,
  equalCons = 0L,
  calcMeth = "Hessian",
  ...
)

Arguments

Value

A list of class TestResult9 containing:

Examples

library(lavaan)
library(dplyr)
library(semfindr)
library(R.utils)


# Import data
df <- PoliticalDemocracy

# Build Model
model <- '
  # measurement model
  ind60 =~ x1 + x2 + x3
  dem60 =~ y1 + y2 + y3 + y4
  dem65 =~ y5 + y6 + y7 + y8
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  y1 ~~ y5
  y2 ~~ y4 + y6
  y3 ~~ y7
  y4 ~~ y8
  y6 ~~ y8
'

var_one <- 'dem65' # first term
var_two <- 'ind60' # second term
PAR <- c("dem65~ind60") # full relation
threshold <- 10

# Fit SEM model
fit <- lavaan::sem(model, data = df)
summary(fit)

# Get Estimates of Parameters from SEM
estimates <- parameterEstimates(fit)

# Determine The Value of The Parameter of Interest
conc <- data.frame(lhs = estimates$lhs, rhs = estimates$rhs, est = estimates$est)
int <- conc %>% filter(lhs == var_one & rhs == var_two)
par_value <- int$est # this is the value of the parameter of interest

# Compute max number of points to be dropped
max_final <- ceiling(threshold * nrow(df) / 100) # perform rounding if necessary
N <- nrow(df) # store number of observations in df for convenience

# Determine whether parameter is negative or positive in order
# to assess which direction to perturb it
signFactor <- ifelse(par_value >= 0L, TRUE, FALSE)

Test9_result <- Test9(df, model, var_one, var_two, PAR, threshold, fit, estimates,
conc, int, par_value, max_final, N, signFactor, equalCons=0, calcMeth = "Hessian")
summary(Test9_result)

Get the value of a specified SEM path parameter after case deletion

Description

This helper function refits the specified SEM model after dropping the given cases and extracts the parameter estimate for the specified path (e.g., var_one ~ var_two).

Usage

getValue(drops_index, df, model, var_one, var_two)

Arguments

Value

A numeric scalar giving the parameter estimate for the specified path after removing the selected observations.