sa.tabu {SEMsens}

Sensitivity Analysis for SEM using Tabu Search

Description

This function conducts sensitivity analysis for SEM using tabu search.

Usage

sa.tabu(
  model,
  sens.model,
  data = NULL,
  sample.cov = NULL,
  sample.nobs = NULL,
  opt.fun = 1,
  sig.level = 0.05,
  ...
)

Arguments

model

The analytic model of interest.

sens.model

Sensitivity analysis model template for structural equation modeling with a phantom variable. This is the model of interest with a phantom variable and sensitivity parameters added. See examples provided.

data

The data set used for analysis.

sample.cov

covariance matrix for SEM analysis when data are not available.

sample.nobs

Number of observations for covariance matrix.

opt.fun

Customized or preset optimization function. The argument can be customized as a function, e.g., opt.fun = quote(new.par$pvalue[paths]-old.par$pvalue[paths]), where new.par and old.par are the parameter estimates from the sensitivity analysis and analytic models, respectively. When opt.fun is 1, the optimization function is the average departure of new estimate from the old estimate divided by the old estimate y <- mean(abs(new.par$est[paths] - old.par$est[paths]))/mean(abs(old.par$est[paths])); When opt.fun is 2, the optimization function is the standard deviation of deviance divided by the old estimate y <- stats::sd(new.par$est[paths] - old.par$est[paths])/ mean(abs(old.par$est[paths])); When opt.fun is 3, the optimization function is the average p value changed or y <- mean(abs(new.par$pvalue[paths] - old.par$pvalue[paths])); When opt.fun is 4, the optimization function is the average distance from significance level or y <- mean(abs(new.par$pvalue[paths] - rep(sig.level,length(paths)))); When opt.fun is 5, we assess the change of RMSEA or y <- abs(unname(lavaan::fitmeasures(new.out)["rmsea"]) - unname(lavaan::fitmeasures(old.out)["rmsea"])); When opt.fun is 6, we optimize how close RMSEA is to 0.05 or y <- 1/abs(unname(lavaan::fitmeasures(new.out)["rmsea"]) - 0.05).

sig.level

Significance level, default value is 0.05.

...

Additional arguments from the lavaan package.

Value

A list with five components: model: The old model; old.model.par: Parameters of the old model; model.results: Sensitivity analysis model results; best.param: Parameters that optimize the objective function; best.obj: The optimized objective function value; sens.par: NULL. Included for compatibility; outcome: NULL. Included for compatibility.

Examples

library(lavaan)
# Generate data, this is optional as lavaan also takes variance covariance matrix
sim.model <- ' x =~ x1 + 0.8*x2 + 1.2*x3
               y =~ y1 + 0.5*y2 + 1.5*y3
               m ~ 0.5*x
               y ~ 0.5*x + 0.8*m'
set.seed(10)
data <- simulateData(sim.model, sample.nobs = 1000L)
# standardize dataset
data = data.frame(apply(data,2,scale))

# Step 1: Set up the analytic model of interest
model <- 'x =~ x1 + x2 + x3
          y =~ y1 + y2 + y3
          m ~ x
          y ~ x + m'

# Step 2: Set up the sensitivity analysis model.
#         The sensitivity parameters are phantom1, phantom2, and phantom3 in this example.
sens.model = 'x =~ x1 + x2 + x3
              y =~ y1 + y2 + y3
              m ~ x
              y ~ x + m
              x ~ phantom1*phantom
              m ~ phantom2*phantom
              y ~ phantom3*phantom
              phantom =~ 0 # added for mean of zero
              phantom ~~ 1*phantom' # added for unit variance
# Step 3: Set up the paths of interest to be evaluated in sensitivity analysis.
# Suppose we are interested in all direct and indirect paths.
  paths <- 'm ~ x
            y ~ x + m'
# Step 4: Perform sensitivity analysis
out <- sa.tabu(model = model,
               sens.model = sens.model,
               data = data,
               opt.fun = 1,
               max.iter = 2,
               max.iter.obj = 2)
 # Note, please specify larger numbers for
 # max.iter (e.g., 50) and max.iter.obj (e.g., 10)

# Step 5: Summarize sensitivity analysis results.
# See sens.tables function for explanation of results.
tables <- sens.tables(out)