sa.sa {SEMsens}

Sensitivity Analysis for Structural Equation Modeling Using Simulated Annealing (SA)

Description

This function can perform sensitivity analysis for structural equation modeling using simulated annealing (SA)

Usage

sa.sa(
  data = NULL,
  sample.cov,
  sample.nobs,
  model,
  sens.model,
  opt.fun = 1,
  d = NULL,
  paths = NULL,
  verbose = TRUE,
  n.iter = 10,
  e = 1e-10,
  k = 10,
  sig.level = 0.05,
  Ntemps = 10,
  C.criteria = 1,
  steepness = 6,
  measurement = FALSE
)

Arguments

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.

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.

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$est.std[paths] - old.par$est.std[paths]))/mean(abs(old.par$est.std[paths])); When opt.fun is 2, the optimization function is the standard deviation of deviance divided by the old estimate y <- stats::sd(new.par$est.std[paths] - old.par$est.std[paths])/ mean(abs(old.par$est.std[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).

d

Domains for initial sampling, default is c(-1 ,1) for all sensitivity analysis parameters.

paths

Paths in the model to be evaluated in a sensitivity analysis. If not specified, all paths will be evaluated. It can be specified in a numeric format or in a model format. For example, if we evaluate the changes (in p value or parameter estimation) for paths in an analytic model, we may specify paths in a model format, e.g., paths = 'm ~ x y ~ x + m'. Or, alternatively, as specify paths = c(1:3) if these paths present in line 1 to 3 in the sensitivity analysis model results.

verbose

Print out evaluation process if TRUE, default is TRUE.

n.iter

Maximal number of function evaluations within each temperature.

e

Maximum error value used when solution quality used as the stopping criterion, default is 1e-10.

k

Size of the solution archive, default is 100.

sig.level

Significance level, default value is 0.05.

Ntemps

Number of temperatures that the algorithm visits. Default value is 10.

C.criteria

Convergence criterion. Default value is 1.

steepness

Steepness of cooling schedule. Default value is 6.

measurement

Logical. If TRUE, the argument paths will include measurement paths in the lavaanify format. Default is FALSE.

Value

Sensitivity analysis results, including the number of evaluations (n.eval), number of iterations (n.iter), the maximum value of the objective function (max.y) and associated sensitivity parameters values (phantom.coef), analytic model (old.model), its results (old.model.par) and fit measures (old.model.fit), sensitivity analysis model (sens.model), its fit measures (sens.fit), outcome of the objective function (outcome), sensitivity parameters across all converged evaluations (sens.pars), sensitivity analysis model results (model.results), analytic model results (old.out), and the first converged sensitivity analysis model results (sens.out).

References

Fisk, C., Harring, J., Shen, Z., Leite, W., Suen, K., & Marcoulides, K. (2022). Using simulated annealing to investigate sensitivity of SEM to external model misspecification. Educational and Psychological Measurement. <doi:10.1177/00131644211073121>

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
mysa <- sa.sa(data = data, model = model,
sens.model = sens.model, paths = paths,
 n.iter = 3,  Ntemps = 2)
# We set Ntemps = 2 and n.iter = 3 to reduce the running time.
# You may leave them as default values or specify larger numbers.