summaryMisspec: Provide summary of the population misfit and misspecified-parameter values across replications

Description

This function provides the summary of the population misfit and misspecified-parameter values across replications. The summary will be summarized for the convergent replications only.

Usage

summaryMisspec(object, improper = FALSE)

Arguments

object

SimResult object being described

improper

If TRUE, include the replications that provided improper solutions

Value

A data frame that provides the summary of population misfit and misspecified-parameter values imposed on the real parameters. The discrepancy value ($f_0$; Browne & Cudeck, 1992) is calculated by $$F_0 = tr\left( \tilde{\Sigma} \Sigma^{-1} \right) - \log{\left| \tilde{\Sigma} \Sigma^{-1} \right|} - p + \left( \tilde{\mu} - \mu \right)^{\prime} \Sigma^{-1} \left( \tilde{\mu} - \mu \right).$$ where $\mu$ is the model-implied mean from the real parameters, $\Sigma$ is the model-implied covariance matrix from the real parameters, $\tilde{\mu}$ is the model-implied mean from the real and misspecified parameters, $\tilde{\Sigma}$ is the model-implied covariance matrix from the real and misspecified parameter, p is the number of indicators. For the multiple groups, the resulting $f_0$ value is the sum of this value across groups. The root mean squared error of approximation (rmsea) is calculated by $$rmsea = \sqrt{\frac{f_0}{df}}$$ where $df$ is the degree of freedom in the real model. The standardized root mean squared residual (srmr) can be calculated by $$srmr = \sqrt{\frac{2\sum_{g} \sum_{i} \sum_{j \le i} \left( \frac{s_{gij}}{\sqrt{s_{gii}}\sqrt{s_{gjj}}} - \frac{\hat{\sigma}_{gij}}{\sqrt{\hat{\sigma}_{gii}}\sqrt{\hat{\sigma}_{gjj}}} \right)}{g \times p(p + 1)}}$$ where $s_{gij}$ is the observed covariance between indicators i and j in group g, $\hat{\sigma}_{ij}$ is the model-implied covariance between indicators i and j in group g, p is the number of indicators.

References

Browne, M. W., & Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research, 21, 230-258.

Examples

Run this code

path <- matrix(0, 4, 4)
path[3, 1:2] <- NA
path[4, 3] <- NA
pathVal <- matrix("", 4, 4)
pathVal[3, 1:2] <- "runif(1, 0.3, 0.5)"
pathVal[4, 3] <- "runif(1, 0.5, 0.7)"
pathMis <- matrix(0, 4, 4)
pathMis[4, 1:2] <- "runif(1, -0.1, 0.1)"
BE <- bind(path, pathVal, pathMis)

residual.error <- diag(4)
residual.error[1,2] <- residual.error[2,1] <- NA
RPS <- binds(residual.error, "rnorm(1, 0.3, 0.1)")

Path.Model <- model(RPS = RPS, BE = BE, modelType="Path")

# The number of replications in actual analysis should be much more than 5
ParamObject <- sim(5, n=200, Path.Model)

# Summarize the model misspecification that is specified in the 'pathMis' object
summaryMisspec(ParamObject)