# Provide summary of the population misfit and misspecified-parameter values across replications 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. ```r summaryMisspec(object, improper = TRUE) ``` ## Arguments - `object`: `SimResult` object being described - `improper`: If TRUE, include the replications that provided improper solutions ## Returns 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. ## Author(s) Sunthud Pornprasertmanit (psunthud@gmail.com ) ## References Browne, M. W., & Cudeck, R. (1992). Alternative ways of assessing model fit. **Sociological Methods & Research, 21**, 230-258. ## See Also `SimResult` for the object input ## Examples ```r ## Not run: 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) ## End(Not run) ```

summaryMisspec function