The model-implied covariance matrix from the real parameters
misspecM
The model-implied mean from the real and misspecified parameters
misspecCM
The model-implied covariance matrix from the real and misspecified parameters
dfParam
The degree of freedom of the real model
fit.measures
The names of indices used to calculate population misfit. There are three types of misfit: 1) discrepancy function ("f0"; see popDiscrepancy), 2) root mean squared error of approximation
Value
The vector of the misfit indices
Details
The root mean squared error of approximation (RMSEA) is calculated by
$$RMSEA = \sqrt{\frac{F_0}{df}}$$
where $F_0$ is the discrepancy value between two means vectors and covariance matrices (see popDiscrepancy) and $df$ is the degree of freedom in the real model.
The standardized root mean squared residual can be calculated by
$$SRMR = \sqrt{\frac{2\sum_{i} \sum_{j \le i} \left( \frac{s_{ij}}{\sqrt{s_{ii}}\sqrt{s_{jj}}} - \frac{\hat{\sigma}_{ij}}{\sqrt{\hat{\sigma}_{ii}}\sqrt{\hat{\sigma}_{jj}}} \right)}{p(p + 1)}}$$
where $s_{ij}$ is the observed covariance between indicators i and j, $\hat{\sigma}_{ij}$ is the model-implied covariance between indicators i and j, 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.