simsem (version 0.2-8)

popDiscrepancy: Find the discrepancy value between two means and covariance matrices

Description

Find the discrepancy value between two means and covariance matrices

Usage

popDiscrepancy(paramM, paramCM, misspecM, misspecCM)

Arguments

paramM

The model-implied mean from the real parameters

paramCM

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

Value

• The discrepancy between two means and covariance matrices

Details

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.

References

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

Examples

m1 <- rep(0, 3)
m2 <- c(0.1, -0.1, 0.05)
S1 <- matrix(c(1, 0.6, 0.5, 0.6, 1, 0.4, 0.5, 0.4, 1), 3, 3)
S2 <- matrix(c(1, 0.55, 0.55, 0.55, 1, 0.55, 0.55, 0.55, 1), 3, 3)
popDiscrepancy(m1, S1, m2, S2)