I am doing two-level CFA and have difficulties interpreting some results. I first performed a conventional CFA, which delivered an appropriate fit. Next, I did a CFA on the within covariance matrix, also showing a good fit (RMSEA= 0.079; CFI= 0.986; TLI= 0.980; SRMR= 0.022). However, the CFA on the between covariance matrix (using the same factor compositions) showed a bad fit (RMSEA= 0.523; CFI= 0.807; TLI= 0.723; SRMR= 0.014). Yet, when doing the actual multilevel CFA (same factors on between and within level), a good fit was found (RMSEA= 0.052; CFI= 0.988; TLI= 0.983; SRMR value for within= 0.023; SRMR value for between= 0.016). Do you have any idea on how to interpret and handle the bad fit of the CFA on the between covariance matrix?