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Clearly it's possible, because it happened. Typically when you have very low chi-squares, you sometimes have very lower CFI/TLI - that was the first think I looked at, because they indicate lower power. You don't have low power, you just have a well fitting model. This is not a problem.


Note that it is very common to have a non-significant Chi-squared fit statistic in CFA testing, as it is heavily sensitive to large sample sizes and higher model complexity (i.e. a number of indicators in your model). In your case, it is very unsurprising that the Chi-squared in non-significant, but both CFI and TLI are large. I will gently echo @JeremyMiles ...


The multilevel model allows you to simultaneously model within- and between-plot variation. Consider a simplified multilevel model, with the Xs representing within-plot variables and W representing a between-plot variable. The within-plot model: $y_{ij}$ = $\beta0_j$ + $\beta1_jX_{1ij}$ + $\beta2X_{2ij}...$ + $e_{ij}$ Here you can include as many X ...


You can just run on the sempreds object to turn it into a data.frame. Note that this isn't actually prediction; you're estimating factor scores. This covered in any SEM textbook (e.g., Bollen 1989). Factor scores are imperfect estimates of the latent variable that can often be used in subsequent analyses or for descriptive purposes. That ...


These high correlations mean that you have highly reliable measures. In particular, verbal_letters and matrix are highly correlated, and measure the same construct. The only reason to be concerned about this is that your measure of generaliq has a lot to do with verbal_letters and matrix, and less to do with rotate.


In a model with observed variables only, you can count degrees of freedom by counting the excluded paths. Marking the excluded path is important because the chi-square statistic only reacts to excluded or fixed parameter estimates--it is not an F test that assesses the magnitude of included parameter estimates. Generally speaking, chi-square will not give ...

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